An automated pipeline to generate initial estimates for population pharmacokinetic models

An automated pipeline to generate initial estimates for population pharmacokinetic models | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article An automated pipeline to generate initial estimates for population pharmacokinetic models Zhonghui Huang, Matthew Fidler, Minshi Lan, lek L Cheng, Frank Kloprogge, and 1 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-5806446/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 06 Nov, 2025 Read the published version in Journal of Pharmacokinetics and Pharmacodynamics → Version 1 posted 9 You are reading this latest preprint version Abstract Nonlinear mixed-effects models rely on adequate initial parameter estimates for efficient parameter optimization. Poor initial estimates can result in failed model convergence or termination with incorrect parameter estimates. Non-compartmental analysis (NCA) and other manual methods have typically been used to derive initial estimates for pharmacokinetic (PK) parameters. However, NCA struggles with sparse data and recent advances in automated modeling increasingly emphasize the need for initial estimates that require no user input. This study aimed to develop an integrated pipeline for the computation of initial estimates applicable to various data types and model structures. Multiple methods were involved in this pipeline: the adaptive single-point method using individual-level data, graphic methods, and NCA performed after naïve pooling, as well as parameter sweeping on model-specific parameters. The relative root mean square error (rRMSE) was used as a metric to select the most appropriate initial estimates from candidates generated by the pipeline. The pipeline’s performance was evaluated across twenty-one simulated datasets and thirteen real-life datasets. The results suggested that this pipeline performed well in all test cases. Initial estimates recommended by the pipeline resulted in final parameter estimates closely aligned with pre-set original values in simulated datasets or aligned with literature references in the case of real-life data. This study provides an efficient and reliable tool for delivering PK initial estimates for population pharmacokinetic modeling in both rich and sparse data scenarios, and an open-source R package has been created. initial estimates population pharmacokinetics automated modeling sparse data Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Introduction Population pharmacokinetic (PopPK) model analysis involves constructing mathematical and statistical models and performing parameter estimation to characterize the absorption, distribution, metabolism, and elimination of drugs. It is necessary to provide initial estimates to the parameter optimizers, which will then undergo iterative parameter optimization and estimation. Initial estimates are usually determined by the modeler. A common approach is to conduct a preliminary exploration of data from one or more individuals or to set the initial estimates based on published literature [ 1 ]. However, modeler-led approaches lack automation, rendering them time-consuming and difficult to standardize. Some PopPK modeling tools offer features to automatically set initial estimates. For example, Monolix optimizes initial estimates through a custom optimization on pooled data disregarding inter-individual variability (IIV) [ 2 ]. This process needs to collect initial values from the panel as starting points of optimization. Babelmixr2 [ 3 ], a package that can connect nlmixr2 with PKNCA [ 4 ], computes initial estimates by performing non-compartmental analysis (NCA) and applying empirical settings. Nevertheless, it may be sensitive to the types of data used, particularly for sparse data [ 5 ]. NONMEM lacks a built-in automatic setting for initial estimates, but external tools like pyDarwin can be utilized. As an automated PopPK modeling tool, pyDarwin can incorporate initial estimates along with other model features into the search space for optimization within an evolutionary algorithm [ 6 ]. Another automatic tool, Pharmpy, requires users to input initial values for the starting model [ 7 ], and in one practice, NCA’s results were used as a reference for the starting models’ initial estimates [ 8 ]. Other approaches based on data exploration are available. The single-point method, an earlier approach that utilizes a specific time point to predict trough concentrations [ 8 , 9 ], along with more recent practices that estimate AUC using a single trough concentration [ 10 , 11 ], were potential solutions for handling sparse data. Performing NCA on pooled data is another choice. The practice involves treating all data as from a single subject [ 13 ] and may involve combining data points at the same time interval [ 14 ]. The graphic methods [ 15 , 16 ], offer a flexible approach applicable to both sparse and rich data. For complex models, especially those where multiple parameters lack pre-determined values, parameter sweeping can be useful. It tests a user-defined range of possible parameter values and evaluates their outputs to select a suitable value with the best performance [ 17 , 18 ]. There is a clear gap in tools that can automatically generate initial estimates without user input, which are universal, time-efficient, and effective for both manual modeling and automated modeling algorithms. Hence, the pipeline presented here aimed to provide references for initial estimates of structural model parameters when no prior information from other sources is available and accommodate a wide range of PK scenarios, including those involving sparse data. This was accomplished by the use of data exploration-based parameter analysis, including adaptive single-point method, graphic methods and NCA at pooled data, and parameter sweeping. Method Pipeline overview A pipeline was established to compute PK parameters from datasets formatted according to nlmixr2 data standards (see Fig. 1 ). It comprised of two main parts: (1) one-compartment model parameter analysis and (2) model-specific parameter analysis in nonlinear/multi-compartment models. Part 1 analyzed base parameters (clearance (CL), volume of distribution (V d ), and absorption rate constant (K a ) through three main approaches: Adaptive single-point method : This method was originally inspired by calculating parameters from a single concentration point [ 8 , 9 ]. This study re-designed the single-point approach to incorporate data points under both initial-dose and steady-state conditions. An “extra phase” was added to address parameters not calculated in the base phase, providing the pipeline with the flexibility to handle different data types. NCA : This approach incorporated the Wagner-Nelson method [ 19 ] to assist in calculating the K a to derive the necessary pharmacokinetic parameters. Graphic methods : These methods were built upon established methodologies for one-compartment models [ 15 , 16 ]. Only one output from these three methods was selected based on predictive performance on a one-compartment model, measured by rRMSE. Part 2 focused on model-specific parameters and applied a parameter sweeping approach. A pre-defined range of candidate parameters was tested by conducting a series of simulations within the specified model using the information from the input dataset. The best-fitting parameter set was identified using by comparing simulated concentrations with observations from input datasets using rRMSE. Pipeline development Part 1 : parameter calculation for one-compartment models Adaptive single-point (base). Post-first-dose and steady-state data were extracted for individuals. Steady-state was defined as regularly spaced doses covering at least three half-lives or five doses, with dose intervals and fluctuations within ± 25% of the median. Half-life was estimated through linear regression on naïve pooled data. V d was calculated as the ratio of the dose to the concentration observed at the first sampling point after the initial dose. This point was required to be collected within 20% of the half-life after dosing. Maximum (C ss,max ) and minimum (C ss,max ) concentrations were extracted from the same interval under steady state, and their mean (C ss,avg ) was used to calculate CL (see Table 1 ). For cases where both extracted points were observed to fall near the dosing event (within 20% of the dosing interval from either the previous or the next dose), their mean was treated as C ss,max or C ss,min . CL was subsequently derived solely based on the C ss,max or C ss,min , and this calculation was only applicable to intravenous cases. A geometric mean with a trim value of 0.05 (i.e., removing the top and bottom 2.5% of the data) was used to summarize PK parameters derived from individuals, given as a more robust alternative, resistant to outliers approach [ 20 ]. 1.1 Adaptive single-point (extra). This extended module was designed to address scenarios where not all one-compartment parameters have been determined during the base phase due to limited data. Undetermined CL or V d values were derived using the estimated half-life (see Table 1 ). When both were undetermined, the central volume of distribution (V c ) was used as a substitute for V d . The former was calculated as the ratio of dose to the maximum concentration at the time occurring within 20% of the half-life after the single dose. For multiple doses, the accumulation ratio (R ac ) was applied to adjust C ss,max back to C max . K a was calculated by solving the analytical concentration-time equations for a one-compartment pharmacokinetic model after a single or multiple doses. Concentration data from the absorption phase (individual sampling points at sampling times ≤ peak time) were used. CL and V d in the equations were obtained from previous steps, and bioavailability was assumed to be 1. K a was subsequently determined within a wide range of values (0-1000) using Brent’s method implemented in R’s uniroot function [ 21 ]. K a and V c were summarized by calculating the trimmed geometric mean of individual values. Naïve pooled NCA A naïve pooling approach was applied to process concentration-time data prior to NCA and analysis using graphic methods. Pooling was based on three groups: first-dose data, non-first-dose data (considered to be multiple-dose data), and all data. All concentration-time data within each group were pooled and binned according to pre-defined time windows with a default number of 8 to ensure adequate coverage of the PK profile. These intervals were generated by dividing unique time points into quantiles, with each group containing an approximately equal number of time points. If fewer than eight unique time points were available, the intervals were adjusted to match the actual number. Within each time window, the median time and drug concentration were calculated for each group, serving as representative values for time and concentration within that time window. Naïve pooling of normalized concentration-by-dose data was used. The area under the curve (AUC) was calculated using the linear trapezoidal rule. The elimination rate constant (k e ) was determined by performing linear regression on the last three data points of the log-transformed concentration-time curve. For single-dose data, AUC from time 0 to infinity (AUC 0-∞ ) was used for CL calculation, while for multiple-dose data, AUC 0-τ was applied where τ was defined as the most commonly used dosing interval determined by frequency of administration (see Table 1 ). CL was calculated by dividing the dose (standardized to 1) by the AUC, and the volume of distribution of terminal phase (V z ) was calculated using the formula V z = CL/k e . For the oral case, K a was estimated by the Wagner-Nelson method [ 19 ]. The cumulative drug exposure at time AUC 0-t was calculated, and a linear regression analysis on the fraction of the drug that remained unabsorbed during the absorption phase was performed to determine the K a . Graphic methods. First doses from the naïve pool data were isolated for this analysis. The plasma drug concentration versus time data was first plotted on a semi-logarithmic scale. Linear regression was performed on the terminal elimination phase, and the slope is used to estimate K e , from which the half-life (t 1/2 ) was derived. In the case of intravenous administration, the intercept, extrapolated to the y-axis, was used to calculate V d . For oral administration, the method of residuals was employed to determine the K a . This involved identifying the terminal elimination phase and subtracting it from the total plasma concentration-time curve, leaving the residuals corresponding to the absorption phase. The semi-logarithmic plot of these residuals was then used to calculate the K a . Detailed equations are listed in Table 1 . Part 1 evaluation and selection. Each approach in Part 1 produced a set of parameter values for CL, Vd, and Ka. These sets of parameter values were evaluated based on their goodness-of-fit performance in a one-compartment model. The predictive performance was examined through relative root mean squared error (rRMSE), as shown in the following equation. This metric was used in this pipeline as an assessment of model fitting performance given previous practice to evaluate model fitting performance across different algorithms or initial estimates. The set with the lowest value of rRMSE was selected as pipeline initial estimate recommendations for nonlinear mixed-effects modeling and utilized to inform parameter sweeping in Part 2 of the pipeline. $$\:rRMSE\%\:\:=\:\:\:\frac{1}{n}\:\sum\:\left(\frac{{\left(Pre{d}_{x}-Ob{s}_{y}\right)}^{2}}{{\left(\frac{Pre{d}_{x}+Ob{s}_{y}}{2}\right)}^{2}}\right)\times\:100$$ Where Pred x is the predicted concentration generated using calculated parameters, and Obs y is the corresponding observed concentration. Table 1 Available methods for pipeline one-compartment pharmacokinetic calculations Method Calculation Description Equations Adaptive single-point method (base) • V d is calculated using C 1 after administration, provided it occurs within 0.2 times the estimated half-life (approximately 13% elimination). This calculation is only applicable in the intravenous cases. • CL is calculated based on the mean of C ss,max and C ss,min . A single point of C ss,max and C ss,min can be used for CL calculation in intravenous cases. τ is the most recent dosing interval. \(\:{V}_{d}=\frac{\text{Dose}}{{C}_{1}}\) \(\:CL=\frac{\text{Dose}}{{C}_{ss,avg}\times\:\tau\:}\) \(\:{\text{C}}_{ss,min}={C}_{ss,max}\times\:{e}^{-\frac{ln\left(2\right)}{{t}_{1/2}}\tau\:}\left(\text{b}\text{o}\text{l}\text{u}\text{s}\right)\) \(\:{C}_{ss,min}={C}_{ss,max}\times\:{e}^{-\left[\frac{\text{ln}\left(2\right)}{{t}_{1/2}}\right]\cdot\:\left({\tau\:}-{t}_{\text{inf}}\right)}\left(infusion\right)\) \(\:{C}_{ss,avg}=\frac{{C}_{ss,max}+{C}_{ss,min}}{2}\) Adaptive single-point method (extra) • If V d and CL cannot be determined from the base part, then estimated half-life is introduced. • V c is estimated using observed C max values, with R ac applied to covert the C max,ss to C max . • For oral cases, k a is determined by solving one-compartment equations using observed concentrations during the absorption phase, with F bio assumed to be 1. \(\:{V}_{d}=\frac{CL\cdot\:{t}_{1/2}}{\text{l}\text{n}\left(2\right)}\) \(\:{V}_{c}=\frac{Dose}{{C}_{max}}\) \(\:{C}_{max}=\frac{{C}_{max,ss}}{{R}_{ac}}{(R}_{ac}=\frac{1}{1-{e}^{-{\lambda\:}_{z}}})\) \(\:{C}_{t}=\frac{{F}_{bio}Dose{k}_{a}}{{V}_{d}\left({k}_{a}-{k}_{e}\right)}({e}^{-{k}_{e}t}-{e}^{-{k}_{a}t})\:\) \(\:{C}_{t}=\frac{{F}_{bio}Dose{K}_{a}}{{V}_{d}\left({k}_{a}-{k}_{e}\right)}(\frac{{e}^{-{k}_{e}t}}{1-{e}^{-{k}_{e}\tau\:}}-\frac{{e}^{-{k}_{a}t}}{1-{e}^{-{k}_{a}\tau\:}})\) NCA • For single-dose data, AUC 0-∞ is used for CL calculation. • For data after multiple doses, AUC 0-τ is for CL calculation. V z is based on the ratio of CL and λ z \(\:AU{C}_{0-{\infty\:}}={\int\:}_{0}^{tlast}{C}_{p}\hspace{0.17em}dt+\:\frac{{C}_{last}}{{\lambda\:}_{z}}\) \(\:AU{C}_{0-\tau\:}={\int\:}_{0}^{\tau\:}{C}_{p}\hspace{0.17em}dt\) \(\:CL=\frac{\text{1}}{AUC}\) \(\:{V}_{z}=CL/{\lambda\:}_{z}\) Graphic methods (IV) • It is for single-dose analysis. • V extrap is calculated as the inverse of the y-intercept obtained by extrapolating the terminal phase line. CL is derived from the regression of the terminal phase. \(\:{V}_{extrap}=\frac{1}{{Y}_{intercept}}\) \(\:CL={\lambda\:}_{z}\:\times\:{V}_{extrap}\) Graphic analysis (Oral, method of residuals) • Concentration at the elimination phase is extrapolated, and C residual is calculated extrapolated concentration C extrap minus concentration C t on the profile. The slope of the residual line represents the ka. • V d is approximated as Dose/C extrap assuming k a > > k e \(\:{C}_{extrap}=\:{\:C}_{0}{e}^{-{k}_{e}t}\:\) \(\:({\:C}_{0}=\frac{{F}_{bio}Dose{k}_{a}}{{V}_{d}\left({k}_{a}-{k}_{e}\right)})\) \(\:{C}_{residual}={{C}_{extrap}-\:C}_{t}\) \(\:{ln(C}_{residual})=\:ln{\:C}_{0}-{k}_{a}t\) Wanger Nelson method • Cumulative absorption exposure is calculated. The fraction of absorption is calculated based on all exposure and cumulative absorption exposure at each time t. The magnitude of the slope of the fraction remaining to be absorbed line in the natural logarithm scale is k a . \(\:{\text{AUC}}_{0-t}={\sum\:}_{i=1}^{n}\left(\frac{{C}_{i}+{C}_{i-1}}{2}\right){\Delta\:}{t}_{i}\) \(\:F\:(\text{t)}=\frac{{C}_{t}+{k}_{e}\cdot\:{\text{AUC}}_{0-t}}{{k}_{e}\cdot\:{\text{AUC}}_{0-{\infty\:}}}\) \(\:\text{F'(t)}=1-\:F\left(t\right)\) \(\:{k}_{a}=-\text{slope\:of\:}(\text{ln}\left(\text{F'(t)}\right)\text{\:vs}\text{.