Broadening the candidate set of parametric models when extrapolating survival: the case for models with U-shaped hazards.

Broadening the candidate set of parametric models when extrapolating survival: the case for models with U-shaped hazards. | 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 Broadening the candidate set of parametric models when extrapolating survival: the case for models with U-shaped hazards. Daniel Gallacher, Martin Connock This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-5303870/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 4 You are reading this latest preprint version Abstract In health technology assessment (HTA), extrapolation of time-to-event data is common to estimate the benefit of a new health technology beyond the observed period of data. The regular set of parametric models commonly used for extrapolation does not include models which assume a U-shaped hazard rate, that is initially decreasing and then increasing hazard rate. We compared the visual and statistical fit and prediction of models which assume a U-shaped hazard rate (Chen, bathtub and Rayleigh) to the regular set of parametric models (exponential, log-normal, log-logistic, Weibull, generalised gamma, Gompertz) across a range of settings and data types, including hip arthroplasty, functional tricuspid regurgitation and knee osteoarthritis. U-shaped hazard models outperformed or matched standard parametric models in visual fit, goodness of fit statistics and long-term predictions when compared to extended follow-up. Bathtub models should feature routinely in HTA submissions involving extrapolation of survival data, allowing for exploration of a wider range of scenarios and potentially more accurate predictions, resulting in better informed valuation and decision making for emerging health technologies. Survival Analysis Extrapolation Health Technology Assessment Parametric models Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 BACKGROUND In health technology assessment (HTA) it is often necessary to model the observed data and or to extend analysis beyond maximum follow up to estimate outcomes in the longer term and satisfy the time horizon favoured by decision making authorities; frequently a life-time horizon is required. For time-to-event outcomes, such as overall survival, various parametric models are fitted to data using widely available in software programmes such as Stata and R. Commonly six “standard” distributions are explored (Weibull, Gompertz, loglogistic, lognormal, exponential, generalised gamma) 1 . These models can represent a wide range of hazard behaviours (Fig. 1 ). The exponential is the least flexible, modelling a constant hazard rate. The Weibull or Gompertz can model a monotonic hazard rate, either always increasing or always decreasing. Finally, the lognormal and loglogistic models tend to provide a decreasing hazard over time, sometimes after an initial period of an increasing hazard rate. There are no models in this standard set of models which allow for an initial decreasing hazard rate followed by increasing hazard rate over time. Such models do exist and may be referred to as “bathtub” models due to their “U” shaped hazard. A failure to include these models in candidate sets results in a failure to explore all potential future scenarios in areas of high uncertainty and may bias methods of model averaging. In this paper we explore the potential benefits of expanding the standard set of parametric models to include a 3-parameter bathtub 2 and a 2-parameter bathtub (Chen 2000 3 ) models that here we term “bathtub” and “Chen” respectively. The Chen model (Supplement: section 1) can generate non-linearly increasing hazard as well as “U shaped” bathtub hazard. We also briefly consider Rayleigh models (Peace and Tsai 2009 4 ; Supplement: section 2) that generate linearly increasing hazard. The “stgenreg” user written Stata package (Crowther and Lambert 2013 5 ) enables exploration of such models that are not pre-specified in software packages that sometimes may generate better fit to the observed data than obtained using standard models. A bathtub model with three parameters is described by Collet 2 , whilst Chen 3 describes a two parameter model that can generate a bathtub or non-linearly increasing hazard (Supplement: Section 1). Their survival and hazard functions are shown in equations 1–4. Bathtub 3 parameter hazard function $$\:h\left(t\right)=at+\frac{b}{(1+gt)}\:\:\:\:\:\:\left(1\right)$$ Bathtub 3 parameter survival function $$\:\text{S}\left(\text{t}\right)=\text{e}\text{x}\text{p}\left(-\frac{{\text{a}\text{t}}^{2}}{2}\text{}\right)\cdot\:{\left(1+\text{g}\text{t}\right)}^{-\:\frac{b}{g}}\text{}\:\:\:\:\:\:\left(2\right)$$ Chen hazard function $$\:h\left(t\right)=\lambda\:\beta\:{t}^{\beta\:-1}{e}^{{t}^{\beta\:}}\:\:\:\:\:\:\left(3\right)$$ Chen survival function $$\:\text{e}\text{x}\text{p}(\lambda\:-\lambda\:\text{exp}\left({t}^{\beta\:}\right)\:\:\:\:\:\:(4)$$ METHODS Data sources We fit a range of survival models to data from a wide range of populations and medical interventions with study designs including RCTs, cohort, and registry studies. We lead with a clear example using re-created data from Benfari et al. 6 where standard parametric models are outperformed by models with increasing hazard rates and we provide a wide range of cases where these increasing hazard models show good fit