}\text{\:}\text{t)}\) CL: clearance, C ss,avg : average steady-state concentration, C ss,max : maximum steady-state concentration, C ss,min : minimum steady-state concentration, τ: dosing interval, t 1/2 : half-life, t inf : infusion time, V d : volume of distribution, C 0 : initial concentration, V c : central compartment volume, R ac : accumulation ratio, λ z : terminal elimination rate constant, C t : concentration at time t, F bio : bioavailability, k a : absorption rate constant, k e : elimination rate constant, AUC 0−∞ : area under the curve from time zero to infinity, AUC 0−τ : area under the curve within a dosing interval, C p : plasma concentration, C last : the last measurable concentration, V z : volume of distribution based on terminal phase, V extrap : extrapolated volume of distribution, Y intercept : intercept of regression line, C extrap : extrapolated concentration, C residual : residual concentration. Pipeline development Part 2 : parameter sweeping for multi-compartment and nonlinear models This pipeline provided initial estimate recommendations of V max and K m needed for nonlinear elimination modeling through parameter sweeping. This process involved a series of simulations using predefined parameter values based on a one-compartment model with Michaelis-Menten elimination, which generated simulated concentration profiles according to the dose and sampling events from input datasets. Parameters for simulation were categorized into test parameters (V max and K m ) and non-test parameters (V d and K a ). Non-test parameters (V d ) were fixed based on values obtained from Part 1 . The test range for K m was scaled relatively to C max , covering ratios from 4:1 to 1:20. V max was then calculated based on the Michaelis-Menten kinetic equation (CL = V max (CL + C)), with concentration (C) tested at 0.1 C max , 0.25 C max , 0.5 C max , and 0.75 C max , and CL obtained from Part 1 . Figure 2 displayed the outputs of simulated concentration profiles after running the parameter sweeping in one example based on the specified input parameters and dosing event. Through this battery of simulations, the model-specific parameters that provided the best-fit performance, measured by rRMSE, were identified as pipeline output. Multi-compartmental kinetics . A similar parameter sweeping was applied to explore the V c and V p . The simulated concentration profiles were generated using a two-compartment model with first-order kinetics and predefined parameter values. Among these, K a , CL, and V c were considered non-test parameters, with values obtained from the outputs in Part 1 . There were two candidate values for V c : one from V d (calculated through single-point, NCA, or graphic methods) and the other from the V c (output from single-point extra). V p was calculated based on a predefined range of V c -to-V p ratios, covering 10:1, 5:1, 2:1, 1:1, 1:2, 1:5, and 1:10. Three candidate values for inter-compartmental clearance (Q) were also tested: 1, 10, and the calculated clearance from Part 1 . Simulations were then conducted for each combination once the test spaces for each parameter were determined. The most appropriate estimates were based on the rRMSE. Data Simulated data. All simulated datasets are provided in the supplementary material. Fifteen out of twenty-one datasets were obtained directly from the nlmixr2data package [ 22 ]. Additionally, three rich one-compartment datasets, Bolus_1CPT, Infusion_1CPT, and Oral_1CPT from nlmixr2data, were extended by generating semi-sparse , sparse1 , and sparse2 datasets for each, respectively. The semi-sparse dataset was created by dividing the original IDs into three groups, where each group only included two sampling points within a single dosing interval following multiple doses. The sampling points differed among the groups at 2, 4, 6, 8, 12, and 24 hours. Sparse1 datasets had two or three sampling points available in a different dose interval for all IDs after multiple doses with time after the last dose, 2 (if oral), 20, and 24 hours. Sparse2 datasets had two or three data points collected at 2 (if oral), 20, and 24 hours but after the single dose. Public real-life data. Real-life data consisted of three datasets, theo_sd , theo_md , and pheno_sd sourced from nlmixr2data [ 22 ], as well as ten datasets from nine published articles. Information about these ten datasets is detailed in Supplementary Table 1 . The concentration-time curves for the simulated and real-life datasets were provided in Supplementary Figs. 1 and 2 . Pipeline performance For the simulated dataset, the pipeline was evaluated by re-estimating the simulated cases using the original model that generated the data and the initial estimates recommended by the pipeline, followed by an assessment of the accuracy and precision of the final parameter estimates. Deviations of final estimates from the original parameter values were calculated and summarized to assess the accuracy of final estimates. A threshold of 20%, as an often-used clinical relevance threshold [ 23 , 24 ], was applied to evaluate whether the final estimates recovered the original design values. The pipeline performance was also compared with the following initial estimate designs for simulated datasets. These strategies were: Setting all initial estimates to 1 before back-transformation (expressed as inits = 1 in the following description), with parameters defined using log-transformation. For example, the initial estimate of CL was specified to 1, which corresponds to setting the log-transformed CL to 1 in the initial condition function Setting all estimates to 1 before back-transformation, followed by optimizing the estimates using algorithms nls, nlm, and nlminb (expressed as inits = nls, inits = nlm, inits = nlminb in the following description) through naïve pooled data compartmental analysis For real-life clinical data, where the original model structure and parameter values were unknown, parameter estimation was conducted using one- and two-compartment models with IIV on all parameters and a combined residual error model. Model performance using pipeline and inits = 1 strategy was then compared. The evaluation focused on assessing the precision of the final parameter estimates obtained using both strategies, as well as the model’s goodness-of-fit, measured by AIC, and computation time. Stochastic approximation expectation-maximization (SAEM) and first-order conditional estimation with interaction (FOCEI) algorithms were used for test work in simulated and real-life datasets. Software The pipeline was developed in R, and nlmixr2 was used for model parameter estimation. All code is available on GitHub ( https://github.com/ucl-pharmacometrics/nlmixr2autoinit ). Results Pipeline output- one compartmental PK calculation. Twelve simulated datasets with one-compartment linear pharmacokinetics were analyzed. Figure 3 summarizes the pipeline outputs for initial and final estimates. Overall, the recommended initial estimates enabled the model re-estimation to converge closely (< 20%) to the original parameter values, except for Bolus_1CPT_sparse2 , where V d was slightly higher at 21.0%. Across the three rich datasets, all candidate methods worked. Final re-estimates of CL ranged from 3.9 to 4.01 L/h (original values: 4 L/h), and of V d ranged from 66.81 to 81.26 L (original value: 70 L/h). The pipeline consistently selected the initial estimates from NCA as the recommended output. The pipeline opted for the adaptive single-point method as the output for the three semi-sparse datasets. Among these, the final estimates for two intravenous cases, using NCA output as initial estimates, were within 1% of those obtained from the adaptive single-point method. For the remaining Oral_1CPT_semi_sparse , both NCA and graphical analysis failed to produce output due to the lack of single-dose data. In the sparse1 dataset, the pipeline identified the adaptive single-point method as the best fit for the data. While NCA was also able to output results in the two intravenous cases, its output V d values (252 and 283 L) deviated significantly from the original parameter values (4L/h and 70 L), causing re-estimated parameter values (105.74 and 90.28 L) to exceed the 20% range. In the sparse2 dataset, the graphic analysis was the only method to successfully provide the three values that achieved convergence in parameter re-estimation. Pipeline output-parameter sweeping Figure 4 and Fig. 5 present the initial estimates for model-specific parameters obtained through parameter sweeping, as well as the final estimates derived using these initial estimates across 12 cases originating from either Michaelis-Menten elimination or a two-compartment model. Values of V max and K m proposed by the pipeline successfully achieved convergence during re-estimation across six simulated datasets using SAEM or FOCEI methods. The re-estimated V max and K m values were within 3% (986.8 to 1025.7 mg/h) and 10% (231.0 to 275.8 mg/L) of the original parameter values. The initial estimates of V max and K m selected by the pipeline deviated from the initial estimates by no more than 2-fold in 3 of 6 cases. Following the same procedure, pipeline-proposed initial estimates successfully enabled final estimates converged to original parameter values in the cases of the multi-compartment parameters. The re-estimated V c ranged from 65.7 to 70.7 L, closely matching the original value of 70 L. While V p ranged from 46.2 to 51.5 L, it remained within a reasonable range compared with the original value of 40 L. The ratio of V c to V p proposed by the pipeline was approximately 1:1 or 2:1 in 5 out of 6 cases, aligning closely with the original parameter ratio of 7:4 (approximately 1.75:1). Pipeline performance- comparison with other strategies in simulated datasets Parameter re-estimation results across 21 simulated datasets through 5 initial estimate strategies (inits = 1, nls, nlm, nlminb, pipeline ) were reported in Supplementary Tables 2 and 3 . The statistics of final estimates’ deviation to original values for all 21 cases are shown in Supplemental Tables 4 and 5. Overall, the pipeline achieved final estimates of model structural parameters within a 20% range for 16 (76%) of 21 cases. This percentage increased to 100% when the threshold was expanded to 30%. Five cases had V p deviations from 20–30%. For SAEM, 14 cases had final estimates within this 20% range, while 6 cases had V c or V p with deviations falling within the 20–30% range and one sparse case had a ka estimation deviation of 49.0%. Apart from the pipeline strategy, fewer than half of the cases using other strategies had all final estimates falling within 20% of the original values. When focusing on individual parameters, comparative results of re-estimated CL and Vc using different strategies in 15 cases respectively under the SAEM approach were highlighted in Fig. 6 . It can be observed that only the pipeline consistently achieved final estimates of CL and Vd close to the original values in all cases. In contrast, other strategies had instances of failing to produce estimates or resulting in overestimations. Based on statistical data under the SAEM approach (see Supplementary Table 4 ), following the pipeline 100% success rate on CL, methods using inits = 1 , inits = nls , and inits = nlm as initial estimates achieved 9 to 10 (60–67%) successful cases on CL. For V c (V d ) in the one-compartment model, the pipeline achieved 100% accuracy in 15 cases except for the Bolus_1CPT_sparse2 dataset, as mentioned before. For the remaining strategies, the figures ranged from 6–8, approximately half of the pipeline values. For model-specific parameters, the pipeline was the only method to achieve final parameter estimates of both V max and K m within 20% of the original parameter values regardless of SAEM or FOCEI used. For the remaining strategies, inits = 1 and inits = nlm worked in three one-compartment cases run by the SAEM. Using inits = nls and inits = nlminb succeeded in only 0–1 cases. For V c and V p parameters, the pipeline method remained the best approach with all estimated V c within a 20% range, although 5 cases of V p deviated by 22–29% from the original parameter values. Under the 20% criterion, none of the remaining strategies successfully estimated both V c and V p . However, under the 30% criterion, three linear cases using inits = 1 managed to simultaneously converge both V c and V p to within 30% of the original values in SAEM runs. This was followed by two cases using inits = nls , and inits = nlm , while inits = nlminb had no successful cases. Pipeline performance- comparison with other strategies in clinical trial datasets The results of testing the pipeline and the inits = 1 in both one- and two-compartment models using FOCEI were reported (see Table 2 ). In general, the pipeline outperformed the strategy of inits = 1 of 13 real-life datasets. When performing parameter estimation and fitting using the one-compartment model, both methods produced identical or highly similar parameter estimates in 12 out of 13 cases, with differences within the 20% range. The only exception was the aprindine dataset, where the strategy of inits = 1 resulted in a final estimate of Vc of 4.91 L, whereas the pipeline strategy yielded a final estimate of 272 L. However, the former’s relative standard error (RSE) was much higher than the latter's (35.5% vs. 1.5%). Inits = 1 performed worse than the pipeline when running a one-compartment model by SAEM. Three cases, aprindine, cefaclor, and ceftriaxone, showed substantially different parameter estimation results. Inits = 1 and pipeline resulted in CL values of 102 vs. 1.29, 3350 vs. 30.9, and 225 vs. 0.319 L/h, respectively. Similarly, for Vd, the estimates were 0.0149 vs. 276, 508 vs. 23.1, and 252 vs. 1.49 L. Notably, the three AIC values resulting from the inits = 1 strategy were found to be much larger than those from the pipeline, with differences ranging from 2- to 3-fold. RSE% values exceeded 1000% for all CL and V d estimates using inits = 1 , except for cefaclor CL (142%). In contrast, the RSE values based on pipeline strategy ranged from 1.38–142%. Moreover, the performance of the pipeline run by SAEM remained consistent with that using FOCEI. Regarding computational time run by SAEM and FOCEI, both strategies were completed within one minute, as shown in Supplementary Figs. 4 and 5 . Given that some data might not originate from a two-compartment model, the inaccuracies in parameter estimates increased due to the nature of the data. However, it was still evident that the two strategies differed in both goodness-of-fit and computational time. From the perspective of model fitting performance, there were 10 of 13 cases where the pipeline method’s AIC was lower than that using inits = 1 run by FOCEI. The remaining three cases showed either identical or highly similar AIC performance between the two strategies. Similarly, 9 of 13 cases where AIC values for the pipeline were lower than inits = 1 when running by SAEM (see Supplementary Table 6 ). In the remaining four cases (fluorouracil, oxprenolol (oral), pindolol, and diazepam), RSE% values of CL and V d using the pipeline were all less than 20%. However, when using the inits = 1 strategy, three cases had much larger RSE% for the two parameters, ranging from 32.8–853%, with the only exception being fluorouracil CL, which had a value of 2.59%. For the last case, diazepam, the parameter estimates between the two methods differed by less than 2%. Regarding time spent running with two-compartment models, SAEM was faster than FOCEI. With SAEM, the pipeline took less than 40 seconds, while in the three cases using inits = 1 , the run time exceeded 40 seconds, with a maximum of 104.8 seconds. FOCEI followed this trend, with all cases using the pipeline taking less than 4 minutes. In contrast, the longest times among the three occurred with the inits = 1 method, ranging from 6.5 to 7.3 minutes. Table 2 Comparison of parameter estimation results using initial values set to 1 vs. pipeline recommendations for one- and two-compartment models ( FOCEI) Dataset inits=1 (1cmpt_fo) inits=1 (2cmpt_fo) inits=pipeline (1cmpt_fo) inits=pipeline (2cmpt_fo) PK reference value from source pheno_sd CL=0.00587 [1.54] a V c = 1.44 [15.7] add = 2.61 prop = 0.0417 AIC = 1022 Run_time = 0.0733 mins CL = 2.72 [8.1e+04] V c = 0.509 [295] V p = 2.72 [8.1e+04] Q = 2.72 [8.1e+04] add = 26.4 prop = 7.07e-07 AIC = 1652 Run_time = 0.17 mins CL = 0.00586 [1.55] V c = 1.44 [15.7] add = 2.67 prop = 0.0357 AIC = 1022 Run_time = 0.0413 mins CL = 0.00569 [1.64] V c = 0.802 [99.2] V p = 0.604 [39.4] Q = 0.571 [55.6] add = 2.4 prop = 0.0551 AIC = 1021 Run_time = 2.62 mins CL = 0.0047 L/h/kg V d = 0.96 L/kg [25] theo_sd k a = 1.48 [57.7] CL/F = 2.79 [7.69] V c /F = 32 [1.52] add = 0.276 prop = 0.134 AIC = 363 Run_time = 0.0911 mins k a = 1.31 [72.6] CL/F = 2.75 [7.29] V c /F = 28.9 [1.85] V p /F = 3.29 [36] Q/F = 1.68 [107] add = 0.281 prop = 0.13 AIC = 369 Run_time = 0.261 mins k a = 1.5 [51.2] CL/F = 2.78 [8.72] V c /F = 32 [1.39] add = 0.276 prop = 0.134 AIC = 363 Run_time = 0.0503 mins k a = 1.34 [65.3] CL/F = 2.76 [6.64] V c /F = 29.5 [1.56] V p /F = 2.71 [22.1] Q/F = 1.31 [97.5] add = 0.283 prop = 0.13 AIC = 370 Run_time = 0.21 mins theo_md k a = 1.38 [49.1] CL/F = 2.85 [6.51] V c /F = 31.5 [1.17] add = 0.663 prop = 0.138 AIC = 848 Run_time = 0.22 mins k a = 1.26 [67.2] CL/F = 2.83 [5.97] V c /F = 29.4 [1.04] V p /F = 2.24 [44.3] Q/F = 1.35 [160] add = 0.657 prop = 0.139 AIC = 855 Run_time = 1.2 mins k a = 1.37 [49.4] CL/F = 2.85 [5.94] V c /F = 31.4 [1.28] add = 0.659 prop = 0.139 AIC = 848 Run_time = 0.259 mins k a = 1.28 [69.7] CL/F = 2.63 [42.7] V c /F = 30.3 [1.74] V p /F = 61 [154] Q/F = 0.45 [343] add = 0.705 prop = 0.125 AIC = 850 Run_time = 1.04 mins aprindine k a = 0.00734 [7.85] CL/F = 1.82 [51.2] V c /F= 4.91 [35.5] add = 0.153 prop = 0.283 AIC = 288 Run_time = 0.607 mins k a = 1.73e+03 [3.12] CL/F = 0.00806 [15] V c /F = 0.0399 [11.2] V p /F = 380 [1.17] Q/F = 1.95 [77.9] add = 0.308 prop = 0.268 AIC = 392 Run_time = 7.28 mins k a = 0.433 [34.4] CL/F = 1.33 [105] V c /F = 272 [1.5] add = 0.142 prop = 0.291 AIC = 288 Run_time = 0.154 mins k a = 0.424 [62.1] CL/F = 1.29 [310] V c /F = 269 [5.2] V p /F = 8.19 [622] Q/F = 0.44 [3.94e+03] add = 0.142 prop = 0.293 AIC = 296 Run_time = 1.66 mins cefaclor k a = 1.5 [25.3] CL/F = 32.4 [1.65] V c /F = 23.4 [1.43] add = 0.001 prop = 0.454 AIC = 696 Run_time = 0.457 mins k a = 1.49 [21.9] CL/F = 32.4 [1.84] V c /F = 22.8 [2.75] V p /F = 0.389 [102] Q/F = 23.3 [19.1] add = 0.001 prop = 0.452 AIC = 704 Run_time = 6.46 mins k a = 1.51 [22.3] CL/F = 32.5 [1.74] V c /F = 23.5 [2.03] add = 0.001 prop = 0.453 AIC = 696 Run_time = 0.545 mins k a = 1.45 [34.5] CL/F = 30.7 [24.5] V c /F = 22.6 [5.18] V p /F = 2.31e+03 [352] Q/F = 1.99 [1.89e+03] add = 0.001 prop = 0.447 AIC = 705 Run_time = 1.7 mins ceftriaxone CL/F = 0.159 [12.4] V c /F = 1.27 [75.9] add = 6.93 prop = 0.199 AIC = 696 Run_time = 0.0173 mins CL/F = 0.127 [20.6] V c /F = 0.463 [53.2] V p /F = 0.881 [360] Q/F = 0.661 [90.9] add = 1.13 prop = 0.128 AIC = 709 Run_time = 0.158 mins CL/F = 0.159 [12.4] V c /F = 1.27 [76.5] add = 6.97 prop = 0.2 AIC = 696 Run_time = 0.0163 mins CL/F = 0.132 [31.9] V c /F = 1.05 [746] V p /F = 0.725 [624] Q/F = 0.0828 [38.1] add = 2.26 prop = 0.318 AIC = 697 Run_time = 0.0957 mins CL/F = 0.08 L/h at 3.8 kg V d /F = 1.71 L at 3.8 kg [26] cephalexin k a = 0.874 [78.8] CL/F = 16.7 [1.2] V c /F = 9.19 [9.77] add = 0.001 prop = 0.431 AIC = 1017 Run_time = 0.511 mins k a = 1.42 [55.8] CL/F = 15.7 [1.49] V c /F = 14.5 [5.93] V p /F = 24.5 [16.3] Q/F = 2.42 [32.5] add = 0.001 prop = 0.425 AIC = 1008 Run_time = 2.04 mins k a = 1.81 [22.8] CL/F = 16.7 [1.18] V c /F = 18.5 [2.16] add = 0.001 prop = 0.436 AIC = 1011 Run_time = 0.54 mins k a = 1.45 [55.1] CL/F = 15.7 [1.54] V c /F = 14.8 [7.09] V p /F = 25.7 [18.9] Q/F = 2.4 [35.6] add = 0.001 prop = 0.424 AIC = 1008 Run_time = 2.63 mins diazepam CL = 5.09 [10.4] V c = 23.6 [3.11] add = 0.0517 prop = 0.21 AIC = -272 Run_time = 0.0159 mins CL = 2.74 [15.2] V c = 15.4 [5.42] V p = 24.9 [6.88] Q = 14.4 [8.86] add = 0.00589 prop = 0.185 AIC = -426 Run_time = 0.195 mins CL = 5.08 [10.5] V c = 23.8 [3.1] add = 0.052 prop = 0.21 AIC = -272 Run_time = 0.0127 mins CL = 2.61 [16.2] V c = 16.6 [4.89] V p = 25.8 [7.29] Q = 10.3 [8.01] add = 0.00583 prop = 0.174 AIC = -429 Run_time = 0.36 mins CL (derived) b = 3.09 L/h V c (derived) = 24.11 L V p (derived) = 18.71 L V p2 (derived) = 73.83 L Q (derived) = 56.23 L/h Q 2 (derived) = 8.84 L/h [27] fluorouracil CL = 66.5 [3.51] V c = 12.7 [7.25] add = 0.101 prop = 0.318 AIC = 349 Run_time = 0.0117 mins CL = 61.8 [3.62] V c = 8.97 [12.5] V p = 2.08 [42.4] Q = 13.9 [14.5] add = 0.0903 prop = 0.278 AIC = 349 Run_time = 0.071 mins CL = 67 [3.51] V c = 12.8 [7.27] add = 0.0971 prop = 0.32 AIC = 349 Run_time = 0.0147 mins CL = 25.5 [4.65] V c = 11.3 [7.85] V p = 1.3e+03 [4.08] Q = 36.9 [9.83] add = 0.0169 prop = 0.325 AIC = 342 Run_time = 0.0662 mins CL (derived) = 86.5 L/h V c = 13.1 L [28] CL = 75.9 L/h V c = 20.3 L [29] oxprenolol (iv) CL = 24 [1.68] V c = 43.4 [0.757] add = 7.07 prop = 0.164 AIC = 948 Run_time = 0.0134 mins CL = 24.1 [1.63] V c = 3.17 [54.1] V p = 42.8 [1.39] Q = 813 [5.71] add = 5.26 prop = 0.128 AIC = 924 Run_time = 0.438 mins CL = 24 [1.68] V c = 43.5 [0.757] add = 7.08 prop = 0.166 AIC = 948 Run_time = 0.0142 mins CL = 23 [1.47] V c = 33.6 [0.848] V p = 19.1 [5.59] Q = 20.3 [5.61] add = 2.35 prop = 0.0587 AIC = 819 Run_time = 0.1 mins CL (derived) = 23.56 L/h V c = 34.4 L V p (derived) = 16.39 L Q (derived) = 23.6 L/h [30] oxprenolol (oral) k a = 2.23 [16.5] CL/F = 60.3 [1.53] V c /F = 139 [1.26] add = 1.03 prop = 0.342 AIC = 2243 Run_time = 0.0721 mins k a = 62.9 [1.37] CL/F = 14.5 [2.11] V c /F = 0.257 [9.27] V p /F = 9.36 [4.65] Q/F = 4.88 [7.34] add = 0.836 prop = 0.392 AIC = 2294 Run_time = 0.671 mins k a = 2.22 [16.5] CL/F = 60.7 [1.53] V c /F = 140 [1.26] add = 1.01 prop = 0.339 AIC = 2243 Run_time = 0.0719 mins k a = 2.19 [16.8] CL/F = 59.5 [1.65] V c /F = 139 [1.26] V p /F = 319 [18.3] Q/F = 1.29 [311] add = 1.01 prop = 0.342 AIC = 2251 Run_time = 0.191 mins F bio (mean) = 0.43 CL (derived) = 54.8 L/h V c (derived) = 80 L V p (derived) = 38.1 L Q (derived) = 54.9 L/h [30] pindolol k a = 1.28 [97.5] CL/F = 24.8 [4.44] V c /F = 110 [2.2] add = 1.33 prop = 0.187 AIC = 649 Run_time = 0.0396 mins k a = 22.7 [4.46] CL/F = 7.32 [4.04] V c /F = 0.127 [76.9] V p /F = 13.8 [1.76] Q/F = 3.36 [2.32] add = 0.779 prop = 0.322 AIC = 683 Run_time = 0.639 mins k a = 1.29 [102] CL/F = 24.8 [4.52] V c /F = 110 [2.17] add = 1.31 prop = 0.185 AIC = 649 Run_time = 0.0322 mins k a = 1.29 [131] CL/F = 24.5 [9.76] V c /F = 111 [3.15] V p /F = 107 [996] Q/F = 0.254 [1.43e+03] add = 1.31 prop = 0.188 AIC = 657 Run_time = 0.18 mins CL = 25.5 L/h V c = 142 L [31] tobramycin CL = 4.03 [4.33] V c = 24.8 [1.51] add = 0.001 prop = 0.261 AIC = 788 Run_time = 0.786 mins CL = 3.57 [4.41] V c = 12.4 [10.7] V p = 8.06 [12.9] Q = 3.37 [31.7] add = 0.001 prop = 0.255 AIC = 848 Run_time = 6.5 mins CL = 4.03 [4.53] V c = 24.9 [1.58] add = 0.001 prop = 0.26 AIC = 790 Run_time = 0.65 mins CL = 3.84 [11.2] V c = 21.7 [3.06] V p = 6.56 [87.8] Q = 0.264 [81.4] add = 0.001 prop = 0.24 AIC = 758 Run_time = 3.97 mins CL (derived) = 3.8 L/h V c (derived) = 21.8 L Q (derived) = 0.26 L/h V p (derived) = 9.6 L [32] Abbreviations : 1cmpt_fo, a one-compartment model with first-order elimination (or first-order absorption and elimination in oral cases); 2cmpt_fo, a two-compartment model with first-order elimination (or first-order absorption and elimination in oral cases); Run_time: computational running time; add, additive residual error; prop, proportional residual error a Parameter estimates are presented as typical population estimates with their corresponding relative standard errors (RSE%) indicated in brackets. Except for the pheno_sd case, where the unit of CL is L/h/kg and the unit of V is L/kg, the units of CL and V in all other cases are L/h and L, respectively. b Parameter (derived) refers to the value that was not explicitly reported in the original reference but was calculated based on other reported parameters. The following formulas were applied when calculating parameters: k 12 = Q/V c , k 21 = Q/V p , and k el = CL/V c , k 13 =Q 2 /V c , k 31 =Q 2 /Vp 2 , Here, k 12 and k 13 represent the rate constant describing the transfer of the drug from the central compartment to the peripheral compartment and second peripheral compartment, k 21 and k 31 is the rate constant for the transfer of the drug from the peripheral compartment and second peripheral compartment to the central compartment, and k el is the elimination rate constant. For parameters with covariate models, calculation was based on median covariate values. In the case of diazepam which reported parameters of four individuals, parameter values were summarized using the geometric mean. Discussion In this study, an automated pipeline was developed to generate initial estimates for PopPK modeling. This pipeline can recommend initial estimates for structural model parameters, especially in the absence of a priori information or when no iterative optimization has yet been performed to provide a reasonable starting point for the first round of modeling. Assessment results showed that the pipeline performs well both based on simulated and real-life clinical datasets, and that the initial estimates it generate enable reliable and accurate fitting in subsequent re-estimation or model development. The pipeline provides three approaches for calculating one-compartment parameters. Results from Fig. 3 indicate that the designed adaptive single-point method works in most cases, NCA handles rich data effectively, and graphic methods can address sparse data after a single oral dose, a scenario where the other two might encounter limitations. This aligns with the original design goal of developing a pipeline capable of adapting to a wide range of PK scenarios by using different methods that complement each other. For model-specific parameters, recommended initial estimates illustrated reliability across all twelve nonlinear and multi-compartmental models tested. Despite observing a deviation of 22–29% between the final estimates of V p and the initially set values, this discrepancy can likely be attributed to the sampling design. The results from the simulated datasets illustrate that the pipeline outperformed other strategies. The pipeline’s final FOCEI and SAEM estimates performed similarly under the 30% threshold criterion, with a 95.2% vs. 100% ( Supplementary Table 4 and 5 ) success rate in converging all structural parameters. However, inits=1 successfully converged for 47.6% of cases, and this number dropped to 0 when using FOCEI, with most estimates failing to move from the initial setting during estimation. This finding aligns with previous literature suggesting that SAEM generally provides better estimates than FOCEI [33, 34]. More significantly, this study additionally found that this could be particularly true when initial estimates are poor. Another observation from this study was that using optimization methods (nls, nlm, and nlminb) to optimize initial estimates was far less effective than directly following pipeline recommendations. One possible reason is nonlinear parameter estimation is also highly sensitive to initial estimates [35]. Therefore, it may be necessary to provide initial guesses for the estimates or introduce boundary setting. The pipeline consistently demonstrates superior performance compared to the inits=1 strategy when applied to real-life data. The inits= 1 strategy shows the potential to cause severe parameter estimation bias. In the aprindine case, the inits=1 strategy led to a final FOCEI V c estimate of 4.95 L ( Table 2 ), which deviated significantly from a previously reported range of 164–351 L [36]. In contrast, the pipeline had a more accurate final value of 272 L. Similarly, the inits=1 strategy and the pipeline yielded CL estimates of 0.00806 and 1.29 L/h at multiple doses (200 to 100 mg). Reported values were 50.6 and 13.4 L/h at doses of 50 and 100 mg [36]. Value from the pipeline is more acceptable given the nonlinear kinetics and CL decrease ratio. Furthermore, the pipeline may play a more effective role in facilitating appropriate model selection. For tobramycin, the AIC generated by the pipeline for the two-compartment model (758) was lower than the AIC for the one-compartment model (790), leading the pipeline to select the better-performing two-compartment model, as also suggested in the source reference [32]. In contrast, using the inits=1 strategy resulted in an AIC of 848 for the two-compartment model and 788 for the one-compartment model, leading to the opposite selection. Regarding time efficiency, it was clear that the use of pipeline-recommended initial estimates significantly reduced computational time, particularly when employing the FOCEI algorithm, compared to using inits=1 . The time savings can reach to five-fold when using SAEM or FOCEI when using a two-compartment model. In the practice of automated modeling, where thousands of models may be tested [37], excessive runtime on poorly fitted or incorrect models can lead to a substantial waste of both resources and time. Therefore, utilizing the pipeline’s adaptive approach to provide more accurate initial estimates enhances model accuracy and optimizes computational efficiency, making it a valuable tool for large-scale pharmacokinetic modeling. There are several implicit limitations in this study. A one-compartment model with linear kinetics was assumed when designing the adaptive-single-point method and the graphic methods, and their outputs were also tested within the same model. Parameter scanning for V max and K m was based on the one-compartment model, while multi-compartment parameter scanning was carried out under the assumption of first-order kinetics. These assumptions may introduce bias when applied to drugs that follow a two-compartment model or exhibit nonlinear absorption or metabolism. Although results from these studies have shown good performance for two-compartment and nonlinear models, further testing is needed to evaluate how these assumptions may impact real-life applications. Moreover, additional validation may be necessary for extreme data points, such as drugs with very long half-lives (e.g., several months) or very short half-lives (e.g., less than 1 hour), to ensure the robustness of the pipeline under such conditions. Currently, the pipeline can generate initial estimates of one-compartment model parameters (K a , V d , and CL) as well as model-specific parameters (including V max , K m , V c , V p , and Q). Three-compartment parameters are also available in the pipeline. The current test datasets are based on the nlmixr2 standard, but the pipeline is expected to support the development of PopPK models in other software programs and to be particularly helpful for beginners who struggle with defining initial estimates. While the pipeline does not yet directly link to PopPK software such as NONMEM or Monolix, it has the potential to build an initial estimates bridge in the future through R packages, such as babelmixr2, which can run NONMEM and Monolix in R environment. In conclusion, the automated pipeline developed in this study was able to not only provide reliable initial estimates for population pharmacokinetic modeling, but also proved particularly suitable for scenarios with sparse sampling or lack of a priori information scenarios. By integrating multiple computational methods, it is a great and promising tool for the provision of initial estimates for both manual and automated modeling applications. Declarations Competing Interests Matthew Fidler is an employee of Novartis. All other authors declared no competing interests for this work. Author Contribution ZHH, FK and JS: design and conceptualization; ZHH and MSL: algorithm programming; ZHH, MSL and IC: data analysis; ZHH and MF: data interpretation and methodological best practices; ZHH: first draft of manuscript; All authors contributed to writing, editing and reviewing the manuscript. Acknowledgement The authors wish to thank William S. Denney for his contributions to this manuscript. F.K. is recipient of a Sir Henry Dale Fellowship jointly funded by the Wellcome Trust and the Royal Society (Grant Number 220587/Z/20/Z). Data Availability Simulated datasets are provided within the supplementary material. Real-life datasets are obtained from open sources. References Han S, Jeon S, Yim D-S (2016) Tips for the choice of initial estimates in NONMEM. 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Eur J Clin Pharmacol 26:129–131. https://doi.org/10.1007/BF00546721 Ismail M, Sale M, Yu Y, et al (2022) Development of a genetic algorithm and NONMEM workbench for automating and improving population pharmacokinetic/pharmacodynamic model selection. J Pharmacokinet Pharmacodyn 49:243–256. https://doi.org/10.1007/s10928-021-09782-9 Additional Declarations Competing interest reported. Matthew Fidler is an employee of Novartis. All other authors declared no competing interests for this work. Supplementary Files ESM1.docx ESM2.csv Cite Share Download PDF Status: Published Journal Publication published 06 Nov, 2025 Read the published version in Journal of Pharmacokinetics and Pharmacodynamics → Version 1 posted Editorial decision: Revision requested 28 Apr, 2025 Reviews received at journal 23 Apr, 2025 Reviews received at journal 09 Mar, 2025 Reviewers agreed at journal 16 Feb, 2025 Reviewers agreed at journal 13 Feb, 2025 Reviewers invited by journal 03 Feb, 2025 Editor assigned by journal 10 Jan, 2025 Submission checks completed at journal 10 Jan, 2025 First submitted to journal 10 Jan, 2025 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-5806446","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":401572703,"identity":"6f533bd1-cbf7-474f-a411-297cd4daf517","order_by":0,"name":"Zhonghui Huang","email":"data:image/png;base64,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","orcid":"","institution":"University College London","correspondingAuthor":true,"prefix":"","firstName":"Zhonghui","middleName":"","lastName":"Huang","suffix":""},{"id":401572704,"identity":"5599be77-51c1-4068-a1fa-3046dd2535ba","order_by":1,"name":"Matthew Fidler","email":"","orcid":"","institution":"Novartis Pharmaceuticals Corporation","correspondingAuthor":false,"prefix":"","firstName":"Matthew","middleName":"","lastName":"Fidler","suffix":""},{"id":401572705,"identity":"9819c209-83c0-4e83-b78b-a0da93c2b637","order_by":2,"name":"Minshi Lan","email":"","orcid":"","institution":"University College London","correspondingAuthor":false,"prefix":"","firstName":"Minshi","middleName":"","lastName":"Lan","suffix":""},{"id":401572706,"identity":"1019ff72-beeb-478a-bbbe-19112d4c3be8","order_by":3,"name":"lek L Cheng","email":"","orcid":"","institution":"University College London","correspondingAuthor":false,"prefix":"","firstName":"lek","middleName":"L","lastName":"Cheng","suffix":""},{"id":401572707,"identity":"8c0caf44-d6e3-455f-829c-ccf21bd38f1e","order_by":4,"name":"Frank Kloprogge","email":"","orcid":"","institution":"University College London","correspondingAuthor":false,"prefix":"","firstName":"Frank","middleName":"","lastName":"Kloprogge","suffix":""},{"id":401572708,"identity":"d0d30d62-e8d1-4983-80ee-885f99c0dd29","order_by":5,"name":"Joseph F Standing","email":"","orcid":"","institution":"University College London","correspondingAuthor":false,"prefix":"","firstName":"Joseph","middleName":"F","lastName":"Standing","suffix":""}],"badges":[],"createdAt":"2025-01-10 22:23:02","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-5806446/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-5806446/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1007/s10928-025-10000-z","type":"published","date":"2025-11-06T15:57:48+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":74435182,"identity":"b6e1c806-a108-45c4-8fcb-fe6b17ecea5e","added_by":"auto","created_at":"2025-01-22 09:22:25","extension":"jpg","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":89664,"visible":true,"origin":"","legend":"\u003cp\u003eWorkflow diagram of the automated pipeline for generating initial estimates of commonly used pharmacokinetic (PK) parameters. The work was divided into two parts: the first focused on computing one-compartment parameters, including clearance (CL), volume of distribution (V\u003csub\u003ed\u003c/sub\u003e), and absorption rate constant (K\u003csub\u003ea\u003c/sub\u003e) (yellow part), while the second part concentrated on determining multi-compartmental parameters and Michaelis-Menten kinetics model by parameter sweeping (blue part). V\u003csub\u003ec\u003c/sub\u003e (central volume of distribution), V\u003csub\u003ep\u003c/sub\u003e (volume of distribution of peripheral compartment), Q (inter-compartmental clearance) ), K\u003csub\u003ee\u003c/sub\u003e (elimination rate constant), t\u003csub\u003e1/2 \u003c/sub\u003e(half-life), maximum elimination rate (V\u003csub\u003emax\u003c/sub\u003e), and Michaelis constant (K\u003csub\u003em\u003c/sub\u003e)\u003c/p\u003e","description":"","filename":"1.jpg","url":"https://assets-eu.researchsquare.com/files/rs-5806446/v1/6666e75e51321ca943b93c94.jpg"},{"id":74435184,"identity":"a9f4d6fa-fa6c-4867-94d8-4b7443e60c27","added_by":"auto","created_at":"2025-01-22 09:22:25","extension":"jpg","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":62982,"visible":true,"origin":"","legend":"\u003cp\u003eExample simulation outputs from a parameter sweep exploring different K\u003csub\u003em\u003c/sub\u003e/C\u003csub\u003emax\u003c/sub\u003e ratios (A) and V\u003csub\u003ec\u003c/sub\u003e/V\u003csub\u003ep\u003c/sub\u003e ratios (B). Panel A showed simulation results using K\u003csub\u003em\u003c/sub\u003e/C\u003csub\u003emax\u003c/sub\u003e ratios ranging from 4:1 to 1:20, modeled using a one-compartment model with Michaelis-Menten elimination. Panel B presented outputs for V\u003csub\u003ec\u003c/sub\u003e/V\u003csub\u003ep\u003c/sub\u003e ratios ranging from 10:1 to 1:10, simulated in a multi-compartmental model. The dose event was set as a single intravenous administration of 100 mg. Input parameters included CL = 4 L/h and V\u003csub\u003ec\u003c/sub\u003e = 70 L, with C\u003csub\u003emax \u003c/sub\u003e= 100 ng/ml. In this example, V\u003csub\u003emax \u003c/sub\u003ewas calculated as CL (K\u003csub\u003em\u003c/sub\u003e ± 10%C\u003csub\u003emax\u003c/sub\u003e) in Panel A, and Q was set equal to CL in Panel B. Other values were also examined during the actual parameter sweep, including V\u003csub\u003emax\u003c/sub\u003e calculated at 25%, 50%, and 75% of C\u003csub\u003emax\u003c/sub\u003e, and Q empirically set to 1 or 10.\u003c/p\u003e","description":"","filename":"2.jpg","url":"https://assets-eu.researchsquare.com/files/rs-5806446/v1/7fec93dc4f43ec6916a01e84.jpg"},{"id":74435186,"identity":"dec089ce-0038-4ad7-8f73-87beffa351f9","added_by":"auto","created_at":"2025-01-22 09:22:25","extension":"jpg","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":285968,"visible":true,"origin":"","legend":"\u003cp\u003eHeat map of candidate methods for PK calculation as initial estimates for re-estimation in simulated one-compartment linear-kinetics datasets. Purple represented the methods selected by the pipeline based on the lowest rRMSE after evaluation. Blue color referred to other methods that successfully calculated PK values and allowed re-estimation but were not selected due to higher rRMSE after evaluation. Light blue (calculated, deviated) were methods that produced initial estimates but with parameter values and re-estimated final estimates deviating significantly (\u0026gt;20%) from the original parameter values. Gray (Failed Calculation)indicated methods that failed to calculate any result for the given datasets.