motivating their inclusion for regular consideration when extrapolating survival in a HTA setting. RCTs included the left atrial appendage study of Whitlock et al., 2021 7 and the tricuspid valve replacement study TRISCEND II 8 . Cohort studies included the Benfari et al., 2019 6 , Essayagh et al., 2021 9 , and Tribouilloy et al 2024 10 investigations of patients with isolated functional tricuspid regurgitation, and the Bae et al., 11 Korean study of microfracture treatment for osteoarthritic knees. Registry studies included: The National Joint Registry of England and Wales reports 9 12 and 20 13 and Swedish Hip Arthroplasty Register 2018 and 2023 14, 15 on failure after Primary Total Hip Replacement (THR) procedures (registry data sources include very substantial numbers of individuals followed for many years so that the trajectory of the time to event plots is internally consistent and less changeable compared to that in smaller studies). Relevant details from the included studies are briefly summarised in Table 1 . Analyses Published Kaplan-Meier (KM) plots were digitised using Digitzelt ( http://www.digitizelt.xyz ) and IPD reconstructed using the method of Guyot et al. 16 . In registry data where KM plots encompassed thousands of events that could not all be captured by digitisation; we proportionately reduced the patient numbers to handleable size, preserving the underlying survival distribution. All models were fitted using the streg or stgenreg command in Stata 18 (REF) or using stgenreg command of Crowther and Lambert 5 . The 2-parameter 3 and 3-parameter 2 bathtub models and Rayleigh models 4 were generated using following stgenreg commands: Rayleigh 1-parameter model: stgenreg, haz(2:*exp([ln_lambda2]):*#t)nodes(30) Rayleigh 2-parameter model: stgenreg, haz([lambda1] :+ 2:*[lambda2]:*#t)nodes(30) Collet bathtub model (3 parameters): stgenreg, haz(([alpha]:*#t:+ [beta]:/(1:+[gamma]:*#t)))nodes(30) Chen model (2 parameters): stgenreg, loghazard( [ln_lambda] :+ [ln_beta] :+ (exp([ln_beta]) :- 1):* log(#t) :+ exp(exp([ln_beta]) :* log(#t))) Models were assessed for goodness of fit using AIC and BIC values, visual fit, and clinical plausibility in extrapolation. Table 1 Overview of data sources used Data source Description Sample size/events Length of follow-up Benfari et al., 2019 ∞, 6 Mortality of patients with four different levels of functional tricuspid regurgitation (FTR): Trivial, mild, moderate and severe.: Trivial .Mild Moderate Severe N 4329/1795 deaths N 4178/ 2173 deaths N 2255/ 1371 deaths N 745/ 502 deaths Maximum follow-up 10 yrs Essayagh et al., 2021 ∞, 9 Mortality under medical management of patients with four different levels of functional tricuspid regurgitation. Trivial . Mild .Moderate Severe N 2288/ 20% dead at 10 yrs N 1858/ 35% dead at 10 yrs N 767/ 53% dead at 10 yrs N 157/ 81% dead at 10 yrs Maximum follow-up 10 yrs National Joint Registry for England and Wales Report 20 13 Cumulative revision of primary total hip replacement (THR) in patients with osteoarthritis. Cumulative revision of primary total hip replacement (THR) with cemented metal on polythene devices. Cumulative revision of primary total hip replacement (THR) with cemented ceramic on polythene devices. Cumulative re-revision of revised primary total hip replacement (THR) Cumulative revision of primary total hip replacement (THR) with uncemented metal on polythene devices. 1,273,746/ ~7.3% required revision 358,641/ ~6.6% required revision 59,975/ ~ 5% required revision 43,682/ ~20% required re-revision 205,001/ ~8.5% required revision Maximum follow-up 18 yrs National Joint Registry for England and Wales Report 9* , 12 Cumulative revision of primary total hip replacement (THR) with cemented metal on polythene devices. Cumulative revision of primary total hip replacement (THR) with cemented ceramic on polythene devices. Cumulative revision of primary total hip replacement (THR) with uncemented metal on polythene devices. 125,285/ ~2.4% required revision 13,871/ ~2% required revision 59,993/ ~3.2% required revision Maximum follow-up 8 yrs Whitlock et al., 2021 7 RCT Cumulative incidence of stroke or embolism after: No occlusion of left atrial appendage preformed during heart surgery. Occlusion of left atrial appendage preformed during heart surgery. 2391/ 168 events 2379/ 114 events Maximum follow-up 6 yrs Tribouilloy et al., 2024 10 Cumulative mortality of patients with functional tricuspid regurgitation and co-morbidities, mean age 75 ± 12 years 715/ 175 deaths Maximum follow-up 5 yrs Bae et al., 2013 11 Time to the requirement for total knee replacement (TKR) after microfracture procedure for osteoarthritis of the knee. Mean age 61.3 years, most patients female. 