\u003c/p\u003e","description":"","filename":"3.jpg","url":"https://assets-eu.researchsquare.com/files/rs-5806446/v1/2ecbe5436bc21971eb03abf2.jpg"},{"id":74435192,"identity":"2cb4f356-3897-47bd-9477-f2eb22a06af1","added_by":"auto","created_at":"2025-01-22 09:22:26","extension":"jpg","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":69305,"visible":true,"origin":"","legend":"\u003cp\u003eBar chart of re-estimated V\u003csub\u003emax\u003c/sub\u003e and K\u003csub\u003em\u003c/sub\u003e values using pipeline-selected initial estimates. Re-estimation was performed using SAEM (blue bars) and FOCEI (orange bars), with the initial estimates (displayed in the right insets) selected by the Pipeline. Horizontal reference lines were the original values of V\u003csub\u003emax\u003c/sub\u003e (1000 mg/h) and Km (250 mg/L)\u003c/p\u003e","description":"","filename":"4.jpg","url":"https://assets-eu.researchsquare.com/files/rs-5806446/v1/859a84d5495ac54f73694b75.jpg"},{"id":74436613,"identity":"2a84211b-731e-43af-acf0-45e836b0a2d7","added_by":"auto","created_at":"2025-01-22 09:30:26","extension":"jpg","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":64525,"visible":true,"origin":"","legend":"\u003cp\u003eBar chart of re-estimated V\u003csub\u003ec\u003c/sub\u003e and V\u003csub\u003ep\u003c/sub\u003e values using pipeline-selected initial estimates. Re-estimation was performed using SAEM (blue bars) and FOCEI (orange bars), with the initial estimates (displayed in the right insets) selected by the Pipeline. Horizontal reference lines were the original values of V\u003csub\u003ec\u003c/sub\u003e (70 L) and V\u003csub\u003ep\u003c/sub\u003e(40 L)\u003c/p\u003e","description":"","filename":"5.jpg","url":"https://assets-eu.researchsquare.com/files/rs-5806446/v1/23f4fe9e3133168b9d1bdaf5.jpg"},{"id":74437006,"identity":"27a706cb-e008-439a-bc39-213c39346303","added_by":"auto","created_at":"2025-01-22 09:38:26","extension":"jpg","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":463887,"visible":true,"origin":"","legend":"\u003cp\u003eComparison of re-estimated clearance (up) and volume of distribution (bottom) in simulated datasets across different strategies of setting initial estimates run by SAEM. This figure contained re-estimation of clearance and volume of distribution using five different initial estimate strategies, represented by distinct colors. \"inits = 1\" sets all initial estimates to 1, while \"inits = nls,\" \"inits = nlm,\" and \"inits = nlminb\" used parameter estimates from respective algorithms as initial values. \"inits = pipeline\" referred to pipeline-specific recommendations. To address excessively large initial estimates, the y-axis is capped at 2-fold the original values. Bars exceeding this limit are truncated at the 2-fold value and annotated with \"\u0026gt;2-fold\" to indicate their magnitude\u003c/p\u003e","description":"","filename":"6.jpg","url":"https://assets-eu.researchsquare.com/files/rs-5806446/v1/75686e0c005558122521489f.jpg"},{"id":95564272,"identity":"a3c45122-2501-44a4-8809-aac85f5a6044","added_by":"auto","created_at":"2025-11-10 16:09:34","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":2596296,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-5806446/v1/dc08081e-74ad-403c-869a-b5b72c0d32fa.pdf"},{"id":74436611,"identity":"2df6c7e8-5400-47be-a51f-487d06473722","added_by":"auto","created_at":"2025-01-22 09:30:25","extension":"docx","order_by":0,"title":"","display":"","copyAsset":false,"role":"supplement","size":7418445,"visible":true,"origin":"","legend":"","description":"","filename":"ESM1.docx","url":"https://assets-eu.researchsquare.com/files/rs-5806446/v1/dd4f90480e3e028b0795fd92.docx"},{"id":74436612,"identity":"ab2aa6e4-53e1-490f-a79a-8fa878b4027c","added_by":"auto","created_at":"2025-01-22 09:30:26","extension":"csv","order_by":1,"title":"","display":"","copyAsset":false,"role":"supplement","size":4193716,"visible":true,"origin":"","legend":"","description":"","filename":"ESM2.csv","url":"https://assets-eu.researchsquare.com/files/rs-5806446/v1/88e3d40b272c77b1e139f50e.csv"}],"financialInterests":"Competing interest reported. Matthew Fidler is an employee of Novartis. All other authors declared no competing interests for this work.","formattedTitle":"An automated pipeline to generate initial estimates for population pharmacokinetic models","fulltext":[{"header":"Introduction","content":"\u003cp\u003ePopulation pharmacokinetic (PopPK) model analysis involves constructing mathematical and statistical models and performing parameter estimation to characterize the absorption, distribution, metabolism, and elimination of drugs. It is necessary to provide initial estimates to the parameter optimizers, which will then undergo iterative parameter optimization and estimation. Initial estimates are usually determined by the modeler. A common approach is to conduct a preliminary exploration of data from one or more individuals or to set the initial estimates based on published literature [\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e]. However, modeler-led approaches lack automation, rendering them time-consuming and difficult to standardize.\u003c/p\u003e \u003cp\u003eSome PopPK modeling tools offer features to automatically set initial estimates. For example, Monolix optimizes initial estimates through a custom optimization on pooled data disregarding inter-individual variability (IIV) [\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e]. This process needs to collect initial values from the panel as starting points of optimization. Babelmixr2 [\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e], a package that can connect nlmixr2 with PKNCA [\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e], computes initial estimates by performing non-compartmental analysis (NCA) and applying empirical settings. Nevertheless, it may be sensitive to the types of data used, particularly for sparse data [\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e]. NONMEM lacks a built-in automatic setting for initial estimates, but external tools like pyDarwin can be utilized. As an automated PopPK modeling tool, pyDarwin can incorporate initial estimates along with other model features into the search space for optimization within an evolutionary algorithm [\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e]. Another automatic tool, Pharmpy, requires users to input initial values for the starting model [\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e], and in one practice, NCA\u0026rsquo;s results were used as a reference for the starting models\u0026rsquo; initial estimates [\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eOther approaches based on data exploration are available. The single-point method, an earlier approach that utilizes a specific time point to predict trough concentrations [\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e, \u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e], along with more recent practices that estimate AUC using a single trough concentration [\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e, \u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e], were potential solutions for handling sparse data. Performing NCA on pooled data is another choice. The practice involves treating all data as from a single subject [\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e] and may involve combining data points at the same time interval [\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e]. The graphic methods [\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e, \u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e], offer a flexible approach applicable to both sparse and rich data. For complex models, especially those where multiple parameters lack pre-determined values, parameter sweeping can be useful. It tests a user-defined range of possible parameter values and evaluates their outputs to select a suitable value with the best performance [\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e, \u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eThere is a clear gap in tools that can automatically generate initial estimates without user input, which are universal, time-efficient, and effective for both manual modeling and automated modeling algorithms. Hence, the pipeline presented here aimed to provide references for initial estimates of structural model parameters when no prior information from other sources is available and accommodate a wide range of PK scenarios, including those involving sparse data. This was accomplished by the use of data exploration-based parameter analysis, including adaptive single-point method, graphic methods and NCA at pooled data, and parameter sweeping.\u003c/p\u003e"},{"header":"Method","content":"\u003cdiv id=\"Sec3\" class=\"Section2\"\u003e \u003ch2\u003ePipeline overview\u003c/h2\u003e \u003cp\u003eA pipeline was established to compute PK parameters from datasets formatted according to nlmixr2 data standards (see Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e). It comprised of two main parts: (1) one-compartment model parameter analysis and (2) model-specific parameter analysis in nonlinear/multi-compartment models.\u003c/p\u003e \u003cp\u003e \u003cem\u003ePart 1\u003c/em\u003e analyzed base parameters (clearance (CL), volume of distribution (V\u003csub\u003ed\u003c/sub\u003e), and absorption rate constant (K\u003csub\u003ea\u003c/sub\u003e) through three main approaches:\u003c/p\u003e \u003cp\u003e \u003col\u003e \u003cspan\u003e \u003cli\u003e \u003cp\u003e \u003cb\u003eAdaptive single-point method\u003c/b\u003e: This method was originally inspired by calculating parameters from a single concentration point [\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e, \u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e]. This study re-designed the single-point approach to incorporate data points under both initial-dose and steady-state conditions. An \u0026ldquo;extra phase\u0026rdquo; was added to address parameters not calculated in the base phase, providing the pipeline with the flexibility to handle different data types.\u003c/p\u003e \u003c/li\u003e \u003c/span\u003e \u003cspan\u003e \u003cli\u003e \u003cp\u003e \u003cb\u003eNCA\u003c/b\u003e: This approach incorporated the Wagner-Nelson method [\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e] to assist in calculating the K\u003csub\u003ea\u003c/sub\u003e to derive the necessary pharmacokinetic parameters.\u003c/p\u003e \u003c/li\u003e \u003c/span\u003e \u003cspan\u003e \u003cli\u003e \u003cp\u003e \u003cb\u003eGraphic methods\u003c/b\u003e: These methods were built upon established methodologies for one-compartment models [\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e, \u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e].\u003c/p\u003e \u003c/li\u003e \u003c/span\u003e \u003c/ol\u003e \u003c/p\u003e \u003cp\u003eOnly one output from these three methods was selected based on predictive performance on a one-compartment model, measured by rRMSE.\u003c/p\u003e \u003cp\u003e \u003cem\u003ePart 2\u003c/em\u003e focused on model-specific parameters and applied a parameter sweeping approach. A pre-defined range of candidate parameters was tested by conducting a series of simulations within the specified model using the information from the input dataset. The best-fitting parameter set was identified using by comparing simulated concentrations with observations from input datasets using rRMSE.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003cb\u003ePipeline development\u003c/b\u003e \u003cb\u003ePart 1\u003c/b\u003e: \u003cb\u003eparameter calculation for one-compartment models\u003c/b\u003e\u003c/p\u003e \u003cp\u003e \u003col\u003e \u003cspan\u003e \u003cli\u003e \u003cp\u003e \u003cb\u003eAdaptive single-point (base).\u003c/b\u003e Post-first-dose and steady-state data were extracted for individuals. Steady-state was defined as regularly spaced doses covering at least three half-lives or five doses, with dose intervals and fluctuations within \u0026plusmn;\u0026thinsp;25% of the median. Half-life was estimated through linear regression on na\u0026iuml;ve pooled data. V\u003csub\u003ed\u003c/sub\u003e was calculated as the ratio of the dose to the concentration observed at the first sampling point after the initial dose. This point was required to be collected within 20% of the half-life after dosing. Maximum (C\u003csub\u003ess,max\u003c/sub\u003e) and minimum (C\u003csub\u003ess,max\u003c/sub\u003e) concentrations were extracted from the same interval under steady state, and their mean (C\u003csub\u003ess,avg\u003c/sub\u003e) was used to calculate CL (see Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e). For cases where both extracted points were observed to fall near the dosing event (within 20% of the dosing interval from either the previous or the next dose), their mean was treated as C\u003csub\u003ess,max\u003c/sub\u003e or C\u003csub\u003ess,min\u003c/sub\u003e. CL was subsequently derived solely based on the C\u003csub\u003ess,max\u003c/sub\u003e or C\u003csub\u003ess,min\u003c/sub\u003e, and this calculation was only applicable to intravenous cases. A geometric mean with a trim value of 0.05 (i.e., removing the top and bottom 2.5% of the data) was used to summarize PK parameters derived from individuals, given as a more robust alternative, resistant to outliers approach [\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e].\u003c/p\u003e \u003c/li\u003e \u003c/span\u003e \u003c/ol\u003e \u003c/p\u003e \u003cp\u003e \u003cb\u003e1.1 Adaptive single-point (extra).\u003c/b\u003e This extended module was designed to address scenarios where not all one-compartment parameters have been determined during the base phase due to limited data. Undetermined CL or V\u003csub\u003ed\u003c/sub\u003e values were derived using the estimated half-life (see Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e). When both were undetermined, the central volume of distribution (V\u003csub\u003ec\u003c/sub\u003e) was used as a substitute for V\u003csub\u003ed\u003c/sub\u003e. The former was calculated as the ratio of dose to the maximum concentration at the time occurring within 20% of the half-life after the single dose. For multiple doses, the accumulation ratio (R\u003csub\u003eac\u003c/sub\u003e) was applied to adjust C\u003csub\u003ess,max\u003c/sub\u003e back to C\u003csub\u003emax\u003c/sub\u003e. K\u003csub\u003ea\u003c/sub\u003e was calculated by solving the analytical concentration-time equations for a one-compartment pharmacokinetic model after a single or multiple doses. Concentration data from the absorption phase (individual sampling points at sampling times\u0026thinsp;\u0026le;\u0026thinsp;peak time) were used. CL and V\u003csub\u003ed\u003c/sub\u003e in the equations were obtained from previous steps, and bioavailability was assumed to be 1. K\u003csub\u003ea\u003c/sub\u003e was subsequently determined within a wide range of values (0-1000) using Brent\u0026rsquo;s method implemented in R\u0026rsquo;s uniroot function [\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e]. K\u003csub\u003ea\u003c/sub\u003e and V\u003csub\u003ec\u003c/sub\u003e were summarized by calculating the trimmed geometric mean of individual values.\u003c/p\u003e \u003cp\u003e \u003col start=\"2\"\u003e \u003cspan\u003e \u003cli\u003e \u003cp\u003e \u003cb\u003eNa\u0026iuml;ve pooled NCA\u003c/b\u003e A na\u0026iuml;ve pooling approach was applied to process concentration-time data prior to NCA and analysis using graphic methods. Pooling was based on three groups: first-dose data, non-first-dose data (considered to be multiple-dose data), and all data. All concentration-time data within each group were pooled and binned according to pre-defined time windows with a default number of 8 to ensure adequate coverage of the PK profile. These intervals were generated by dividing unique time points into quantiles, with each group containing an approximately equal number of time points. If fewer than eight unique time points were available, the intervals were adjusted to match the actual number. Within each time window, the median time and drug concentration were calculated for each group, serving as representative values for time and concentration within that time window.\u003c/p\u003e \u003c/li\u003e \u003c/span\u003e \u003c/ol\u003e \u003cdiv class=\"BlockQuote\"\u003e \u003cp\u003eNa\u0026iuml;ve pooling of normalized concentration-by-dose data was used. The area under the curve (AUC) was calculated using the linear trapezoidal rule. The elimination rate constant (k\u003csub\u003ee\u003c/sub\u003e) was determined by performing linear regression on the last three data points of the log-transformed concentration-time curve. For single-dose data, AUC from time 0 to infinity (AUC\u003csub\u003e0-\u0026infin;\u003c/sub\u003e) was used for CL calculation, while for multiple-dose data, AUC\u003csub\u003e0-τ\u003c/sub\u003e was applied where τ was defined as the most commonly used dosing interval determined by frequency of administration (see Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e). CL was calculated by dividing the dose (standardized to 1) by the AUC, and the volume of distribution of terminal phase (V\u003csub\u003ez\u003c/sub\u003e) was calculated using the formula V\u003csub\u003ez\u003c/sub\u003e = CL/k\u003csub\u003ee\u003c/sub\u003e. For the oral case, K\u003csub\u003ea\u003c/sub\u003e was estimated by the Wagner-Nelson method [\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e]. The cumulative drug exposure at time AUC\u003csub\u003e0-t\u003c/sub\u003e was calculated, and a linear regression analysis on the fraction of the drug that remained unabsorbed during the absorption phase was performed to determine the K\u003csub\u003ea\u003c/sub\u003e.\u003c/p\u003e \u003c/div\u003e \u003c/p\u003e \u003cp\u003e \u003col start=\"3\"\u003e \u003cspan\u003e \u003cli\u003e \u003cp\u003e \u003cb\u003eGraphic methods.\u003c/b\u003e First doses from the na\u0026iuml;ve pool data were isolated for this analysis. The plasma drug concentration versus time data was first plotted on a semi-logarithmic scale. Linear regression was performed on the terminal elimination phase, and the slope is used to estimate K\u003csub\u003ee\u003c/sub\u003e, from which the half-life (t\u003csub\u003e1/2\u003c/sub\u003e) was derived. In the case of intravenous administration, the intercept, extrapolated to the y-axis, was used to calculate V\u003csub\u003ed\u003c/sub\u003e. For oral administration, the method of residuals was employed to determine the K\u003csub\u003ea\u003c/sub\u003e. This involved identifying the terminal elimination phase and subtracting it from the total plasma concentration-time curve, leaving the residuals corresponding to the absorption phase. The semi-logarithmic plot of these residuals was then used to calculate the K\u003csub\u003ea\u003c/sub\u003e. Detailed equations are listed in Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e.\u003c/p\u003e \u003c/li\u003e \u003c/span\u003e \u003c/ol\u003e \u003c/p\u003e \u003cp\u003e \u003cb\u003ePart 1 evaluation and selection.\u003c/b\u003e Each approach in \u003cem\u003ePart 1\u003c/em\u003e produced a set of parameter values for CL, Vd, and Ka. These sets of parameter values were evaluated based on their goodness-of-fit performance in a one-compartment model. The predictive performance was examined through relative root mean squared error (rRMSE), as shown in the following equation. This metric was used in this pipeline as an assessment of model fitting performance given previous practice to evaluate model fitting performance across different algorithms or initial estimates. The set with the lowest value of rRMSE was selected as pipeline initial estimate recommendations for nonlinear mixed-effects modeling and utilized to inform parameter sweeping in \u003cem\u003ePart 2\u003c/em\u003e of the pipeline.\u003cdiv id=\"Equa\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equa\" name=\"EquationSource\"\u003e\n$$\\:rRMSE\\%\\:\\:=\\:\\:\\:\\frac{1}{n}\\:\\sum\\:\\left(\\frac{{\\left(Pre{d}_{x}-Ob{s}_{y}\\right)}^{2}}{{\\left(\\frac{Pre{d}_{x}+Ob{s}_{y}}{2}\\right)}^{2}}\\right)\\times\\:100$$\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eWhere Pred\u003csub\u003ex\u003c/sub\u003e is the predicted concentration generated using calculated parameters, and Obs\u003csub\u003ey\u003c/sub\u003e is the corresponding observed concentration.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab1\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eAvailable methods for pipeline one-compartment pharmacokinetic calculations\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"3\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eMethod\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eCalculation Description\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eEquations\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eAdaptive single-point method (base)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u0026bull; V\u003csub\u003ed\u003c/sub\u003e is calculated using C\u003csub\u003e1\u003c/sub\u003e after administration, provided it occurs within 0.2 times the estimated half-life (approximately 13% elimination). This calculation is only applicable in the intravenous cases.\u003c/p\u003e \u003cp\u003e\u0026bull; CL is calculated based on the mean of C\u003csub\u003ess,max\u003c/sub\u003e and C\u003csub\u003ess,min\u003c/sub\u003e. A single point of C\u003csub\u003ess,max\u003c/sub\u003e and C\u003csub\u003ess,min\u003c/sub\u003e can be used for CL calculation in intravenous cases. τ is the most recent dosing interval.\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{V}_{d}=\\frac{\\text{Dose}}{{C}_{1}}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:CL=\\frac{\\text{Dose}}{{C}_{ss,avg}\\times\\:\\tau\\:}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\text{C}}_{ss,min}={C}_{ss,max}\\times\\:{e}^{-\\frac{ln\\left(2\\right)}{{t}_{1/2}}\\tau\\:}\\left(\\text{b}\\text{o}\\text{l}\\text{u}\\text{s}\\right)\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{C}_{ss,min}={C}_{ss,max}\\times\\:{e}^{-\\left[\\frac{\\text{ln}\\left(2\\right)}{{t}_{1/2}}\\right]\\cdot\\:\\left({\\tau\\:}-{t}_{\\text{inf}}\\right)}\\left(infusion\\right)\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{C}_{ss,avg}=\\frac{{C}_{ss,max}+{C}_{ss,min}}{2}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eAdaptive single-point method (extra)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u0026bull; If V\u003csub\u003ed\u003c/sub\u003e and CL cannot be determined from the base part, then estimated half-life is introduced.\u003c/p\u003e \u003cp\u003e\u0026bull; V\u003csub\u003ec\u003c/sub\u003e is estimated using observed C\u003csub\u003emax\u003c/sub\u003e values, with R\u003csub\u003eac\u003c/sub\u003e applied to covert the C\u003csub\u003emax,ss\u003c/sub\u003e to C\u003csub\u003emax\u003c/sub\u003e.\u003c/p\u003e \u003cp\u003e\u0026bull; For oral cases, k\u003csub\u003ea\u003c/sub\u003e is determined by solving one-compartment equations using observed concentrations during the absorption phase, with F\u003csub\u003ebio\u003c/sub\u003e assumed to be 1.\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{V}_{d}=\\frac{CL\\cdot\\:{t}_{1/2}}{\\text{l}\\text{n}\\left(2\\right)}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{V}_{c}=\\frac{Dose}{{C}_{max}}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{C}_{max}=\\frac{{C}_{max,ss}}{{R}_{ac}}{(R}_{ac}=\\frac{1}{1-{e}^{-{\\lambda\\:}_{z}}})\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{C}_{t}=\\frac{{F}_{bio}Dose{k}_{a}}{{V}_{d}\\left({k}_{a}-{k}_{e}\\right)}({e}^{-{k}_{e}t}-{e}^{-{k}_{a}t})\\:\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{C}_{t}=\\frac{{F}_{bio}Dose{K}_{a}}{{V}_{d}\\left({k}_{a}-{k}_{e}\\right)}(\\frac{{e}^{-{k}_{e}t}}{1-{e}^{-{k}_{e}\\tau\\:}}-\\frac{{e}^{-{k}_{a}t}}{1-{e}^{-{k}_{a}\\tau\\:}})\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eNCA\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u0026bull; For single-dose data, AUC\u003csub\u003e0-\u0026infin;\u003c/sub\u003e is used for CL calculation.\u003c/p\u003e \u003cp\u003e\u0026bull; For data after multiple doses, AUC\u003csub\u003e0-τ\u003c/sub\u003e is for CL calculation. V\u003csub\u003ez\u003c/sub\u003e is based on the ratio of CL and λ\u003csub\u003ez\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:AU{C}_{0-{\\infty\\:}}={\\int\\:}_{0}^{tlast}{C}_{p}\\hspace{0.17em}dt+\\:\\frac{{C}_{last}}{{\\lambda\\:}_{z}}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:AU{C}_{0-\\tau\\:}={\\int\\:}_{0}^{\\tau\\:}{C}_{p}\\hspace{0.17em}dt\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:CL=\\frac{\\text{1}}{AUC}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{V}_{z}=CL/{\\lambda\\:}_{z}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eGraphic methods (IV)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u0026bull; It is for single-dose analysis.\u003c/p\u003e \u003cp\u003e\u0026bull; V\u003csub\u003eextrap\u003c/sub\u003e is calculated as the inverse of the y-intercept obtained by extrapolating the terminal phase line. CL is derived from the regression of the terminal phase.\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{V}_{extrap}=\\frac{1}{{Y}_{intercept}}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:CL={\\lambda\\:}_{z}\\:\\times\\:{V}_{extrap}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eGraphic analysis (Oral, method of residuals)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u0026bull; Concentration at the elimination phase is extrapolated, and C\u003csub\u003eresidual\u003c/sub\u003e is calculated extrapolated concentration C\u003csub\u003eextrap\u003c/sub\u003e minus concentration C\u003csub\u003et\u003c/sub\u003e on the profile. The slope of the residual line represents the ka.\u003c/p\u003e \u003cp\u003e\u0026bull; V\u003csub\u003ed\u003c/sub\u003e is approximated as Dose/C\u003csub\u003eextrap\u003c/sub\u003e assuming k\u003csub\u003ea\u003c/sub\u003e\u0026thinsp;\u0026gt;\u0026thinsp;\u0026gt;\u0026thinsp;k\u003csub\u003ee\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{C}_{extrap}=\\:{\\:C}_{0}{e}^{-{k}_{e}t}\\:\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:({\\:C}_{0}=\\frac{{F}_{bio}Dose{k}_{a}}{{V}_{d}\\left({k}_{a}-{k}_{e}\\right)})\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{C}_{residual}={{C}_{extrap}-\\:C}_{t}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{ln(C}_{residual})=\\:ln{\\:C}_{0}-{k}_{a}t\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eWanger Nelson method\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u0026bull; Cumulative absorption exposure is calculated. The fraction of absorption is calculated based on all exposure and cumulative absorption exposure at each time t. The magnitude of the slope of the fraction remaining to be absorbed line in the natural logarithm scale is k\u003csub\u003ea\u003c/sub\u003e.\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\text{AUC}}_{0-t}={\\sum\\:}_{i=1}^{n}\\left(\\frac{{C}_{i}+{C}_{i-1}}{2}\\right){\\Delta\\:}{t}_{i}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:F\\:(\\text{t)}=\\frac{{C}_{t}+{k}_{e}\\cdot\\:{\\text{AUC}}_{0-t}}{{k}_{e}\\cdot\\:{\\text{AUC}}_{0-{\\infty\\:}}}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\text{F\u0026#039;(t)}=1-\\:F\\left(t\\right)\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{k}_{a}=-\\text{slope\\:of\\:}(\\text{ln}\\left(\\text{F\u0026#039;(t)}\\right)\\text{\\:vs}\\text{.}\\text{\\:}\\text{t)}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eCL: clearance, C\u003csub\u003ess,avg\u003c/sub\u003e: average steady-state concentration, C\u003csub\u003ess,max\u003c/sub\u003e: maximum steady-state concentration, C\u003csub\u003ess,min\u003c/sub\u003e: minimum steady-state concentration, τ: dosing interval, t\u003csub\u003e1/2\u003c/sub\u003e: half-life, t\u003csub\u003einf\u003c/sub\u003e: infusion time, V\u003csub\u003ed\u003c/sub\u003e: volume of distribution, C\u003csub\u003e0\u003c/sub\u003e: initial concentration, V\u003csub\u003ec\u003c/sub\u003e: central compartment volume, R\u003csub\u003eac\u003c/sub\u003e: accumulation ratio, λ\u003csub\u003ez\u003c/sub\u003e: terminal elimination rate constant, C\u003csub\u003et\u003c/sub\u003e: concentration at time t, F\u003csub\u003ebio\u003c/sub\u003e: bioavailability, k\u003csub\u003ea\u003c/sub\u003e: absorption rate constant, k\u003csub\u003ee\u003c/sub\u003e: elimination rate constant, AUC\u003csub\u003e0\u0026minus;\u0026infin;\u003c/sub\u003e: area under the curve from time zero to infinity, AUC\u003csub\u003e0\u0026minus;τ\u003c/sub\u003e: area under the curve within a dosing interval, C\u003csub\u003ep\u003c/sub\u003e: plasma concentration, C\u003csub\u003elast\u003c/sub\u003e: the last measurable concentration, V\u003csub\u003ez\u003c/sub\u003e: volume of distribution based on terminal phase, V\u003csub\u003eextrap\u003c/sub\u003e: extrapolated volume of distribution, Y\u003csub\u003eintercept\u003c/sub\u003e: intercept of regression line, C\u003csub\u003eextrap\u003c/sub\u003e: extrapolated concentration, C\u003csub\u003eresidual\u003c/sub\u003e: residual concentration.\u003c/p\u003e \u003cp\u003e \u003cb\u003ePipeline development\u003c/b\u003e \u003cb\u003ePart 2\u003c/b\u003e: \u003cb\u003eparameter sweeping for multi-compartment and nonlinear models\u003c/b\u003e\u003c/p\u003e \u003cp\u003eThis pipeline provided initial estimate recommendations of V\u003csub\u003emax\u003c/sub\u003e and K\u003csub\u003em\u003c/sub\u003e needed for nonlinear elimination modeling through parameter sweeping. This process involved a series of simulations using predefined parameter values based on a one-compartment model with Michaelis-Menten elimination, which generated simulated concentration profiles according to the dose and sampling events from input datasets. Parameters for simulation were categorized into test parameters (V\u003csub\u003emax\u003c/sub\u003e and K\u003csub\u003em\u003c/sub\u003e) and non-test parameters (V\u003csub\u003ed\u003c/sub\u003e and K\u003csub\u003ea\u003c/sub\u003e). Non-test parameters (V\u003csub\u003ed\u003c/sub\u003e) were fixed based on values obtained from \u003cem\u003ePart 1\u003c/em\u003e. The test range for K\u003csub\u003em\u003c/sub\u003e was scaled relatively to C\u003csub\u003emax\u003c/sub\u003e, covering ratios from 4:1 to 1:20. V\u003csub\u003emax\u003c/sub\u003e was then calculated based on the Michaelis-Menten kinetic equation (CL\u0026thinsp;=\u0026thinsp;V\u003csub\u003emax\u003c/sub\u003e(CL\u0026thinsp;+\u0026thinsp;C)), with concentration (C) tested at 0.1 C\u003csub\u003emax\u003c/sub\u003e, 0.25 C\u003csub\u003emax\u003c/sub\u003e, 0.5 C\u003csub\u003emax\u003c/sub\u003e, and 0.75 C\u003csub\u003emax\u003c/sub\u003e, and CL obtained from \u003cem\u003ePart 1\u003c/em\u003e. Figure\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e displayed the outputs of simulated concentration profiles after running the parameter sweeping in one example based on the specified input parameters and dosing event. Through this battery of simulations, the model-specific parameters that provided the best-fit performance, measured by rRMSE, were identified as pipeline output.\u003c/p\u003e \u003cp\u003e \u003cb\u003eMulti-compartmental kinetics\u003c/b\u003e. A similar parameter sweeping was applied to explore the V\u003csub\u003ec\u003c/sub\u003e and V\u003csub\u003ep\u003c/sub\u003e. The simulated concentration profiles were generated using a two-compartment model with first-order kinetics and predefined parameter values. Among these, K\u003csub\u003ea\u003c/sub\u003e, CL, and V\u003csub\u003ec\u003c/sub\u003e were considered non-test parameters, with values obtained from the outputs in \u003cem\u003ePart 1\u003c/em\u003e. There were two candidate values for V\u003csub\u003ec\u003c/sub\u003e: one from V\u003csub\u003ed\u003c/sub\u003e (calculated through single-point, NCA, or graphic methods) and the other from the V\u003csub\u003ec\u003c/sub\u003e (output from single-point extra). V\u003csub\u003ep\u003c/sub\u003e was calculated based on a predefined range of V\u003csub\u003ec\u003c/sub\u003e-to-V\u003csub\u003ep\u003c/sub\u003e ratios, covering 10:1, 5:1, 2:1, 1:1, 1:2, 1:5, and 1:10. Three candidate values for inter-compartmental clearance (Q) were also tested: 1, 10, and the calculated clearance from \u003cem\u003ePart 1\u003c/em\u003e. Simulations were then conducted for each combination once the test spaces for each parameter were determined. The most appropriate estimates were based on the rRMSE.\u003c/p\u003e \u003c/div\u003e\n\u003ch3\u003eData\u003c/h3\u003e\n\u003cp\u003e \u003cb\u003eSimulated data.\u003c/b\u003e All simulated datasets are provided in the supplementary material. Fifteen out of twenty-one datasets were obtained directly from the nlmixr2data package [\u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e]. Additionally, three rich one-compartment datasets, Bolus_1CPT, Infusion_1CPT, and Oral_1CPT from nlmixr2data, were extended by generating \u003cem\u003esemi-sparse\u003c/em\u003e, \u003cem\u003esparse1\u003c/em\u003e, and \u003cem\u003esparse2\u003c/em\u003e datasets for each, respectively. The \u003cem\u003esemi-sparse\u003c/em\u003e dataset was created by dividing the original IDs into three groups, where each group only included two sampling points within a single dosing interval following multiple doses. The sampling points differed among the groups at 2, 4, 6, 8, 12, and 24 hours. \u003cem\u003eSparse1\u003c/em\u003e datasets had two or three sampling points available in a different dose interval for all IDs after multiple doses with time after the last dose, 2 (if oral), 20, and 24 hours. \u003cem\u003eSparse2\u003c/em\u003e datasets had two or three data points collected at 2 (if oral), 20, and 24 hours but after the single dose.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003cb\u003ePublic real-life data.\u003c/b\u003e Real-life data consisted of three datasets, \u003cem\u003etheo_sd\u003c/em\u003e, \u003cspan type=\"ItalicUnderline\" class=\"ItalicUnderline\" name=\"Emphasis\"\u003etheo_md\u003c/span\u003e, and \u003cem\u003epheno_sd\u003c/em\u003e sourced from nlmixr2data [\u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e], as well as ten datasets from nine published articles. Information about these ten datasets is detailed in \u003cb\u003eSupplementary Table\u0026nbsp;1\u003c/b\u003e. The concentration-time curves for the simulated and real-life datasets were provided in \u003cb\u003eSupplementary Figs.\u0026nbsp;1 and 2\u003c/b\u003e.\u003c/p\u003e\n\u003ch3\u003ePipeline performance\u003c/h3\u003e\n\u003cp\u003eFor the simulated dataset, the pipeline was evaluated by re-estimating the simulated cases using the original model that generated the data and the initial estimates recommended by the pipeline, followed by an assessment of the accuracy and precision of the final parameter estimates. Deviations of final estimates from the original parameter values were calculated and summarized to assess the accuracy of final estimates. A threshold of 20%, as an often-used clinical relevance threshold [\u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e, \u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e], was applied to evaluate whether the final estimates recovered the original design values. The pipeline performance was also compared with the following initial estimate designs for simulated datasets.\u003c/p\u003e \u003cp\u003eThese strategies were:\u003c/p\u003e \u003cp\u003e \u003col\u003e \u003cspan\u003e \u003cli\u003e \u003cp\u003eSetting all initial estimates to 1 before back-transformation (expressed as \u003cem\u003einits\u0026thinsp;=\u0026thinsp;1\u003c/em\u003e in the following description), with parameters defined using log-transformation. For example, the initial estimate of CL was specified to 1, which corresponds to setting the log-transformed CL to 1 in the initial condition function\u003c/p\u003e \u003c/li\u003e \u003c/span\u003e \u003cspan\u003e \u003cli\u003e \u003cp\u003eSetting all estimates to 1 before back-transformation, followed by optimizing the estimates using algorithms nls, nlm, and nlminb (expressed as \u003cem\u003einits\u0026thinsp;=\u0026thinsp;nls, inits\u0026thinsp;=\u0026thinsp;nlm, inits\u0026thinsp;=\u0026thinsp;nlminb\u003c/em\u003e in the following description) through na\u0026iuml;ve pooled data compartmental analysis\u003c/p\u003e \u003c/li\u003e \u003c/span\u003e \u003c/ol\u003e \u003c/p\u003e \u003cp\u003eFor real-life clinical data, where the original model structure and parameter values were unknown, parameter estimation was conducted using one- and two-compartment models with IIV on all parameters and a combined residual error model. Model performance using pipeline and \u003cem\u003einits\u0026thinsp;=\u0026thinsp;1\u003c/em\u003e strategy was then compared. The evaluation focused on assessing the precision of the final parameter estimates obtained using both strategies, as well as the model\u0026rsquo;s goodness-of-fit, measured by AIC, and computation time. Stochastic approximation expectation-maximization (SAEM) and first-order conditional estimation with interaction (FOCEI) algorithms were used for test work in simulated and real-life datasets.\u003c/p\u003e\n\u003ch3\u003eSoftware\u003c/h3\u003e\n\u003cp\u003eThe pipeline was developed in R, and nlmixr2 was used for model parameter estimation. All code is available on GitHub (\u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://github.com/ucl-pharmacometrics/nlmixr2autoinit\u003c/span\u003e\u003cspan address=\"https://github.com/ucl-pharmacometrics/nlmixr2autoinit\" targettype=\"URL\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e).\u003c/p\u003e"},{"header":"Results","content":"\u003cp\u003e \u003cb\u003ePipeline output- one compartmental PK calculation.\u003c/b\u003e \u003c/p\u003e \u003cp\u003eTwelve simulated datasets with one-compartment linear pharmacokinetics were analyzed. Figure\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e summarizes the pipeline outputs for initial and final estimates. Overall, the recommended initial estimates enabled the model re-estimation to converge closely (\u0026lt;\u0026thinsp;20%) to the original parameter values, except for \u003cem\u003eBolus_1CPT_sparse2\u003c/em\u003e, where V\u003csub\u003ed\u003c/sub\u003e was slightly higher at 21.0%. Across the three rich datasets, all candidate methods worked. Final re-estimates of CL ranged from 3.9 to 4.01 L/h (original values: 4 L/h), and of V\u003csub\u003ed\u003c/sub\u003e ranged from 66.81 to 81.26 L (original value: 70 L/h). The pipeline consistently selected the initial estimates from NCA as the recommended output.