134 knees / 51 TKR Maximum follow-up 12 yrs TRISCEND II RCT as reported by US FDA 8 All-cause Mortality: .After percutaneous replacement of tricuspid valve using the EVOQUE device OR .Optimal Medical Therapy 259/ 14.8% dead at 18 mos 113/ 23.4% dead at 18 mos Maximum follow-up 18 mos yrs years; mos months ∞ Patient comorbidities differed between FTR levels * The National Joint Registry truncates Kaplan Meier plots at the time it is judged that uncertainty is unacceptably high. RESULTS Benfari et al.,2019 study of mortality in patients with four levels of functional tricuspid regurgitation 6 Figure 2 shows the poor fit of regular parametric models to the follow-up from Benfari et al. for trivial FTR, suggesting the need for an alternative approach. In Fig. 3 a, bathtub and Chen models have been fitted separately to all four FTR groups from both Benfari et al. For the Benfari et al. trivial group (best prognosis), it is clear that the Chen and bathtub models provide a superior visual fit. This is supported by the goodness of fit statistics which show a significant improvement over the regular parametric models (Table 2 ). This is maintained across all four levels of FTR where the bathtub and Chen models provided almost identical visual fit (Fig. 3 ) and at least one of these models provided the best AIC/BIC score. Either bathtub or Chen models provided the best AIC and BIC scores (Table 2 ) and neither model strayed from the 95% CIs of the KM plots. In contrast standard parametric models provided poorer AIC and BIC scores, poorer visual fit and almost all models strayed outside the KM 95% CIs (Supplementary section 2). Chen models were very similar to bathtub over 10 years observation time but following further extrapolation Chen models predicted more favourable longer-term survival (Supplement: section 3). Essayagh et al., 2021 study of mortality in patients with four levels of FTR under medical management 9 KM plot 95% CIs were wider than in the larger Benfari et al. study. For all four levels of FTR bathtub and Chen models provided similar and the best models according to visual fit (Fig. 3 b (right)). Either bathtub or Chen models provided the best AIC and BIC scores (Table 2 ) and both models did not stray appreciably outside the KM 95% CIs. Standard models presented poorer visual fit. (Supplement: section 4) Table 2 Information criteria (AIC BIC) scores for parametric models; Tricuspid Regurgitation, microfracture and atrial occlusion studies Model AIC BIC Model AIC BIC Model AIC BIC Model AIC BIC Benfari et al., Trivial functional regurgitation Essayagh et al., Trivial functional regurgitation Tribouilloy et al., functional regurgitation Bae et al., microfracture of the knee bathtub 11391.6 11410.72 bathtub 2273.44 2290.66 ggamma 1182.412 1196.128 ggamma 227.83 236.53 Chen 11457.57 11470.31 Chen 2281.45 2292.93 bathtub 1184.632 1198.349 Gompertz 227.83 233.63 ggamma 11489.82 11508.94 Weibull 2281.51 2292.99 lognormal 1185.011 1194.156 Weibull 228.84 234.64 Weibull 11550.12 11562.86 ggamma 2281.76 2298.98 loglogistic 1194.666 1203.81 Chen 228.30 234.09 loglogistic 11643.51 11656.26 exponential 2282.99 2288.73 Weibull 1196.236 1205.381 Rayleigh 2 229.11 234.90 Gompertz 11733.51 11746.25 loglogistic 2283.69 2295.17 Gompertz 1198.722 1207.866 Rayleigh 1 229.52 232.41 lognormal 11745.43 11758.18 gompertz 2284.83 2296.31 exponential 1208.135 1212.707 loglogistic 232.44 238.24 exponential 11769.46 11775.83 Rayleigh 2 2284.85 2296.33 Chen 1208.419 1217.564 lognormal 237.58 243.38 Rayleigh 2 11741.83 11754.58 lognormal 2294.47 2305.96 Rayleigh 1 1501.44 1506.012 exponential 272.94 275.84 Rayleigh 1 14945.58 14951.95 Rayleigh 1 2580.30 2586.04 Rayleigh 2 NA NA bathtub NA NA Benfari.et al Mild functional regurgitation Essayagh. et al Mild functional regurgitation TRISCEND II control arm bathtub 11903.75 11922.76 Chen 2790.99 2802.04 lognormal 294.6 301.4 Chen 11981.74 11994.42 Ggamma 2859.81 2876.39 ggamma 294.7 304.9 lognormal 12203.39 12216.07 Weibull 2874.22 2885.27 bathtub 294.9 305.1 ggamma 12015.36 12034.37 loglogistic 2892.36 2903.41 loglogistic 296.5 303.3 Weibull 12062.17 12074.84 bathtub 2893.42 2910.00 Chen 296.7 303.5 loglogistic 12158.08 12170.76 exponential 2906.42 2911.95 Weibull 296.9 303.7 Gompertz 12382.84 12395.51 gompertz 2908.39 2919.44 Gompertz 297.0 303.8 exponential 12505.97 12512.31 Rayleigh 2 2908.39 2919.45 exponential 309.4 312.8 Rayleigh 2 12416.85 12429.52 lognormal 3016.19 3027.24 Rayleigh 1 385.8 389.2 Rayleigh 1 16861.08 16867.41 Rayleigh 1 3528.87 3534.40 Rayleigh 2 Benfari.et al. Moderate functional regurgitation Essayagh et al., Moderate functional regurgitation Whitlock et al., left atrial appendage No occlusion Chen 7019.15 7030.59 bathtub 1587.68 1601.61 Chen 1847 1859 bathtub 7019.35 7036.51 ggamma 1592.95 1606.88 bathtub 1851 1869 ggamma 7046.38 7063.54 Weibull 1593.39 1602.68 lognormal 1901 1912 Weibull 7072.59 7084.03 Chen 1594.52 1603.80 Weibull 1905 1917 loglogistic 7165.33 7176.77 loglogistic 1600.24 1609.53 loglogistic 1905 1917 lognormal 7214.13 7225.57 Gompertz 1602.95 1612.24 ggamma 1907 1924 Gompertz 7255.78 7267.22 Rayleigh 2 1603.59 1612.87 Gompertz 2117 2129 Rayleigh 2 7272.49 7283.93 exponential 1604.87 1609.52 Rayleigh 2 2159 2171 exponential 7322.90 7328.62 lognormal 1610.09 1619.37 exponential 2199 2205 Rayleigh 1 10139.16 10144.88 Rayleigh 1 1990.27 1994.92 Rayleigh 1 3007 3013 Benfari.et al) Severe functional regurgitation Essayagh.et al. Severe functional regurgitation Whitlock et al., left atrial appendage occlusion bathtub 2442.81 2456.65 bathtub 457.1133 466.2821 Chen 1353.035 1364.584 ggamma 2466.09 2479.93 loglogistic 457.9641 464.0766 ggamma 1378.3 1341.1 lognormal 2469.57 2478.80 lognormal 454.7669 460.8794 bathtub 1381.676 1398.999 Weibull 2470.93 2480.16 Ggamma 456.7364 465.9051 lognormal 1400.537 1412.086 loglogistic 2485.78 2495.01 Weibull 459.2854 465.3979 loglogistic 1406.278 1417.827 Chen 2487.90 2497.12 gompertz 459.9671 466.0796 Weibull 1406.585 1418.134 Gompertz 2515.70 2524.92 Rayleigh 2 461.6414 467.7539 Gompertz 1542.111 1553.659 exponential 2565.68 2570.30 exponential 466.8290 469.8853 exponential 1651.162 1656.937 Rayleigh 1 3710.03 3714.64 Chen 467.3864 473.4988 Rayleigh 1 2266.306 2272.08 Rayleigh 2 NA NA Rayleigh 1 648.6065 651.6627 Rayleigh 2 NA NA NA = Not applicable model did not converge Tribouilloy et al 2024 of mortality in a French cohort with isolated functional tricuspid regurgitation 10 Chen and bathtub models generated very similar good visual fit (Fig. 4 b (middle)). Generalised gamma and bathtub provided the best AIC BIC scores, while Chen provided poor AIC BIC scores (Table 2 ). With extrapolation to 25 years the generalised gamma model predicted clinically implausible 50% survival and other standard parametric models similarly predicted substantial proportion of patients surviving beyond 25 years (Supplementary: section 3) generating overoptimistic survival curves for an elderly population with serious comorbidities. Only bathtub and Chen models generated plausible long-term extrapolations and both generated U shaped hazard plots (Supplement: section 5). Bae et al., 2013; Korean Cohort with degenerative osteoarthritic knee treated by microfracture 11 After ten years of follow-up, around 50% of microfracture-treated knees required TKA in this cohort. Over the observation period all parametric models except lognormal loglogistic and exponential generated reasonably good visual fit with similar AIC BIC scores; Chen, Gompertz and Rayleigh models generated well-fitting models (Fig. 4 a (left), Supplement: section 7). On extrapolation of models to 25 years there were considerable differences between models with only Gompertz and Chen models predicting 100% failure within 20 years. The hazard for failure of other models barely changed over the observation period and beyond (Supplement: section 7) despite ageing of the population and inevitable wear and tear of the microfracture-treated knee. The more clinically plausible scenario would seem to be an increasing hazard that gets steeper with increasing age of patient, progressive wear and tear, and the exacerbation of osteoarthritis through time. This scenario is best satisfied by the Rayleigh, Gompertz and Chen models. Occlusion versus no-occlusion of left atrial appendage (RCT; Whitlock et al.,2021) A bathtub model for the no-occlusion arm (Fig. 4 c (right)) generated superior AIC/BIC scores relative to standard parametric models and better visual fit; all standard models for the no-occlusion arm generated poor visual fit (Supplement: section 8). The Chen model AIC BIC scores were superior to those for 3-parameter bathtub despite its poor visual fit, and the hazard plot differed from the bathtub (3-parameter) hazard. The Chen model appears unsuited to substantial and rapid initial accumulation of events as found in both arms of this RCT. For the intervention arm (occlusion) the 3-parameter bathtub model again generates a good visual fit and Chen 2-parameter model a poor fit (Fig. 4 c) while several standard models (e.g. Weibull) generated good visual fit for the intervention arm (Supplement: section 8). Total Hip Replacement (THR) (Registry studies) Revision after THR failure varies according to many characteristics of both THR device and patient age, gender, and other demographics of patient populations. The National Joint Registry Annual report 20 (2023) 13 itemises many KM plots for cumulative failure of THR. We analysed failure for THR recipients with osteoarthritis, for recipients of cemented metal on polythene and of ceramic on polythene devices, and for re-revision after first THR revision. In each of these four examples bathtub and Chen models provided the best visual fit and almost identical models (Fig. 5 ) accompanied by the lowest AIC/BIC scores (Table 3 ). Standard models provided poorer visual fit (Supplement: section 9) and poorer AIC/BIC scores. Table 3 Goodness of fit statistics for models fitted to THR data Model AIC BIC Model AIC BIC THR Osteoarthritis THR cemented ceramic on polythene Chen 300.2661 308.4213 Chen 296.4028 305.1967 bathtub 301.9992 314.232 bathtub 296.7181 309.9089 exponential 302.1448 306.2224 Gompertz 298.4029 307.1967 Gompertz 303.7814 311.9367 exponential 298.5097 302.9066 Rayleigh 2 303.8298 311.9851 Rayleigh 2 298.8838 307.6777 Weibull 303.8698 312.0251 Weibull 300.4538 309.2477 loglogistic 304.1212 312.2765 loglogistic 300.6615 309.4553 ggamma 305.6258 317.8587 ggamma 302.2484 315.4392 lognormal 307.6922 315.8475 lognormal 303.9896 312.7835 Rayleigh 1 328.2803 332.358 Rayleigh 1 314.5399 318.9368 THR re-revision THR cemented metal on polythene Chen 346.0576 352.6442 Chen 316.8134 325.2426 bathtub 348.9028 358.7827 bathtub 318.0951 330.7389 Weibull 349.3799 355.9665 exponential 319.2385 323.4531 loglogistic 349.5192 356.1058 Gompertz 319.798 328.2272 lognormal 349.6722 356.2588 Rayleigh 2 319.9957 328.4249 ggamma 351.3068 361.1867 Weibull 321.2365 329.6658 Gompertz 360.9285 367.5151 loglogistic 321.5145 329.9437 exponential 368.2898 371.5831 ggamma 322.9653 335.6091 Rayleigh 1 471.5511 474.8444 lognormal 325.9746 334.4038 Rayleigh 2 NA NA Rayleigh 1 339.8937 344.1083 NA = Not applicable model did not converge Triscend II RCT: tricuspid valve replacement with EVOQUE system for patients with tricuspid regurgitation . 