\u003c/p\u003e \u003cp\u003eThe pipeline opted for the adaptive single-point method as the output for the three semi-sparse datasets. Among these, the final estimates for two intravenous cases, using NCA output as initial estimates, were within 1% of those obtained from the adaptive single-point method. For the remaining \u003cem\u003eOral_1CPT_semi_sparse\u003c/em\u003e, both NCA and graphical analysis failed to produce output due to the lack of single-dose data. In the \u003cem\u003esparse1\u003c/em\u003e dataset, the pipeline identified the adaptive single-point method as the best fit for the data. While NCA was also able to output results in the two intravenous cases, its output V\u003csub\u003ed\u003c/sub\u003e values (252 and 283 L) deviated significantly from the original parameter values (4L/h and 70 L), causing re-estimated parameter values (105.74 and 90.28 L) to exceed the 20% range. In the \u003cem\u003esparse2\u003c/em\u003e dataset, the graphic analysis was the only method to successfully provide the three values that achieved convergence in parameter re-estimation.\u003c/p\u003e \u003cdiv id=\"Sec8\" class=\"Section2\"\u003e \u003ch2\u003ePipeline output-parameter sweeping\u003c/h2\u003e \u003cp\u003eFigure\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e and Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e present the initial estimates for model-specific parameters obtained through parameter sweeping, as well as the final estimates derived using these initial estimates across 12 cases originating from either Michaelis-Menten elimination or a two-compartment model. Values of V\u003csub\u003emax\u003c/sub\u003e and K\u003csub\u003em\u003c/sub\u003e proposed by the pipeline successfully achieved convergence during re-estimation across six simulated datasets using SAEM or FOCEI methods. The re-estimated V\u003csub\u003emax\u003c/sub\u003e and K\u003csub\u003em\u003c/sub\u003e values were within 3% (986.8 to 1025.7 mg/h) and 10% (231.0 to 275.8 mg/L) of the original parameter values. The initial estimates of V\u003csub\u003emax\u003c/sub\u003e and K\u003csub\u003em\u003c/sub\u003e selected by the pipeline deviated from the initial estimates by no more than 2-fold in 3 of 6 cases.\u003c/p\u003e \u003cp\u003eFollowing the same procedure, pipeline-proposed initial estimates successfully enabled final estimates converged to original parameter values in the cases of the multi-compartment parameters. The re-estimated V\u003csub\u003ec\u003c/sub\u003e ranged from 65.7 to 70.7 L, closely matching the original value of 70 L. While V\u003csub\u003ep\u003c/sub\u003e ranged from 46.2 to 51.5 L, it remained within a reasonable range compared with the original value of 40 L. The ratio of V\u003csub\u003ec\u003c/sub\u003e to V\u003csub\u003ep\u003c/sub\u003e proposed by the pipeline was approximately 1:1 or 2:1 in 5 out of 6 cases, aligning closely with the original parameter ratio of 7:4 (approximately 1.75:1).\u003c/p\u003e \u003c/div\u003e\n\u003ch3\u003ePipeline performance- comparison with other strategies in simulated datasets\u003c/h3\u003e\n\u003cp\u003eParameter re-estimation results across 21 simulated datasets through 5 initial estimate strategies \u003cem\u003e(inits\u0026thinsp;=\u0026thinsp;1, nls, nlm, nlminb, pipeline\u003c/em\u003e) were reported in \u003cb\u003eSupplementary Tables\u0026nbsp;2 and 3\u003c/b\u003e. The statistics of final estimates\u0026rsquo; deviation to original values for all 21 cases are shown in \u003cb\u003eSupplemental Tables\u0026nbsp;4 and 5.\u003c/b\u003e Overall, the pipeline achieved final estimates of model structural parameters within a 20% range for 16 (76%) of 21 cases. This percentage increased to 100% when the threshold was expanded to 30%. Five cases had V\u003csub\u003ep\u003c/sub\u003e deviations from 20\u0026ndash;30%. For SAEM, 14 cases had final estimates within this 20% range, while 6 cases had V\u003csub\u003ec\u003c/sub\u003e or V\u003csub\u003ep\u003c/sub\u003e with deviations falling within the 20\u0026ndash;30% range and one sparse case had a ka estimation deviation of 49.0%. Apart from the pipeline strategy, fewer than half of the cases using other strategies had all final estimates falling within 20% of the original values.\u003c/p\u003e \u003cp\u003eWhen focusing on individual parameters, comparative results of re-estimated CL and Vc using different strategies in 15 cases respectively under the SAEM approach were highlighted in Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e. It can be observed that only the pipeline consistently achieved final estimates of CL and Vd close to the original values in all cases. In contrast, other strategies had instances of failing to produce estimates or resulting in overestimations. Based on statistical data under the SAEM approach (see \u003cb\u003eSupplementary Table\u0026nbsp;4\u003c/b\u003e), following the pipeline 100% success rate on CL, methods using \u003cem\u003einits\u0026thinsp;=\u0026thinsp;1\u003c/em\u003e, \u003cem\u003einits\u0026thinsp;=\u0026thinsp;nls\u003c/em\u003e, and \u003cem\u003einits\u0026thinsp;=\u0026thinsp;nlm\u003c/em\u003e as initial estimates achieved 9 to 10 (60\u0026ndash;67%) successful cases on CL. For V\u003csub\u003ec\u003c/sub\u003e (V\u003csub\u003ed\u003c/sub\u003e) in the one-compartment model, the pipeline achieved 100% accuracy in 15 cases except for the \u003cem\u003eBolus_1CPT_sparse2\u003c/em\u003e dataset, as mentioned before. For the remaining strategies, the figures ranged from 6\u0026ndash;8, approximately half of the pipeline values.\u003c/p\u003e \u003cp\u003eFor model-specific parameters, the pipeline was the only method to achieve final parameter estimates of both V\u003csub\u003emax\u003c/sub\u003e and K\u003csub\u003em\u003c/sub\u003e within 20% of the original parameter values regardless of SAEM or FOCEI used. For the remaining strategies, \u003cem\u003einits\u0026thinsp;=\u0026thinsp;1\u003c/em\u003e and \u003cem\u003einits\u0026thinsp;=\u0026thinsp;nlm\u003c/em\u003e worked in three one-compartment cases run by the SAEM. Using \u003cem\u003einits\u0026thinsp;=\u0026thinsp;nls\u003c/em\u003e and \u003cem\u003einits\u0026thinsp;=\u0026thinsp;nlminb\u003c/em\u003e succeeded in only 0\u0026ndash;1 cases. For V\u003csub\u003ec\u003c/sub\u003e and V\u003csub\u003ep\u003c/sub\u003e parameters, the pipeline method remained the best approach with all estimated V\u003csub\u003ec\u003c/sub\u003e within a 20% range, although 5 cases of V\u003csub\u003ep\u003c/sub\u003e deviated by 22\u0026ndash;29% from the original parameter values. Under the 20% criterion, none of the remaining strategies successfully estimated both V\u003csub\u003ec\u003c/sub\u003e and V\u003csub\u003ep\u003c/sub\u003e. However, under the 30% criterion, three linear cases using \u003cem\u003einits\u0026thinsp;=\u0026thinsp;1\u003c/em\u003e managed to simultaneously converge both V\u003csub\u003ec\u003c/sub\u003e and V\u003csub\u003ep\u003c/sub\u003e to within 30% of the original values in SAEM runs. This was followed by two cases using \u003cem\u003einits\u0026thinsp;=\u0026thinsp;nls\u003c/em\u003e, and \u003cem\u003einits\u0026thinsp;=\u0026thinsp;nlm\u003c/em\u003e, while \u003cem\u003einits\u0026thinsp;=\u0026thinsp;nlminb\u003c/em\u003e had no successful cases.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e\n\u003ch3\u003ePipeline performance- comparison with other strategies in clinical trial datasets\u003c/h3\u003e\n\u003cp\u003eThe results of testing the pipeline and the \u003cem\u003einits\u0026thinsp;=\u0026thinsp;1\u003c/em\u003e in both one- and two-compartment models using FOCEI were reported (see \u003cb\u003eTable\u0026nbsp;2\u003c/b\u003e). In general, the pipeline outperformed the strategy of \u003cem\u003einits\u0026thinsp;=\u0026thinsp;1\u003c/em\u003e of 13 real-life datasets. When performing parameter estimation and fitting using the one-compartment model, both methods produced identical or highly similar parameter estimates in 12 out of 13 cases, with differences within the 20% range. The only exception was the aprindine dataset, where the strategy of \u003cem\u003einits\u0026thinsp;=\u0026thinsp;1\u003c/em\u003e resulted in a final estimate of Vc of 4.91 L, whereas the pipeline strategy yielded a final estimate of 272 L. However, the former\u0026rsquo;s relative standard error (RSE) was much higher than the latter's (35.5% vs. 1.5%).\u003c/p\u003e \u003cp\u003e \u003cem\u003eInits\u0026thinsp;=\u0026thinsp;1\u003c/em\u003e performed worse than the pipeline when running a one-compartment model by SAEM. Three cases, aprindine, cefaclor, and ceftriaxone, showed substantially different parameter estimation results. \u003cem\u003eInits\u0026thinsp;=\u0026thinsp;1\u003c/em\u003e and pipeline resulted in CL values of 102 vs. 1.29, 3350 vs. 30.9, and 225 vs. 0.319 L/h, respectively. Similarly, for Vd, the estimates were 0.0149 vs. 276, 508 vs. 23.1, and 252 vs. 1.49 L. Notably, the three AIC values resulting from the \u003cem\u003einits\u0026thinsp;=\u0026thinsp;1\u003c/em\u003e strategy were found to be much larger than those from the pipeline, with differences ranging from 2- to 3-fold. RSE% values exceeded 1000% for all CL and V\u003csub\u003ed\u003c/sub\u003e estimates using \u003cem\u003einits\u0026thinsp;=\u0026thinsp;1\u003c/em\u003e, except for cefaclor CL (142%). In contrast, the RSE values based on pipeline strategy ranged from 1.38\u0026ndash;142%. Moreover, the performance of the pipeline run by SAEM remained consistent with that using FOCEI. Regarding computational time run by SAEM and FOCEI, both strategies were completed within one minute, as shown in \u003cb\u003eSupplementary Figs.\u0026nbsp;4 and 5\u003c/b\u003e.\u003c/p\u003e \u003cp\u003eGiven that some data might not originate from a two-compartment model, the inaccuracies in parameter estimates increased due to the nature of the data. However, it was still evident that the two strategies differed in both goodness-of-fit and computational time. From the perspective of model fitting performance, there were 10 of 13 cases where the pipeline method\u0026rsquo;s AIC was lower than that using \u003cem\u003einits\u0026thinsp;=\u0026thinsp;1\u003c/em\u003e run by FOCEI. The remaining three cases showed either identical or highly similar AIC performance between the two strategies. Similarly, 9 of 13 cases where AIC values for the pipeline were lower than \u003cem\u003einits\u0026thinsp;=\u0026thinsp;1\u003c/em\u003e when running by SAEM (see \u003cb\u003eSupplementary Table\u0026nbsp;6\u003c/b\u003e). In the remaining four cases (fluorouracil, oxprenolol (oral), pindolol, and diazepam), RSE% values of CL and V\u003csub\u003ed\u003c/sub\u003e using the pipeline were all less than 20%. However, when using the \u003cem\u003einits\u0026thinsp;=\u0026thinsp;1\u003c/em\u003e strategy, three cases had much larger RSE% for the two parameters, ranging from 32.8\u0026ndash;853%, with the only exception being fluorouracil CL, which had a value of 2.59%. For the last case, diazepam, the parameter estimates between the two methods differed by less than 2%.\u003c/p\u003e \u003cp\u003eRegarding time spent running with two-compartment models, SAEM was faster than FOCEI. With SAEM, the pipeline took less than 40 seconds, while in the three cases using \u003cem\u003einits\u003c/em\u003e\u0026thinsp;=\u0026thinsp;\u003cem\u003e1\u003c/em\u003e, the run time exceeded 40 seconds, with a maximum of 104.8 seconds. FOCEI followed this trend, with all cases using the pipeline taking less than 4 minutes. In contrast, the longest times among the three occurred with the \u003cem\u003einits\u0026thinsp;=\u0026thinsp;1\u003c/em\u003e method, ranging from 6.5 to 7.3 minutes.\u003c/p\u003e \u003cp\u003e\u003cstrong\u003eTable 2\u003c/strong\u003e\u003cstrong\u003e\u0026nbsp;Comparison of parameter estimation results using initial values set to 1 vs. pipeline recommendations for one- and two-compartment models (\u003c/strong\u003e\u003cstrong\u003eFOCEI)\u003c/strong\u003e\u003c/p\u003e\n\u003ctable border=\"1\" cellspacing=\"0\" cellpadding=\"0\" width=\"100%\"\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 14px;\"\u003e\n \u003cp\u003e\u003cstrong\u003eDataset\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 16px;\"\u003e\n \u003cp\u003e\u003cstrong\u003einits=1 (1cmpt_fo)\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 15px;\"\u003e\n \u003cp\u003e\u003cstrong\u003einits=1 (2cmpt_fo)\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 16px;\"\u003e\n \u003cp\u003e\u003cstrong\u003einits=pipeline (1cmpt_fo)\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 16px;\"\u003e\n \u003cp\u003e\u003cstrong\u003einits=pipeline (2cmpt_fo)\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 19px;\"\u003e\n \u003cp\u003e\u003cstrong\u003ePK reference value from source\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 1px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e\u0026nbsp;\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 14px;\"\u003e\n \u003cp\u003e\u003cstrong\u003epheno_sd\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 16px;\"\u003e\n \u003cp\u003eCL=0.00587 [1.54] \u003csup\u003ea\u003c/sup\u003e\u003cbr\u003eV\u003csub\u003ec\u003c/sub\u003e = 1.44 [15.7]\u003cbr\u003e\u0026nbsp;add = 2.61\u003cbr\u003e\u0026nbsp;prop = 0.0417\u003cbr\u003e\u0026nbsp;AIC = 1022\u003cbr\u003e\u0026nbsp;Run_time \u0026nbsp;= 0.0733 mins\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 15px;\"\u003e\n \u003cp\u003eCL = 2.72 [8.1e+04]\u003cbr\u003eV\u003csub\u003ec\u003c/sub\u003e = 0.509 [295]\u003cbr\u003eV\u003csub\u003ep\u003c/sub\u003e = 2.72 [8.1e+04]\u003cbr\u003e\u0026nbsp;Q = 2.72 [8.1e+04]\u003cbr\u003e\u0026nbsp;add = 26.4\u003cbr\u003e\u0026nbsp;prop = 7.07e-07\u003cbr\u003e\u0026nbsp;AIC = 1652\u003cbr\u003e\u0026nbsp;Run_time \u0026nbsp;= 0.17 mins\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 16px;\"\u003e\n \u003cp\u003eCL = 0.00586 [1.55]\u003cbr\u003eV\u003csub\u003ec\u003c/sub\u003e = 1.44 [15.7]\u003cbr\u003e\u0026nbsp;add = 2.67\u003cbr\u003e\u0026nbsp;prop = 0.0357\u003cbr\u003e\u0026nbsp;AIC = 1022\u003cbr\u003e\u0026nbsp;Run_time \u0026nbsp;= 0.0413 mins\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 16px;\"\u003e\n \u003cp\u003eCL = 0.00569 [1.64]\u003cbr\u003eV\u003csub\u003ec\u003c/sub\u003e = 0.802 [99.2]\u003cbr\u003eV\u003csub\u003ep\u003c/sub\u003e = 0.604 [39.4]\u003cbr\u003e\u0026nbsp;Q = 0.571 [55.6]\u003cbr\u003e\u0026nbsp;add = 2.4\u003cbr\u003e\u0026nbsp;prop = 0.0551\u003cbr\u003e\u0026nbsp;AIC = 1021\u003cbr\u003e\u0026nbsp;Run_time \u0026nbsp;= 2.62 mins\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 19px;\"\u003e\n \u003cp\u003eCL \u0026nbsp; = \u003cstrong\u003e0.0047\u003c/strong\u003e L/h/kg\u003c/p\u003e\n \u003cp\u003eV\u003csub\u003ed\u003c/sub\u003e\u0026nbsp; \u0026nbsp;= \u0026nbsp; \u003cstrong\u003e0.96\u003c/strong\u003e L/kg\u0026nbsp;[25]\u003c/p\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 1px;\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 14px;\"\u003e\n \u003cp\u003e\u003cstrong\u003etheo_sd\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 16px;\"\u003e\n \u003cp\u003ek\u003csub\u003ea\u003c/sub\u003e = 1.48 [57.7]\u003c/p\u003e\n \u003cp\u003eCL/F = 2.79 [7.69]\u003cbr\u003eV\u003csub\u003ec\u003c/sub\u003e/F = 32 [1.52]\u003cbr\u003e\u0026nbsp;add = 0.276\u003cbr\u003e\u0026nbsp;prop = 0.134\u003cbr\u003e\u0026nbsp;AIC = 363\u003cbr\u003e\u0026nbsp;Run_time \u0026nbsp;= 0.0911 mins\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 15px;\"\u003e\n \u003cp\u003ek\u003csub\u003ea\u003c/sub\u003e = 1.31 [72.6]\u003c/p\u003e\n \u003cp\u003eCL/F = 2.75 [7.29]\u003cbr\u003eV\u003csub\u003ec\u003c/sub\u003e/F = 28.9 [1.85]\u003cbr\u003eV\u003csub\u003ep\u003c/sub\u003e/F\u0026nbsp;\u0026nbsp;= 3.29 [36]\u003cbr\u003e\u0026nbsp;Q/F\u0026nbsp;\u0026nbsp;= 1.68 [107]\u003cbr\u003e\u0026nbsp;add = 0.281\u003cbr\u003e\u0026nbsp;prop = 0.13\u003cbr\u003e\u0026nbsp;AIC = 369\u003cbr\u003e\u0026nbsp;Run_time \u0026nbsp;= 0.261 mins\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 16px;\"\u003e\n \u003cp\u003ek\u003csub\u003ea\u003c/sub\u003e = 1.5 [51.2]\u003c/p\u003e\n \u003cp\u003eCL/F = 2.78 [8.72]\u003cbr\u003eV\u003csub\u003ec\u003c/sub\u003e/F = 32 [1.39]\u003cbr\u003e\u0026nbsp;add = 0.276\u003cbr\u003e\u0026nbsp;prop = 0.134\u003cbr\u003e\u0026nbsp;AIC = 363\u003cbr\u003e\u0026nbsp;Run_time \u0026nbsp;= 0.0503 mins\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 16px;\"\u003e\n \u003cp\u003ek\u003csub\u003ea\u003c/sub\u003e = 1.34 [65.3]\u003c/p\u003e\n \u003cp\u003eCL/F = 2.76 [6.64]\u003cbr\u003eV\u003csub\u003ec\u003c/sub\u003e/F = 29.5 [1.56]\u003cbr\u003eV\u003csub\u003ep\u003c/sub\u003e/F = 2.71 [22.1]\u003cbr\u003e\u0026nbsp;Q/F = 1.31 [97.5]\u003cbr\u003e\u0026nbsp;add = 0.283\u003cbr\u003e\u0026nbsp;prop = 0.13\u003cbr\u003e\u0026nbsp;AIC = 370\u003cbr\u003e\u0026nbsp;Run_time \u0026nbsp;= 0.21 mins\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 19px;\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 1px;\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 14px;\"\u003e\n \u003cp\u003e\u003cstrong\u003etheo_md\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 16px;\"\u003e\n \u003cp\u003ek\u003csub\u003ea\u003c/sub\u003e = 1.38 [49.1]\u003c/p\u003e\n \u003cp\u003eCL/F = 2.85 [6.51]\u003cbr\u003eV\u003csub\u003ec\u003c/sub\u003e/F = 31.5 [1.17]\u003cbr\u003e\u0026nbsp;add = 0.663\u003cbr\u003e\u0026nbsp;prop = 0.138\u003cbr\u003e\u0026nbsp;AIC = 848\u003cbr\u003e\u0026nbsp;Run_time \u0026nbsp;= 0.22 mins\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 15px;\"\u003e\n \u003cp\u003ek\u003csub\u003ea\u003c/sub\u003e\u0026nbsp; = \u0026nbsp;1.26 [67.2]\u003c/p\u003e\n \u003cp\u003eCL/F = 2.83 [5.97]\u003cbr\u003eV\u003csub\u003ec\u003c/sub\u003e/F = 29.4 [1.04]\u003cbr\u003eV\u003csub\u003ep\u003c/sub\u003e/F = 2.24 [44.3]\u003cbr\u003e\u0026nbsp;Q/F \u0026nbsp;= \u0026nbsp; \u0026nbsp; 1.35 [160]\u003cbr\u003e\u0026nbsp;add \u0026nbsp;= \u0026nbsp; \u0026nbsp; 0.657\u003cbr\u003e\u0026nbsp;prop \u0026nbsp;= \u0026nbsp; \u0026nbsp; 0.139\u003cbr\u003e\u0026nbsp;AIC \u0026nbsp;= \u0026nbsp; \u0026nbsp; 855\u003cbr\u003e\u0026nbsp;Run_time \u0026nbsp; = \u0026nbsp;1.2 mins\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 16px;\"\u003e\n \u003cp\u003ek\u003csub\u003ea\u003c/sub\u003e = 1.37 [49.4]\u003c/p\u003e\n \u003cp\u003eCL/F = 2.85 [5.94]\u003cbr\u003eV\u003csub\u003ec\u003c/sub\u003e/F = 31.4 [1.28]\u003cbr\u003e\u0026nbsp;add = 0.659\u003cbr\u003e\u0026nbsp;prop = 0.139\u003cbr\u003e\u0026nbsp;AIC = 848\u003cbr\u003e\u0026nbsp;Run_time \u0026nbsp;= 0.259 mins\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 16px;\"\u003e\n \u003cp\u003ek\u003csub\u003ea\u003c/sub\u003e = 1.28 [69.7]\u003c/p\u003e\n \u003cp\u003eCL/F = 2.63 [42.7]\u003cbr\u003eV\u003csub\u003ec\u003c/sub\u003e/F = 30.3 [1.74]\u003cbr\u003eV\u003csub\u003ep\u003c/sub\u003e/F = 61 [154]\u003cbr\u003e\u0026nbsp;Q/F = 0.45 [343]\u003cbr\u003e\u0026nbsp;add = 0.705\u003cbr\u003e\u0026nbsp;prop = 0.125\u003cbr\u003e\u0026nbsp;AIC = 850\u003cbr\u003e\u0026nbsp;Run_time \u0026nbsp;= 1.04 mins\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 19px;\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 1px;\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 14px;\"\u003e\n \u003cp\u003e\u003cstrong\u003eaprindine\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 16px;\"\u003e\n \u003cp\u003ek\u003csub\u003ea\u003c/sub\u003e = 0.00734 [7.85]\u003c/p\u003e\n \u003cp\u003eCL/F = 1.82 [51.2]\u003cbr\u003eV\u003csub\u003ec\u003c/sub\u003e/F= 4.91 [35.5]\u003cbr\u003e\u0026nbsp;add = 0.153\u003cbr\u003e\u0026nbsp;prop = 0.283\u003cbr\u003e\u0026nbsp;AIC = 288\u003cbr\u003e\u0026nbsp;Run_time \u0026nbsp;= 0.607 mins\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 15px;\"\u003e\n \u003cp\u003ek\u003csub\u003ea\u003c/sub\u003e = 1.73e+03 [3.12]\u003c/p\u003e\n \u003cp\u003eCL/F\u0026nbsp;\u0026nbsp;= 0.00806 [15]\u003cbr\u003eV\u003csub\u003ec\u003c/sub\u003e/F\u0026nbsp;\u0026nbsp;= 0.0399 [11.2]\u003cbr\u003e\u0026nbsp;V\u003csub\u003ep\u003c/sub\u003e/F\u0026nbsp;\u0026nbsp;= 380 [1.17]\u003cbr\u003e\u0026nbsp;Q/F\u0026nbsp;\u0026nbsp;= 1.95 [77.9]\u003cbr\u003e\u0026nbsp;add = 0.308\u003cbr\u003e\u0026nbsp;prop = 0.268\u003cbr\u003e\u0026nbsp;AIC = 392\u003cbr\u003e\u0026nbsp;Run_time \u0026nbsp;= 7.28 mins\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 16px;\"\u003e\n \u003cp\u003ek\u003csub\u003ea\u003c/sub\u003e = 0.433 [34.4]\u003c/p\u003e\n \u003cp\u003eCL/F\u0026nbsp;\u0026nbsp;= 1.33 [105]\u003cbr\u003eV\u003csub\u003ec\u003c/sub\u003e/F\u0026nbsp;\u0026nbsp;= 272 [1.5]\u003cbr\u003e\u0026nbsp;add = 0.142\u003cbr\u003e\u0026nbsp;prop = 0.291\u003cbr\u003e\u0026nbsp;AIC = 288\u003cbr\u003e\u0026nbsp;Run_time \u0026nbsp;= 0.154 mins\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 16px;\"\u003e\n \u003cp\u003ek\u003csub\u003ea\u003c/sub\u003e = 0.424 [62.1]\u003c/p\u003e\n \u003cp\u003eCL/F\u0026nbsp;\u0026nbsp;= 1.29 [310]\u003cbr\u003eV\u003csub\u003ec\u003c/sub\u003e/F\u0026nbsp;\u0026nbsp;= 269 [5.2]\u003cbr\u003e\u0026nbsp;V\u003csub\u003ep\u003c/sub\u003e/F\u0026nbsp;\u0026nbsp;= 8.19 [622]\u003cbr\u003e\u0026nbsp;Q/F\u0026nbsp;\u0026nbsp;= 0.44 [3.94e+03]\u003cbr\u003e\u0026nbsp;add = 0.142\u003cbr\u003e\u0026nbsp;prop = 0.293\u003cbr\u003e\u0026nbsp;AIC = 296\u003cbr\u003e\u0026nbsp;Run_time \u0026nbsp;= 1.66 mins\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 19px;\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 1px;\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 14px;\"\u003e\n \u003cp\u003e\u003cstrong\u003ecefaclor\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 16px;\"\u003e\n \u003cp\u003ek\u003csub\u003ea\u003c/sub\u003e = 1.5 [25.3]\u003c/p\u003e\n \u003cp\u003eCL/F = 32.4 [1.65]\u003cbr\u003eV\u003csub\u003ec\u003c/sub\u003e/F = 23.4 [1.43]\u003cbr\u003e\u0026nbsp;add = 0.001\u003cbr\u003e\u0026nbsp;prop = 0.454\u003cbr\u003e\u0026nbsp;AIC = 696\u003cbr\u003e\u0026nbsp;Run_time \u0026nbsp;= 0.457 mins\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 15px;\"\u003e\n \u003cp\u003ek\u003csub\u003ea\u003c/sub\u003e = 1.49 [21.9]\u003c/p\u003e\n \u003cp\u003eCL/F = 32.4 [1.84]\u003cbr\u003eV\u003csub\u003ec\u003c/sub\u003e/F = 22.8 [2.75]\u003cbr\u003eV\u003csub\u003ep\u003c/sub\u003e/F = 0.389 [102]\u003cbr\u003e\u0026nbsp;Q/F = 23.3 [19.1]\u003cbr\u003e\u0026nbsp;add = 0.001\u003cbr\u003e\u0026nbsp;prop = 0.452\u003cbr\u003e\u0026nbsp;AIC = 704\u003cbr\u003e\u0026nbsp;Run_time \u0026nbsp;= 6.46 mins\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 16px;\"\u003e\n \u003cp\u003ek\u003csub\u003ea\u003c/sub\u003e = 1.51 [22.3]\u003c/p\u003e\n \u003cp\u003eCL/F = 32.5 [1.74]\u003cbr\u003eV\u003csub\u003ec\u003c/sub\u003e/F = 23.5 [2.03]\u003cbr\u003e\u0026nbsp;add = 0.001\u003cbr\u003e\u0026nbsp;prop = 0.453\u003cbr\u003e\u0026nbsp;AIC = 696\u003cbr\u003e\u0026nbsp;Run_time \u0026nbsp;= 0.545 mins\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 16px;\"\u003e\n \u003cp\u003ek\u003csub\u003ea\u003c/sub\u003e = 1.45 [34.5]\u003c/p\u003e\n \u003cp\u003eCL/F = 30.7 [24.5]\u003cbr\u003eV\u003csub\u003ec\u003c/sub\u003e/F = 22.6 [5.18]\u003cbr\u003eV\u003csub\u003ep\u003c/sub\u003e/F = 2.31e+03 [352]\u003cbr\u003e\u0026nbsp;Q/F = 1.99 [1.89e+03]\u003cbr\u003e\u0026nbsp;add = 0.001\u003cbr\u003e\u0026nbsp;prop = 0.447\u003cbr\u003e\u0026nbsp;AIC = 705\u003cbr\u003e\u0026nbsp;Run_time \u0026nbsp;= 1.7 mins\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 19px;\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 1px;\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 14px;\"\u003e\n \u003cp\u003e\u003cstrong\u003eceftriaxone\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 16px;\"\u003e\n \u003cp\u003eCL/F = 0.159 [12.4]\u003cbr\u003eV\u003csub\u003ec\u003c/sub\u003e/F = 1.27 [75.9]\u003cbr\u003e\u0026nbsp;add = 6.93\u003cbr\u003e\u0026nbsp;prop = 0.199\u003cbr\u003e\u0026nbsp;AIC = 696\u003cbr\u003e\u0026nbsp;Run_time \u0026nbsp;= 0.0173 mins\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 15px;\"\u003e\n \u003cp\u003eCL/F = 0.127 [20.6]\u003cbr\u003eV\u003csub\u003ec\u003c/sub\u003e/F = 0.463 [53.2]\u003cbr\u003eV\u003csub\u003ep\u003c/sub\u003e/F = 0.881 [360]\u003cbr\u003e\u0026nbsp;Q/F = 0.661 [90.9]\u003cbr\u003e\u0026nbsp;add = 1.13\u003cbr\u003e\u0026nbsp;prop = 0.128\u003cbr\u003e\u0026nbsp;AIC = 709\u003cbr\u003e\u0026nbsp;Run_time \u0026nbsp;= 0.158 mins\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 16px;\"\u003e\n \u003cp\u003eCL/F = 0.159 [12.4]\u003cbr\u003eV\u003csub\u003ec\u003c/sub\u003e/F = 1.27 [76.5]\u003cbr\u003e\u0026nbsp;add = 6.97\u003cbr\u003e\u0026nbsp;prop = 0.2\u003cbr\u003e\u0026nbsp;AIC = 696\u003cbr\u003e\u0026nbsp;Run_time \u0026nbsp;= 0.0163 mins\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 16px;\"\u003e\n \u003cp\u003eCL/F = 0.132 [31.9]\u003cbr\u003eV\u003csub\u003ec\u003c/sub\u003e/F = 1.05 [746]\u003cbr\u003eV\u003csub\u003ep\u003c/sub\u003e/F = 0.725 [624]\u003cbr\u003e\u0026nbsp;Q/F = 0.0828 [38.1]\u003cbr\u003e\u0026nbsp;add = 2.26\u003cbr\u003e\u0026nbsp;prop = 0.318\u003cbr\u003e\u0026nbsp;AIC = 697\u003cbr\u003e\u0026nbsp;Run_time \u0026nbsp;= 0.0957 mins\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 19px;\"\u003e\n \u003cp\u003eCL/F\u0026nbsp;=\u0026nbsp;\u003cstrong\u003e0.08\u003c/strong\u003e L/h at 3.8 kg\u003c/p\u003e\n \u003cp\u003eV\u003csub\u003ed\u003c/sub\u003e/F\u0026nbsp; = \u003cstrong\u003e1.71\u0026nbsp;\u003c/strong\u003eL at 3.8 kg\u0026nbsp;[26]\u003c/p\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 1px;\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 14px;\"\u003e\n \u003cp\u003e\u003cstrong\u003ecephalexin\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 16px;\"\u003e\n \u003cp\u003ek\u003csub\u003ea\u003c/sub\u003e = 0.874 [78.8]\u003c/p\u003e\n \u003cp\u003eCL/F = 16.7 [1.2]\u003cbr\u003eV\u003csub\u003ec\u003c/sub\u003e/F = 9.19 [9.77]\u003cbr\u003e\u0026nbsp;add = 0.001\u003cbr\u003e\u0026nbsp;prop = 0.431\u003cbr\u003e\u0026nbsp;AIC = 1017\u003cbr\u003e\u0026nbsp;Run_time \u0026nbsp;= 0.511 mins\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 15px;\"\u003e\n \u003cp\u003ek\u003csub\u003ea\u003c/sub\u003e = 1.42 [55.8]\u003c/p\u003e\n \u003cp\u003eCL/F = 15.7 [1.49]\u003cbr\u003eV\u003csub\u003ec\u003c/sub\u003e/F = 14.5 [5.93]\u003cbr\u003eV\u003csub\u003ep\u003c/sub\u003e/F = 24.5 [16.3]\u003cbr\u003e\u0026nbsp;Q/F = 2.42 [32.5]\u003cbr\u003e\u0026nbsp;add = 0.001\u003cbr\u003e\u0026nbsp;prop = 0.425\u003cbr\u003e\u0026nbsp;AIC = 1008\u003cbr\u003e\u0026nbsp;Run_time \u0026nbsp;= 2.04 mins\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 16px;\"\u003e\n \u003cp\u003ek\u003csub\u003ea\u003c/sub\u003e = 1.81 [22.8]\u003c/p\u003e\n \u003cp\u003eCL/F = 16.7 [1.18]\u003cbr\u003eV\u003csub\u003ec\u003c/sub\u003e/F = 18.5 [2.16]\u003cbr\u003e\u0026nbsp;add = 0.001\u003cbr\u003e\u0026nbsp;prop = 0.436\u003cbr\u003e\u0026nbsp;AIC = 1011\u003cbr\u003e\u0026nbsp;Run_time \u0026nbsp;= 0.54 mins\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 16px;\"\u003e\n \u003cp\u003ek\u003csub\u003ea\u003c/sub\u003e = 1.45 [55.1]\u003c/p\u003e\n \u003cp\u003eCL/F = 15.7 [1.54]\u003cbr\u003eV\u003csub\u003ec\u003c/sub\u003e/F = 14.8 [7.09]\u003cbr\u003eV\u003csub\u003ep\u003c/sub\u003e/F = 25.7 [18.9]\u003cbr\u003e\u0026nbsp;Q/F = 2.4 [35.6]\u003cbr\u003e\u0026nbsp;add = 0.001\u003cbr\u003e\u0026nbsp;prop = 0.424\u003cbr\u003e\u0026nbsp;AIC = 1008\u003cbr\u003e\u0026nbsp;Run_time \u0026nbsp;= 2.63 mins\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 19px;\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 1px;\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 14px;\"\u003e\n \u003cp\u003e\u003cstrong\u003ediazepam\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 16px;\"\u003e\n \u003cp\u003eCL = 5.09 [10.4]\u003cbr\u003eV\u003csub\u003ec\u003c/sub\u003e = 23.6 [3.11]\u003cbr\u003e\u0026nbsp;add = 0.0517\u003cbr\u003e\u0026nbsp;prop = 0.21\u003cbr\u003e\u0026nbsp;AIC = -272\u003cbr\u003e\u0026nbsp;Run_time \u0026nbsp;= 0.0159 mins\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 15px;\"\u003e\n \u003cp\u003eCL = 2.74 [15.2]\u003cbr\u003eV\u003csub\u003ec\u003c/sub\u003e = 15.4 [5.42]\u003cbr\u003eV\u003csub\u003ep\u003c/sub\u003e = 24.9 [6.88]\u003cbr\u003e\u0026nbsp;Q = 14.4 [8.86]\u003cbr\u003e\u0026nbsp;add = 0.00589\u003cbr\u003e\u0026nbsp;prop = 0.185\u003cbr\u003e\u0026nbsp;AIC = -426\u003cbr\u003e\u0026nbsp;Run_time \u0026nbsp;= 0.195 mins\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 16px;\"\u003e\n \u003cp\u003eCL = 5.08 [10.5]\u003cbr\u003eV\u003csub\u003ec\u003c/sub\u003e = 23.8 [3.1]\u003cbr\u003e\u0026nbsp;add = 0.052\u003cbr\u003e\u0026nbsp;prop = 0.21\u003cbr\u003e\u0026nbsp;AIC = -272\u003cbr\u003e\u0026nbsp;Run_time \u0026nbsp;= 0.0127 mins\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 16px;\"\u003e\n \u003cp\u003eCL = 2.61 [16.2]\u003cbr\u003eV\u003csub\u003ec\u003c/sub\u003e = 16.6 [4.89]\u003cbr\u003eV\u003csub\u003ep\u003c/sub\u003e = 25.8 [7.29]\u003cbr\u003e\u0026nbsp;Q = 10.3 [8.01]\u003cbr\u003e\u0026nbsp;add = 0.00583\u003cbr\u003e\u0026nbsp;prop = 0.174\u003cbr\u003e\u0026nbsp;AIC = -429\u003cbr\u003e\u0026nbsp;Run_time \u0026nbsp;= 0.36 mins\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 19px;\"\u003e\n \u003cp\u003eCL (derived) \u003csup\u003eb\u003c/sup\u003e = \u003cstrong\u003e3.09\u003c/strong\u003e L/h\u0026nbsp;\u003c/p\u003e\n \u003cp\u003eV\u003csub\u003ec\u003c/sub\u003e (derived)\u0026nbsp;= \u003cstrong\u003e24.11\u003c/strong\u003e L\u0026nbsp;\u003c/p\u003e\n \u003cp\u003eV\u003csub\u003ep\u003c/sub\u003e (derived) \u0026nbsp;= \u003cstrong\u003e18.71\u003c/strong\u003e L\u0026nbsp;\u003c/p\u003e\n \u003cp\u003eV\u003csub\u003ep2\u003c/sub\u003e (derived) \u0026nbsp;= \u003cstrong\u003e73.83\u003c/strong\u003e L\u0026nbsp;\u003c/p\u003e\n \u003cp\u003eQ (derived) \u0026nbsp;= \u0026nbsp;\u003cstrong\u003e56.23\u003c/strong\u003e L/h\u0026nbsp;\u003c/p\u003e\n \u003cp\u003eQ\u003csub\u003e2\u003c/sub\u003e (derived)\u0026nbsp; = \u003cstrong\u003e8.84\u003c/strong\u003e L/h\u0026nbsp;[27]\u003c/p\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 1px;\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 14px;\"\u003e\n \u003cp\u003e\u003cstrong\u003efluorouracil\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 16px;\"\u003e\n \u003cp\u003eCL = 66.5 [3.51]\u003cbr\u003eV\u003csub\u003ec\u003c/sub\u003e = 12.7 [7.25]\u003cbr\u003e\u0026nbsp;add = 0.101\u003cbr\u003e\u0026nbsp;prop = 0.318\u003cbr\u003e\u0026nbsp;AIC = 349\u003cbr\u003e\u0026nbsp;Run_time \u0026nbsp;= 0.0117 mins\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 15px;\"\u003e\n \u003cp\u003eCL = 61.8 [3.62]\u003cbr\u003eV\u003csub\u003ec\u003c/sub\u003e = 8.97 [12.5]\u003cbr\u003eV\u003csub\u003ep\u003c/sub\u003e = 2.08 [42.4]\u003cbr\u003e\u0026nbsp;Q = 13.9 [14.5]\u003cbr\u003e\u0026nbsp;add = 0.0903\u003cbr\u003e\u0026nbsp;prop = 0.278\u003cbr\u003e\u0026nbsp;AIC = 349\u003cbr\u003e\u0026nbsp;Run_time \u0026nbsp;= 0.071 mins\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 16px;\"\u003e\n \u003cp\u003eCL = 67 [3.51]\u003cbr\u003eV\u003csub\u003ec\u003c/sub\u003e = 12.8 [7.27]\u003cbr\u003e\u0026nbsp;add = 0.0971\u003cbr\u003e\u0026nbsp;prop = 0.32\u003cbr\u003e\u0026nbsp;AIC = 349\u003cbr\u003e\u0026nbsp;Run_time \u0026nbsp;= 0.0147 mins\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 16px;\"\u003e\n \u003cp\u003eCL = 25.5 [4.65]\u003cbr\u003eV\u003csub\u003ec\u003c/sub\u003e = 11.3 [7.85]\u003cbr\u003eV\u003csub\u003ep\u003c/sub\u003e = 1.3e+03 [4.08]\u003cbr\u003e\u0026nbsp;Q = 36.9 [9.83]\u003cbr\u003e\u0026nbsp;add = 0.0169\u003cbr\u003e\u0026nbsp;prop = 0.325\u003cbr\u003e\u0026nbsp;AIC = 342\u003cbr\u003e\u0026nbsp;Run_time \u0026nbsp;= 0.0662 mins\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 19px;\"\u003e\n \u003cp\u003eCL (derived) = \u003cstrong\u003e86.5 L/h\u003c/strong\u003e\u0026nbsp;\u003c/p\u003e\n \u003cp\u003eV\u003csub\u003ec\u003c/sub\u003e = \u0026nbsp;\u003cstrong\u003e13.1\u003c/strong\u003e L [28]\u003c/p\u003e\n \u003cp\u003eCL = \u003cstrong\u003e75.9\u003c/strong\u003e L/h\u003c/p\u003e\n \u003cp\u003eV\u003csub\u003ec\u003c/sub\u003e = \u003cstrong\u003e20.3\u003c/strong\u003e L [29]\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 1px;\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 14px;\"\u003e\n \u003cp\u003e\u003cstrong\u003eoxprenolol (iv)\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 16px;\"\u003e\n \u003cp\u003eCL = 24 [1.68]\u003cbr\u003eV\u003csub\u003ec\u003c/sub\u003e = 43.4 [0.757]\u003cbr\u003e\u0026nbsp;add = 7.07\u003cbr\u003e\u0026nbsp;prop = 0.164\u003cbr\u003e\u0026nbsp;AIC = 948\u003cbr\u003e\u0026nbsp;Run_time \u0026nbsp;= 0.0134 mins\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 15px;\"\u003e\n \u003cp\u003eCL = 24.1 [1.63]\u003cbr\u003eV\u003csub\u003ec\u003c/sub\u003e = 3.17 [54.1]\u003cbr\u003eV\u003csub\u003ep\u003c/sub\u003e = 42.8 [1.39]\u003cbr\u003e\u0026nbsp;Q = 813 [5.71]\u003cbr\u003e\u0026nbsp;add = 5.26\u003cbr\u003e\u0026nbsp;prop = 0.128\u003cbr\u003e\u0026nbsp;AIC = 924\u003cbr\u003e\u0026nbsp;Run_time \u0026nbsp;= 0.438 mins\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 16px;\"\u003e\n \u003cp\u003eCL = 24 [1.68]\u003cbr\u003eV\u003csub\u003ec\u003c/sub\u003e = 43.5 [0.757]\u003cbr\u003e\u0026nbsp;add = 7.08\u003cbr\u003e\u0026nbsp;prop = 0.166\u003cbr\u003e\u0026nbsp;AIC = 948\u003cbr\u003e\u0026nbsp;Run_time \u0026nbsp;= 0.0142 mins\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 16px;\"\u003e\n \u003cp\u003eCL = 23 [1.47]\u003cbr\u003eV\u003csub\u003ec\u003c/sub\u003e = 33.6 [0.848]\u003cbr\u003eV\u003csub\u003ep\u003c/sub\u003e = 19.1 [5.59]\u003cbr\u003e\u0026nbsp;Q = 20.3 [5.61]\u003cbr\u003e\u0026nbsp;add = 2.35\u003cbr\u003e\u0026nbsp;prop = 0.0587\u003cbr\u003e\u0026nbsp;AIC = 819\u003cbr\u003e\u0026nbsp;Run_time \u0026nbsp;= 0.1 mins\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 19px;\"\u003e\n \u003cp\u003eCL (derived) \u0026nbsp;= \u003cstrong\u003e23.56\u003c/strong\u003e L/h\u003c/p\u003e\n \u003cp\u003eV\u003csub\u003ec\u003c/sub\u003e = \u003cstrong\u003e34.4\u003c/strong\u003e L\u003c/p\u003e\n \u003cp\u003eV\u003csub\u003ep\u003c/sub\u003e (derived) \u0026nbsp;= \u003cstrong\u003e16.39\u003c/strong\u003e L\u003c/p\u003e\n \u003cp\u003eQ (derived) \u0026nbsp;= \u003cstrong\u003e23.6\u0026nbsp;\u003c/strong\u003eL/h\u0026nbsp;[30]\u003c/p\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 1px;\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 14px;\"\u003e\n \u003cp\u003e\u003cstrong\u003eoxprenolol (oral)\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 16px;\"\u003e\n \u003cp\u003ek\u003csub\u003ea\u003c/sub\u003e = 2.23 [16.5]\u003c/p\u003e\n \u003cp\u003eCL/F = 60.3 [1.53]\u003cbr\u003eV\u003csub\u003ec\u003c/sub\u003e/F = 139 [1.26]\u003cbr\u003e\u0026nbsp;add = 1.03\u003cbr\u003e\u0026nbsp;prop = 0.342\u003cbr\u003e\u0026nbsp;AIC = 2243\u003cbr\u003e\u0026nbsp;Run_time \u0026nbsp;= 0.0721 mins\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 15px;\"\u003e\n \u003cp\u003ek\u003csub\u003ea\u003c/sub\u003e = 62.9 [1.37]\u003c/p\u003e\n \u003cp\u003eCL/F = 14.5 [2.11]\u003cbr\u003eV\u003csub\u003ec\u003c/sub\u003e/F = 0.257 [9.27]\u003cbr\u003eV\u003csub\u003ep\u003c/sub\u003e/F = 9.36 [4.65]\u003cbr\u003e\u0026nbsp;Q/F = 4.88 [7.34]\u003cbr\u003e\u0026nbsp;add = 0.836\u003cbr\u003e\u0026nbsp;prop = 0.392\u003cbr\u003e\u0026nbsp;AIC = 2294\u003cbr\u003e\u0026nbsp;Run_time \u0026nbsp;= 0.671 mins\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 16px;\"\u003e\n \u003cp\u003ek\u003csub\u003ea\u003c/sub\u003e = 2.22 [16.5]\u003c/p\u003e\n \u003cp\u003eCL/F = 60.7 [1.53]\u003cbr\u003eV\u003csub\u003ec\u003c/sub\u003e/F = 140 [1.26]\u003cbr\u003e\u0026nbsp;add = 1.01\u003cbr\u003e\u0026nbsp;prop = 0.339\u003cbr\u003e\u0026nbsp;AIC = 2243\u003cbr\u003e\u0026nbsp;Run_time \u0026nbsp;= 0.0719 mins\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 16px;\"\u003e\n \u003cp\u003ek\u003csub\u003ea\u003c/sub\u003e = 2.19 [16.8]\u003c/p\u003e\n \u003cp\u003eCL/F = 59.5 [1.65]\u003cbr\u003eV\u003csub\u003ec\u003c/sub\u003e/F = 139 [1.26]\u003cbr\u003eV\u003csub\u003ep\u003c/sub\u003e/F = 319 [18.3]\u003cbr\u003e\u0026nbsp;Q/F = 1.29 [311]\u003cbr\u003e\u0026nbsp;add = 1.01\u003cbr\u003e\u0026nbsp;prop = 0.342\u003cbr\u003e\u0026nbsp;AIC = 2251\u003cbr\u003e\u0026nbsp;Run_time \u0026nbsp;= 0.191 mins\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 19px;\"\u003e\n \u003cp\u003eF\u003csub\u003ebio\u0026nbsp;\u003c/sub\u003e(mean)\u003csub\u003e\u0026nbsp;\u003c/sub\u003e= 0.43\u003c/p\u003e\n \u003cp\u003eCL (derived) \u0026nbsp;= \u003cstrong\u003e54.8\u003c/strong\u003e L/h\u003c/p\u003e\n \u003cp\u003eV\u003csub\u003ec\u003c/sub\u003e (derived) = \u003cstrong\u003e80\u003c/strong\u003e L\u003c/p\u003e\n \u003cp\u003eV\u003csub\u003ep\u003c/sub\u003e (derived) \u0026nbsp;= \u003cstrong\u003e38.1\u003c/strong\u003e L\u003c/p\u003e\n \u003cp\u003eQ (derived) \u0026nbsp;= \u003cstrong\u003e54.9\u0026nbsp;\u003c/strong\u003eL/h\u0026nbsp;[30]\u003c/p\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 1px;\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 14px;\"\u003e\n \u003cp\u003e\u003cstrong\u003epindolol\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 16px;\"\u003e\n \u003cp\u003ek\u003csub\u003ea\u003c/sub\u003e = 1.28 [97.5]\u003c/p\u003e\n \u003cp\u003eCL/F = 24.8 [4.44]\u003cbr\u003eV\u003csub\u003ec\u003c/sub\u003e/F = 110 [2.2]\u003cbr\u003e\u0026nbsp;add = 1.33\u003cbr\u003e\u0026nbsp;prop = 0.187\u003cbr\u003e\u0026nbsp;AIC = 649\u003cbr\u003e\u0026nbsp;Run_time \u0026nbsp;= 0.0396 mins\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 15px;\"\u003e\n \u003cp\u003ek\u003csub\u003ea\u003c/sub\u003e = 22.7 [4.46]\u003c/p\u003e\n \u003cp\u003eCL/F = 7.32 [4.04]\u003cbr\u003eV\u003csub\u003ec\u003c/sub\u003e/F = 0.127 [76.9]\u003cbr\u003eV\u003csub\u003ep\u003c/sub\u003e/F = 13.8 [1.76]\u003cbr\u003e\u0026nbsp;Q/F = 3.36 [2.32]\u003cbr\u003e\u0026nbsp;add = 0.779\u003cbr\u003e\u0026nbsp;prop = 0.322\u003cbr\u003e\u0026nbsp;AIC = 683\u003cbr\u003e\u0026nbsp;Run_time \u0026nbsp;= 0.639 mins\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 16px;\"\u003e\n \u003cp\u003ek\u003csub\u003ea\u003c/sub\u003e = 1.29 [102]\u003c/p\u003e\n \u003cp\u003eCL/F = 24.8 [4.52]\u003cbr\u003eV\u003csub\u003ec\u003c/sub\u003e/F = 110 [2.17]\u003cbr\u003e\u0026nbsp;add = 1.31\u003cbr\u003e\u0026nbsp;prop = 0.185\u003cbr\u003e\u0026nbsp;AIC = 649\u003cbr\u003e\u0026nbsp;Run_time \u0026nbsp;= 0.0322 mins\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 16px;\"\u003e\n \u003cp\u003ek\u003csub\u003ea\u003c/sub\u003e = 1.29 [131]\u003c/p\u003e\n \u003cp\u003eCL/F = 24.5 [9.76]\u003cbr\u003eV\u003csub\u003ec\u003c/sub\u003e/F = 111 [3.15]\u003cbr\u003eV\u003csub\u003ep\u003c/sub\u003e/F = 107 [996]\u003cbr\u003e\u0026nbsp;Q/F = 0.254 [1.43e+03]\u003cbr\u003e\u0026nbsp;add = 1.31\u003cbr\u003e\u0026nbsp;prop = 0.188\u003cbr\u003e\u0026nbsp;AIC = 657\u003cbr\u003e\u0026nbsp;Run_time \u0026nbsp;= 0.18 mins\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 19px;\"\u003e\n \u003cp\u003eCL \u0026nbsp;= \u003cstrong\u003e25.5\u0026nbsp;\u003c/strong\u003eL/h\u003c/p\u003e\n \u003cp\u003eV\u003csub\u003ec\u003c/sub\u003e =\u003cstrong\u003e142\u003c/strong\u003e L\u0026nbsp;[31]\u003c/p\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 1px;\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 14px;\"\u003e\n \u003cp\u003e\u003cstrong\u003etobramycin\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 16px;\"\u003e\n \u003cp\u003eCL = 4.03 [4.33]\u003cbr\u003eV\u003csub\u003ec\u003c/sub\u003e = 24.8 [1.51]\u003cbr\u003e\u0026nbsp;add = 0.001\u003cbr\u003e\u0026nbsp;prop = 0.261\u003cbr\u003e\u0026nbsp;AIC = 788\u003cbr\u003e\u0026nbsp;Run_time \u0026nbsp;= 0.786 mins\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 15px;\"\u003e\n \u003cp\u003eCL = 3.57 [4.41]\u003cbr\u003eV\u003csub\u003ec\u003c/sub\u003e = 12.4 [10.7]\u003cbr\u003eV\u003csub\u003ep\u003c/sub\u003e = 8.06 [12.9]\u003cbr\u003e\u0026nbsp;Q = 3.37 [31.7]\u003cbr\u003e\u0026nbsp;add = 0.001\u003cbr\u003e\u0026nbsp;prop = 0.255\u003cbr\u003e\u0026nbsp;AIC = 848\u003cbr\u003e\u0026nbsp;Run_time \u0026nbsp;= 6.5 mins\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 16px;\"\u003e\n \u003cp\u003eCL = 4.03 [4.53]\u003cbr\u003eV\u003csub\u003ec\u003c/sub\u003e = 24.9 [1.58]\u003cbr\u003e\u0026nbsp;add = 0.001\u003cbr\u003e\u0026nbsp;prop = 0.26\u003cbr\u003e\u0026nbsp;AIC = 790\u003cbr\u003e\u0026nbsp;Run_time \u0026nbsp;= 0.65 mins\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 16px;\"\u003e\n \u003cp\u003eCL = 3.84 [11.2]\u003cbr\u003eV\u003csub\u003ec\u003c/sub\u003e = 21.7 [3.06]\u003cbr\u003eV\u003csub\u003ep\u003c/sub\u003e = 6.56 [87.8]\u003cbr\u003e\u0026nbsp;Q = 0.264 [81.4]\u003cbr\u003e\u0026nbsp;add = 0.001\u003cbr\u003e\u0026nbsp;prop = 0.24\u003cbr\u003e\u0026nbsp;AIC = 758\u003cbr\u003e\u0026nbsp;Run_time \u0026nbsp;= 3.97 mins\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 19px;\"\u003e\n \u003cp\u003eCL (derived) = \u003cstrong\u003e3.8\u003c/strong\u003e L/h\u003c/p\u003e\n \u003cp\u003eV\u003csub\u003ec\u003c/sub\u003e (derived) = \u003cstrong\u003e21.8\u003c/strong\u003e L\u0026nbsp;\u003c/p\u003e\n \u003cp\u003eQ (derived) =\u0026nbsp;\u003cstrong\u003e0.26\u003c/strong\u003e L/h\u003c/p\u003e\n \u003cp\u003eV\u003csub\u003ep \u0026nbsp;\u003c/sub\u003e(derived) = \u003cstrong\u003e9.6\u003c/strong\u003e L [32]\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 1px;\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n\u003c/table\u003e\n\u003cp\u003eAbbreviations\u003csup\u003e:\u0026nbsp;\u003c/sup\u003e1cmpt_fo, a one-compartment model with first-order elimination (or first-order absorption and elimination in oral cases); 2cmpt_fo, \u0026nbsp;a two-compartment model with first-order elimination (or first-order absorption and elimination in oral cases); Run_time: computational running time; add, additive residual error; prop, proportional residual error\u003c/p\u003e\n\u003cp\u003e\u003csup\u003ea\u003c/sup\u003e Parameter estimates are presented as typical population estimates with their corresponding relative standard errors (RSE%) indicated in brackets. Except for the pheno_sd case, where the unit of CL is L/h/kg and the unit of V is L/kg, the units of CL and V in all other cases are L/h and L, respectively.\u003c/p\u003e\n\u003cp\u003e\u003csup\u003eb\u0026nbsp;\u003c/sup\u003eParameter (derived) refers to the value that was not explicitly reported in the original reference but was calculated based on other reported parameters. The following formulas were applied when calculating parameters: k\u003csub\u003e12\u0026nbsp;\u003c/sub\u003e= Q/V\u003csub\u003ec\u003c/sub\u003e, k\u003csub\u003e21\u003c/sub\u003e = Q/V\u003csub\u003ep\u003c/sub\u003e, and k\u003csub\u003eel\u003c/sub\u003e = CL/V\u003csub\u003ec\u003c/sub\u003e, k\u003csub\u003e13\u003c/sub\u003e=Q\u003csub\u003e2\u003c/sub\u003e/V\u003csub\u003ec\u003c/sub\u003e, k\u003csub\u003e31\u003c/sub\u003e=Q\u003csub\u003e2\u003c/sub\u003e/Vp\u003csub\u003e2\u003c/sub\u003e, Here, k\u003csub\u003e12\u003c/sub\u003e and k\u003csub\u003e13\u003c/sub\u003e represent the rate constant describing the transfer of the drug from the central compartment to the peripheral compartment and second peripheral compartment, k\u003csub\u003e21\u003c/sub\u003e and k\u003csub\u003e31\u0026nbsp;\u003c/sub\u003eis the rate constant for the transfer of the drug from the peripheral compartment and second peripheral compartment to the central compartment, and k\u003csub\u003eel\u003c/sub\u003e is the elimination rate constant. For parameters with covariate models, calculation was based on median covariate values. In the case of diazepam which reported parameters of four individuals, parameter values were summarized using the geometric mean.\u003c/p\u003e"},{"header":"Discussion","content":"\u003cp\u003eIn this study, an automated pipeline was developed to generate initial estimates for PopPK modeling. This pipeline can recommend initial estimates for structural model parameters, especially in the absence of \u003cem\u003ea priori\u003c/em\u003e information or when no iterative optimization has yet been performed to provide a reasonable starting point for the first round of modeling. Assessment results showed that the pipeline performs well both based on simulated and real-life clinical datasets, and that the initial estimates it generate enable reliable and accurate fitting in subsequent re-estimation or model development.\u003c/p\u003e\n\u003cp\u003eThe pipeline provides three approaches for calculating one-compartment parameters. Results from \u003cstrong\u003eFig. 3\u003c/strong\u003e indicate that the designed adaptive single-point method works in most cases, NCA handles rich data effectively, and graphic methods can address sparse data after a single oral dose, a scenario where the other two might encounter limitations. This aligns with the original design goal of developing a pipeline capable of adapting to a wide range of PK scenarios by using different methods that complement each other. For model-specific parameters, recommended initial estimates illustrated reliability across all twelve nonlinear and multi-compartmental models tested. Despite observing a deviation of 22\u0026ndash;29% between the final estimates of V\u003csub\u003ep\u003c/sub\u003e and the initially set values, this discrepancy can likely be attributed to the sampling design.\u003c/p\u003e\n\u003cp\u003eThe results from the simulated datasets illustrate that the pipeline outperformed other strategies. The pipeline\u0026rsquo;s final FOCEI and SAEM estimates performed similarly under the 30% threshold criterion, with a 95.2% vs. 100% (\u003cstrong\u003eSupplementary Table 4 and 5\u003c/strong\u003e) success rate in converging all structural parameters. However, \u003cem\u003einits=1\u003c/em\u003e successfully converged for 47.6% of cases, and this number dropped to 0 when using FOCEI, with most estimates failing to move from the initial setting during estimation. This finding aligns with previous literature suggesting that SAEM generally provides better estimates than FOCEI [33, 34]. More significantly, this study additionally found that this could be particularly true when initial estimates are poor. Another observation from this study was that using optimization methods (nls, nlm, and nlminb) to optimize initial estimates was far less effective than directly following pipeline recommendations.\u0026nbsp;One possible reason is nonlinear parameter estimation is also highly sensitive to initial estimates\u0026nbsp;[35]. Therefore, it may be necessary to provide initial guesses for the estimates or introduce boundary setting.\u003c/p\u003e\n\u003cp\u003eThe pipeline consistently demonstrates superior performance compared to the \u003cem\u003einits=1\u003c/em\u003e strategy when applied to real-life data. The \u003cem\u003einits=\u003c/em\u003e1 strategy shows the potential to cause severe parameter estimation bias.\u003cstrong\u003e\u0026nbsp;\u003c/strong\u003eIn the aprindine case, the \u003cem\u003einits=1\u003c/em\u003e strategy led to a final FOCEI V\u003csub\u003ec\u003c/sub\u003e estimate of 4.95 L (\u003cstrong\u003eTable 2\u003c/strong\u003e), which deviated significantly from a previously reported range of 164\u0026ndash;351 L [36]. In contrast, the pipeline had a more accurate final value of 272 L. Similarly, the \u003cem\u003einits=1\u003c/em\u003e strategy and the pipeline yielded CL estimates of 0.00806 and 1.29 L/h at multiple doses (200 to 100 mg). Reported values were 50.6 and 13.4 L/h at doses of 50 and 100 mg [36]. Value from the pipeline is more acceptable given the nonlinear kinetics and CL decrease ratio. Furthermore, the pipeline may play a more effective role in facilitating appropriate model selection. For tobramycin, the AIC generated by the pipeline for the two-compartment model (758) was lower than the AIC for the one-compartment model (790), leading the pipeline to select the better-performing two-compartment model, as also suggested in the source reference\u0026nbsp;[32]. In contrast, using the \u003cem\u003einits=1\u003c/em\u003e strategy resulted in an AIC of 848 for the two-compartment model and 788 for the one-compartment model, leading to the opposite selection.\u003c/p\u003e\n\u003cp\u003eRegarding time efficiency, it was clear that the use of pipeline-recommended initial estimates significantly reduced computational time, particularly when employing the FOCEI algorithm, compared to using \u003cem\u003einits=1\u003c/em\u003e. The time savings can reach to five-fold when using SAEM or FOCEI when using a two-compartment model. In the practice of automated modeling, where thousands of models may be tested [37], excessive runtime on poorly fitted or incorrect models can lead to a substantial waste of both resources and time. Therefore, utilizing the pipeline\u0026rsquo;s adaptive approach to provide more accurate initial estimates enhances model accuracy and optimizes computational efficiency, making it a valuable tool for large-scale pharmacokinetic modeling.\u003c/p\u003e\n\u003cp\u003eThere are several implicit limitations in this study. A one-compartment model with linear kinetics was assumed when designing the adaptive-single-point method and the graphic methods, and their outputs were also tested within the same model. Parameter scanning for V\u003csub\u003emax\u003c/sub\u003e and K\u003csub\u003em\u003c/sub\u003e was based on the one-compartment model, while multi-compartment parameter scanning was carried out under the assumption of first-order kinetics. These assumptions may introduce bias when applied to drugs that follow a two-compartment model or exhibit nonlinear absorption or metabolism. Although results from these studies have shown good performance for two-compartment and nonlinear models, further testing is needed to evaluate how these assumptions may impact real-life applications. Moreover, additional validation may be necessary for extreme data points, such as drugs with very long half-lives (e.g., several months) or very short half-lives (e.g., less than 1 hour), to ensure the robustness of the pipeline under such conditions.\u003c/p\u003e\n\u003cp\u003eCurrently, the pipeline can generate initial estimates of one-compartment model parameters (K\u003csub\u003ea\u003c/sub\u003e, V\u003csub\u003ed\u003c/sub\u003e, and CL) as well as model-specific parameters (including V\u003csub\u003emax\u003c/sub\u003e, K\u003csub\u003em\u003c/sub\u003e, V\u003csub\u003ec\u003c/sub\u003e, V\u003csub\u003ep\u003c/sub\u003e, and Q). Three-compartment parameters are also available in the pipeline. The current test datasets are based on the nlmixr2 standard, but the pipeline is expected to support the development of PopPK models in other software programs and to be particularly helpful for beginners who struggle with defining initial estimates.\u0026nbsp;While the pipeline does not yet directly link to PopPK software such as NONMEM or Monolix, it has the potential to build an initial estimates bridge in the future through R packages, such as babelmixr2, which can run NONMEM and Monolix in R environment.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; In conclusion, the automated pipeline developed in this study was able to not only provide reliable initial estimates for population pharmacokinetic modeling, but also proved particularly suitable for scenarios with sparse sampling or lack of a priori information scenarios. By integrating multiple computational methods, it is a great and promising tool for the provision of initial estimates for both manual and automated modeling applications.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e\u003cstrong\u003eCompeting Interests\u003c/strong\u003e\u003cp\u003eMatthew Fidler is an employee of Novartis. All other authors declared no competing interests for this work.\u003c/p\u003e\u003c/p\u003e\u003ch2\u003eAuthor Contribution\u003c/h2\u003e\u003cp\u003eZHH, FK and JS: design and conceptualization; ZHH and MSL: algorithm programming; ZHH, MSL and IC: data analysis; ZHH and MF: data interpretation and methodological best practices; ZHH: first draft of manuscript; All authors contributed to writing, editing and reviewing the manuscript.\u003c/p\u003e\u003ch2\u003eAcknowledgement\u003c/h2\u003e\u003cp\u003eThe authors wish to thank William S. Denney for his contributions to this manuscript. F.K. is recipient of a Sir Henry Dale Fellowship jointly funded by the Wellcome Trust and the Royal Society (Grant Number 220587/Z/20/Z).\u003c/p\u003e\u003ch2\u003eData Availability\u003c/h2\u003e\u003cp\u003eSimulated datasets are provided within the supplementary material. Real-life datasets are obtained from open sources.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n\u003cli\u003eHan S, Jeon S, Yim D-S (2016) Tips for the choice of initial estimates in NONMEM. Transl Clin Pharmacol 24:119\u0026ndash;123. https://doi.org/10.12793/tcp.2016.24.3.119\u003c/li\u003e\n\u003cli\u003eTraynard P, Ayral G, Twarogowska M, Chauvin J (2020) Efficient Pharmacokinetic Modeling Workflow With the MonolixSuite: A Case Study of Remifentanil. 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Eur J Clin Pharmacol 26:129\u0026ndash;131. https://doi.org/10.1007/BF00546721\u003c/li\u003e\n\u003cli\u003eIsmail M, Sale M, Yu Y, et al (2022) Development of a genetic algorithm and NONMEM workbench for automating and improving population pharmacokinetic/pharmacodynamic model selection. J Pharmacokinet Pharmacodyn 49:243\u0026ndash;256. https://doi.org/10.1007/s10928-021-09782-9\u003c/li\u003e\n\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"journal-of-pharmacokinetics-and-pharmacodynamics","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"jopa","sideBox":"Learn more about [Journal of Pharmacokinetics and Pharmacodynamics](http://link.springer.com/journal/10928)","snPcode":"10928","submissionUrl":"https://submission.nature.com/new-submission/10928/3","title":"Journal of Pharmacokinetics and Pharmacodynamics","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"initial estimates, population pharmacokinetics, automated modeling, sparse data","lastPublishedDoi":"10.21203/rs.3.rs-5806446/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-5806446/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eNonlinear mixed-effects models rely on adequate initial parameter estimates for efficient parameter optimization. Poor initial estimates can result in failed model convergence or termination with incorrect parameter estimates. Non-compartmental analysis (NCA) and other manual methods have typically been used to derive initial estimates for pharmacokinetic (PK) parameters. However, NCA struggles with sparse data and recent advances in automated modeling increasingly emphasize the need for initial estimates that require no user input. This study aimed to develop an integrated pipeline for the computation of initial estimates applicable to various data types and model structures. Multiple methods were involved in this pipeline: the adaptive single-point method using individual-level data, graphic methods, and NCA performed after na\u0026iuml;ve pooling, as well as parameter sweeping on model-specific parameters. The relative root mean square error (rRMSE) was used as a metric to select the most appropriate initial estimates from candidates generated by the pipeline. The pipeline\u0026rsquo;s performance was evaluated across twenty-one simulated datasets and thirteen real-life datasets. The results suggested that this pipeline performed well in all test cases. Initial estimates recommended by the pipeline resulted in final parameter estimates closely aligned with pre-set original values in simulated datasets or aligned with literature references in the case of real-life data. This study provides an efficient and reliable tool for delivering PK initial estimates for population pharmacokinetic modeling in both rich and sparse data scenarios, and an open-source R package has been created.\u003c/p\u003e","manuscriptTitle":"An automated pipeline to generate initial estimates for population pharmacokinetic models","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-01-22 09:22:17","doi":"10.21203/rs.3.rs-5806446/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Revision requested","date":"2025-04-28T06:29:15+00:00","index":"","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-04-23T15:52:42+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-03-09T21:47:06+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"54656471130301267376036415696643137022","date":"2025-02-16T08:21:49+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"25403749562154770620390116949229206391","date":"2025-02-13T12:27:51+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2025-02-03T10:25:31+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2025-01-11T04:10:20+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2025-01-11T04:08:56+00:00","index":"","fulltext":""},{"type":"submitted","content":"Journal of Pharmacokinetics and Pharmacodynamics","date":"2025-01-10T22:07:24+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"journal-of-pharmacokinetics-and-pharmacodynamics","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"jopa","sideBox":"Learn more about [Journal of Pharmacokinetics and Pharmacodynamics](http://link.springer.com/journal/10928)","snPcode":"10928","submissionUrl":"https://submission.nature.com/new-submission/10928/3","title":"Journal of Pharmacokinetics and Pharmacodynamics","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false}}],"origin":"","ownerIdentity":"2e2a4e93-2e62-4660-ab23-22798ff844a4","owner":[],"postedDate":"January 22nd, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"published-in-journal","subjectAreas":[],"tags":[],"updatedAt":"2025-11-10T16:07:19+00:00","versionOfRecord":{"articleIdentity":"rs-5806446","link":"https://doi.org/10.1007/s10928-025-10000-z","journal":{"identity":"journal-of-pharmacokinetics-and-pharmacodynamics","isVorOnly":false,"title":"Journal of Pharmacokinetics and Pharmacodynamics"},"publishedOn":"2025-11-06 15:57:48","publishedOnDateReadable":"November 6th, 2025"},"versionCreatedAt":"2025-01-22 09:22:17","video":"","vorDoi":"10.1007/s10928-025-10000-z","vorDoiUrl":"https://doi.org/10.1007/s10928-025-10000-z","workflowStages":[]},"version":"v1","identity":"rs-5806446","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-5806446","identity":"rs-5806446","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}