8 The US FDA presented KM plots for mortality in the TRISCEND II trial (see Supplementary: section 6). For the medical treatment arm bathtub and Chen models generated almost identical good visual fit for the cumulative incidence of death. Weibull and generalised gamma models delivered marginally lower IC values than bathtub and Chen models but on extrapolation produced less plausible mortality curves for such an aged population with extensive comorbidities. The bathtub g parameter is almost zero so that bathtub and Rayleigh 2 models predict virtually identical curves for survival and for hazard. All models fitted to the intervention arm generated clearly implausible survival curves. Longer follow up with more patients is required for modelling. Are bathtub and Chen model predictions supported by longer term follow up Registry findings? We compared extrapolated bathtub and Chen model predictions for Registry cumulative failure rates with that reported for later registry analyses. For this we used the National Joint registry 9th annual report (NJR9) for England and Wales 12 with the 20th annual report 13 (NJR20) . The NJR9 and NJR20 KM plots for frequently used devices show increasing revision rates over time (Fig. 6 ). Performance of cemented MOP and cemented COP devices was reasonably consistent across these time spans, but in the case of uncemented MOP revision performance appears to have improved with time. Using NJR9, 12 ) Chen and bathtub models of 125,285 cemented MOP recipients suggests predict between 6% and 7% cumulative revision rate at 18 years, consistent with 6.6% reported in NJR20, when about 2.94 times as many recipients (N = 368,641) were available for analysis (Fig. 6 a top). Chen and bathtub extrapolations for 59,983 uncemented MOP recipients predict 6% and 12% cumulative revision respectively. In this case, the NJR20 (N = 205,001) revision rate is 8.5%, suggesting an average of these two models outperforms a single extrapolation (Fig. 6 b middle). Chen and bathtub models of 13,871 cemented COP recipients from NJR9 predict about 5% and 6% cumulative revision respectively corresponding very closely to the 18-year follow up reported in NJR20 (Fig. 6 c bottom). Similar results were found in analyses conducted using the Swedish Arthroplasty Registry (Supplement: section 10). Discussion This paper has demonstrated the utility of the Chen and bathtub models when extrapolating time-to-event data across a range of settings. Their distinct forms show that there are situations where they outperform or provide substantially different extrapolations compared to the routine models. Broadening the set of candidate models might allow for more accurate predictions, or at least exploration of a wider set of alternative scenarios exploring potential uncertainty. Hence, models with U-shaped hazard rates such as Chen or bathtub, alongside other alternative models, such as Rayleigh-1 or -2 parameter models should be included in the routine set of models considered when extrapolating these outcomes in a HTA setting. The improved accuracy of predicting long-term outcomes can result in fairer valuations of health technologies for technology developers and healthcare providers, and better decisions being made. This is particularly relevant for first-in-class technologies, where there exists no data on long-term effects of any similar technology and therefore the probability of a future adverse outcome is higher. U-shaped models should also be considered in applications of model averaging, which has already been shown to be beneficial in some cases 17 . In cases where little is known about patient outcomes beyond an observed follow-up period, it can only be considered fair to include candidate models where the hazard rate increases over time when you are also including models which assume the opposite (e.g. log-normal and log-logistic). Of course, models should be scrutinised for plausibility which may rule out certain functional forms, and so we do not see any downsides to including the U-shaped models described in this paper within the set of candidate models. These results raise the question of why these models are not already included within HTA submissions. This may be because U-shaped models are not referred to in the NICE Technical Support Documents which relate to survival analysis. 18 , 19 Given their tendency for an increasing hazard rate, we anticipate that their extrapolations will be more pessimistic compared to the routine parametric models. Hence, it is unlikely that submissions to NICE from pharmaceutical companies will introduce these models without prompting, where more optimistic extrapolations are typically preferred, allowing the quality adjusted life-year gains to be collected over a longer time-period. These models could also be used in a mixture cure model (MCM) setting, which would permit an increasing hazard rate for a subgroup of the population, whilst the remaining population are considered cured or are subject to a background event rate. MCMs are increasingly relevant as emerging technologies such as gene and CAR-T therapies show potential to transform patient outcomes. Use of bathtub or Chen models in this setting might be more palatable to pharmaceutical companies, as the increasing hazard rate would not apply to “cured” patients and so they will not necessarily produce the most pessimistic extrapolations. A strength of this work is how the benefits of U-shaped models have been shown to apply beyond a single case-study or disease area. We have has used publicly available data, and provided code where helpful, maximising the transparency, reproducibility and ease of implementation of the models described. A limitation of this research is that we have not considered flexible models such as fractional polynomials or restricted cubic splines. Whilst these can fit very well to the data, they are in danger of overfitting and providing implausible extrapolations, or of relying on key assumptions to be made beyond the observed period of follow-up that can make them equivalent to an underlying parametric model. The flexibility of splines may sometimes result in a U-shaped hazard rate but may also take on many other forms, hence they cannot be relied upon to provide balance to models with n-shaped hazard rates. These models also rely on specification of combinations of terms, scales and knot locations in order to be optimised making a meaningful comparison more difficult, particularly across the range of different types of dataset in this paper. Standard parametric models have less subjectivity in how they are fitted making a comparison more straightforward, however future work could compare the fit and extrapolations of U-shaped models to these flexible approaches. Conclusion This study has shown how models with U-shaped hazard rates can match or outperform models routinely used in HTA when fitting to observed data and predicting future survival rates in a range of fields. These models should be included in the regular set of parametric models considered when extrapolating time-to-event data. Bathtub and Chen models do not necessarily generate the same predictions despite having U-shaped hazard rate, they may differ slightly or greatly depending on the data and should both be considered. Declarations Ethics approval and consent to participate: Not applicable Consent for publication: Not applicable Availability of data and materials: Not applicable Competing interests: None to declare Funding: No funding was received specific to this work however DG is supported by NIHR award 14/25/05 Authors' contributions: MC had the original research idea and performed all modelling. DG produced the manuscript and contributed to developing the research idea. Clinical trial number: Not applicable Acknowledgements: None References Gallacher, D, Auguste, P, Connock, M. How Do Pharmaceutical Companies Model Survival of Cancer Patients? A Review of NICE Single Technology Appraisals in 2017. International Journal of Technology Assessment in Health Care 2019;35(2):160-167. Collet, D. Modelling survival data in medical research . 2 ed.: Chapman & Hall, 2003. Chen, Z. A new two-parameter lifetime distribution with bathtub shape or increasing failure rate function. Statistics & Probability Letters 2000;49:155-161. Peace, KE. Design and analysis od clinical trials with time-to-event endpoints . Chapman & Hall/CRC, 2009. Crowther, MJ, Lambert,P.C. stgenreg: A Stata Package for General Parametric Survival Analysis. Journal of Statistical Software 2013;53(`12). Benfari, G, Antoine, C, Miller, WL, et al. Excess Mortality Associated With Functional Tricuspid Regurgitation Complicating Heart Failure With Reduced Ejection Fraction. Circulation 2019;140(3):196-206. Whitlock, RP, Belley-Cote, EP, Paparella, D, et al. Left Atrial Appendage Occlusion during Cardiac Surgery to Prevent Stroke. N Engl J Med 2021;384(22):2081-2091. FDA. PMA P230013: FDA Summary of Safety and Effectiveness Data 2024. https://www.accessdata.fda.gov/cdrh_docs/pdf23/P230013B.pdf. Accessed. Essayagh, B, Sabbag, A, Antoine, C, et al. The Mitral Annular Disjunction of Mitral Valve Prolapse: Presentation and Outcome. JACC Cardiovasc Imaging 2021;14(11):2073-2087. Tribouilloy, C, Vanhaecke, P, Dreyfus, J, et al. Natural History of Isolated Functional Tricuspid Regurgitation. J Am Heart Assoc 2024;13(9):e033933. Bae, DK, Song, SJ, Yoon, KH, et al. Survival analysis of microfracture in the osteoarthritic knee-minimum 10-year follow-up. Arthroscopy 2013;29(2):244-250. NJR. National Joint Registry for England and Wales 9'th Annual Report; 2012. https://reports.njrcentre.org.uk/downloads. Accessed. NJR. National Joint Registry Report for England and Wales 20'th annual report; 2023. http://www.ncbi.nlm.nih.gov. Accessed. Kärrholm, J, Rogmark, C, Naucler, E, et al. Swedish hip arthroplasty register: annual report, 2018. Department of Orthopaedics, Sahlgrenska University Hospital 2019. W-Dahl, A, Kärrholm, J, Rogmark, C, et al. Swedish hip arthroplasty register: annual report, 2023. Department of Orthopaedics, Sahlgrenska University Hospital 2024. Guyot, P, Ades, AE, Ouwens, MJ, et al. Enhanced secondary analysis of survival data: reconstructing the data from published Kaplan-Meier survival curves. BMC Med Res Methodol 2012;12:9. Gallacher, D, Kimani, P, Stallard, N. Extrapolating Parametric Survival Models in Health Technology Assessment Using Model Averaging: A Simulation Study. Medical Decision Making 2021;41(4):476-484. Rutherford, MJ, Lambert, PC, Sweeting, MJ, et al. NICE DSU technical support document 21: flexible methods for survival analysis. Decision Support Unit, ScHARR, University of Sheffield 2020. Latimer, N. NICE DSU technical support document 14: survival analysis for economic evaluations alongside clinical trials-extrapolation with patient-level data. Report by the Decision Support Unit 2011. Additional Declarations No competing interests reported. Supplementary Files SUPPLEMENTAERYv7.docx Cite Share Download PDF Status: Under Review Version 1 posted Editorial decision: Revision requested 29 Oct, 2024 Editor assigned by journal 25 Oct, 2024 Submission checks completed at journal 25 Oct, 2024 First submitted to journal 21 Oct, 2024 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. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. 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-5303870","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":371772529,"identity":"ce385b65-3bc7-48dd-9bac-5c9ed51d7059","order_by":0,"name":"Daniel Gallacher","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAABEElEQVRIiWNgGAWjYDCCA0D8oICBwYCBgfEBSIANCMFAAp+WBAOwFmYDkrWwQRUR0MJ3gP3ihwQDO3lz9t5n1Tw19xL72I8lMPyoYUic2YBdi+QBnmKJBINkw509x81u8xwrTmzjSTvA2HOMIXE2DlsMDvAkALUwJxjcSGO7ncOWkNsmwd7AwNvAkDgPt5bkHwkG9QkG95+xFef8g2hh/ItXC/sxoC2HgbawsTHntoG0sB1gBtmCy2GSh3nYLBIMjhtuOJPGLP23L6Ee6JeEwzLHJIxxeZ/vePvjGx8qquUNjh9j/DjjW4KxfPsxw4dvamxkZxzAYQ0zjwGm4AE8EQkE7A/wSI6CUTAKRsEoAAIAjAxZT/HSKdMAAAAASUVORK5CYII=","orcid":"","institution":"University of Warwick","correspondingAuthor":true,"prefix":"","firstName":"Daniel","middleName":"","lastName":"Gallacher","suffix":""},{"id":371772530,"identity":"0c67928a-84f6-419d-9236-cf431d4dbc3a","order_by":1,"name":"Martin Connock","email":"","orcid":"","institution":"University of Warwick","correspondingAuthor":false,"prefix":"","firstName":"Martin","middleName":"","lastName":"Connock","suffix":""}],"badges":[],"createdAt":"2024-10-21 11:23:03","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-5303870/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-5303870/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":68213905,"identity":"a99e3868-9012-40ef-a3f2-5026038507ab","added_by":"auto","created_at":"2024-11-04 18:34:28","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":72486,"visible":true,"origin":"","legend":"\u003cp\u003eRepresentation of hazard shapes that can be generated by parametric models; for additional information regarding Chen models of hazard see (Supplementary: section 1).\u003c/p\u003e","description":"","filename":"1.png","url":"https://assets-eu.researchsquare.com/files/rs-5303870/v1/e85c40f623f857409db714c4.png"},{"id":68213906,"identity":"fb455bdb-7ce4-42a1-b29e-8a836d189d1b","added_by":"auto","created_at":"2024-11-04 18:34:29","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":75663,"visible":true,"origin":"","legend":"\u003cp\u003eRegular parametric models fitted to reconstructed time-to-event data for trivial functional tricuspid regurgitation from Benfari et al.\u003c/p\u003e","description":"","filename":"2.png","url":"https://assets-eu.researchsquare.com/files/rs-5303870/v1/23f9715a8c3e9703797af817.png"},{"id":68213438,"identity":"34aad682-1ccc-4a4f-aa1c-fe18f7472721","added_by":"auto","created_at":"2024-11-04 18:26:29","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":1260838,"visible":true,"origin":"","legend":"\u003cp\u003eKaplan Meier (95% CI) with bathtub and Chen models. Left Benfari et al., 2019; Right Essayagh et al., 2021.\u003c/p\u003e","description":"","filename":"3.png","url":"https://assets-eu.researchsquare.com/files/rs-5303870/v1/45e6d185b4e170645b84ac45.png"},{"id":68213435,"identity":"a9d72995-de6f-4c54-b7bc-c0937de9a0ab","added_by":"auto","created_at":"2024-11-04 18:26:28","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":810284,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cem\u003eChen and bathtub models. Left: Failure after microfracture treatment of the osteoarthritic knee in the cohort study of Bae et al., 2012; Gompertz (not shown) and Chen models were coincident over 12 years (in this analysis the bathtub model did not converge). Middle: Mortality in the cohort study of Tribouilloy et al., 2024. Right: Cumulative incidence of stroke or embolism in occlusion and no occlusion arms of the Whitlock et al., 2012 RCT.\u003c/em\u003e\u003c/p\u003e","description":"","filename":"4.png","url":"https://assets-eu.researchsquare.com/files/rs-5303870/v1/f50c65534aa86f18d6cc3938.png"},{"id":68213907,"identity":"2fbd539b-69b1-46ee-b2e0-9432c5276616","added_by":"auto","created_at":"2024-11-04 18:34:29","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":167969,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cem\u003eBathtub and Chen models of National Joint Registry recipients of THR. MOP cemented metal on polythene; COP cemented ceramic on polythene.\u003c/em\u003e\u003c/p\u003e","description":"","filename":"5.png","url":"https://assets-eu.researchsquare.com/files/rs-5303870/v1/07947c59161de80c05d2f1ce.png"},{"id":68213440,"identity":"3fe3a569-5cfa-4525-82fd-48d25af5f14a","added_by":"auto","created_at":"2024-11-04 18:26:29","extension":"png","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":1473392,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cem\u003eBathtub and Chen models of THR recipients’ revision based on National Joint Registry annual reports 9 and 20.\u003c/em\u003e\u003c/p\u003e","description":"","filename":"6.png","url":"https://assets-eu.researchsquare.com/files/rs-5303870/v1/e862662c3492bbb8b3321647.png"},{"id":68214179,"identity":"c34cfa96-1fee-4cce-8c0c-aacd0035e80b","added_by":"auto","created_at":"2024-11-04 18:42:36","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":4514265,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-5303870/v1/1bd096a4-7a2c-45ab-a07f-7cf71888ce55.pdf"},{"id":68213441,"identity":"21968788-a156-4247-97d5-673b4f6f2316","added_by":"auto","created_at":"2024-11-04 18:26:29","extension":"docx","order_by":1,"title":"","display":"","copyAsset":false,"role":"supplement","size":28944531,"visible":true,"origin":"","legend":"","description":"","filename":"SUPPLEMENTAERYv7.docx","url":"https://assets-eu.researchsquare.com/files/rs-5303870/v1/bcd8ee25d2f8686d7a96a6e1.docx"}],"financialInterests":"No competing interests reported.","formattedTitle":"Broadening the candidate set of parametric models when extrapolating survival: the case for models with U-shaped hazards.","fulltext":[{"header":"BACKGROUND","content":"\u003cp\u003eIn health technology assessment (HTA) it is often necessary to model the observed data and or to extend analysis beyond maximum follow up to estimate outcomes in the longer term and satisfy the time horizon favoured by decision making authorities; frequently a life-time horizon is required. For time-to-event outcomes, such as overall survival, various parametric models are fitted to data using widely available in software programmes such as Stata and R.\u003c/p\u003e\n\u003cp\u003eCommonly six \u0026ldquo;standard\u0026rdquo; distributions are explored (Weibull, Gompertz, loglogistic, lognormal, exponential, generalised gamma)\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e1\u003c/span\u003e\u003c/sup\u003e. These models can represent a wide range of hazard behaviours (Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003e). The exponential is the least flexible, modelling a constant hazard rate. The Weibull or Gompertz can model a monotonic hazard rate, either always increasing or always decreasing. Finally, the lognormal and loglogistic models tend to provide a decreasing hazard over time, sometimes after an initial period of an increasing hazard rate. There are no models in this standard set of models which allow for an initial decreasing hazard rate followed by increasing hazard rate over time. Such models do exist and may be referred to as \u0026ldquo;bathtub\u0026rdquo; models due to their \u0026ldquo;U\u0026rdquo; shaped hazard. A failure to include these models in candidate sets results in a failure to explore all potential future scenarios in areas of high uncertainty and may bias methods of model averaging. In this paper we explore the potential benefits of expanding the standard set of parametric models to include a 3-parameter bathtub\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e2\u003c/span\u003e\u003c/sup\u003e and a 2-parameter bathtub (Chen 2000 \u003csup\u003e3\u003c/sup\u003e) models that here we term \u0026ldquo;bathtub\u0026rdquo; and \u0026ldquo;Chen\u0026rdquo; respectively. The Chen model (Supplement: section 1) can generate non-linearly increasing hazard as well as \u0026ldquo;U shaped\u0026rdquo; bathtub hazard. We also briefly consider Rayleigh models (Peace and Tsai 2009 \u003csup\u003e4\u003c/sup\u003e; Supplement: section 2) that generate linearly increasing hazard. The \u0026ldquo;stgenreg\u0026rdquo; user written Stata package (Crowther and Lambert 2013 \u003csup\u003e5\u003c/sup\u003e) enables exploration of such models that are not pre-specified in software packages that sometimes may generate better fit to the observed data than obtained using standard models.\u003c/p\u003e\n\u003cp\u003eA bathtub model with three parameters is described by Collet\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e2\u003c/span\u003e\u003c/sup\u003e, whilst Chen\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e3\u003c/span\u003e\u003c/sup\u003e describes a two parameter model that can generate a bathtub or non-linearly increasing hazard (Supplement: Section 1). Their survival and hazard functions are shown in equations 1\u0026ndash;4.\u003c/p\u003e\n\u003cp\u003eBathtub 3 parameter hazard function\u003c/p\u003e\n\u003cdiv id=\"Equa\" class=\"Equation\"\u003e\n \u003cdiv class=\"mathdisplay\" id=\"FileID_Equa\" name=\"EquationSource\"\u003e$$\\:h\\left(t\\right)=at+\\frac{b}{(1+gt)}\\:\\:\\:\\:\\:\\:\\left(1\\right)$$\u003c/div\u003e\n\u003c/div\u003e\n\u003cp\u003eBathtub 3 parameter survival function\u003c/p\u003e\n\u003cdiv id=\"Equb\" class=\"Equation\"\u003e\n \u003cdiv class=\"mathdisplay\" id=\"FileID_Equb\" name=\"EquationSource\"\u003e$$\\:\\text{S}\\left(\\text{t}\\right)=\\text{e}\\text{x}\\text{p}\\left(-\\frac{{\\text{a}\\text{t}}^{2}}{2}\\text{}\\right)\\cdot\\:{\\left(1+\\text{g}\\text{t}\\right)}^{-\\:\\frac{b}{g}}\\text{}\\:\\:\\:\\:\\:\\:\\left(2\\right)$$\u003c/div\u003e\n\u003c/div\u003e\n\u003cp\u003eChen hazard function\u003c/p\u003e\n\u003cdiv id=\"Equc\" class=\"Equation\"\u003e\n \u003cdiv class=\"mathdisplay\" id=\"FileID_Equc\" name=\"EquationSource\"\u003e$$\\:h\\left(t\\right)=\\lambda\\:\\beta\\:{t}^{\\beta\\:-1}{e}^{{t}^{\\beta\\:}}\\:\\:\\:\\:\\:\\:\\left(3\\right)$$\u003c/div\u003e\n\u003c/div\u003e\n\u003cp\u003eChen survival function\u003c/p\u003e\n\u003cdiv id=\"Equd\" class=\"Equation\"\u003e\n \u003cdiv class=\"mathdisplay\" id=\"FileID_Equd\" name=\"EquationSource\"\u003e$$\\:\\text{e}\\text{x}\\text{p}(\\lambda\\:-\\lambda\\:\\text{exp}\\left({t}^{\\beta\\:}\\right)\\:\\:\\:\\:\\:\\:(4)$$\u003c/div\u003e\n\u003c/div\u003e"},{"header":"METHODS","content":"\u003cdiv id=\"Sec3\" class=\"Section2\"\u003e\n \u003ch2\u003eData sources\u003c/h2\u003e\n \u003cp\u003eWe fit a range of survival models to data from a wide range of populations and medical interventions with study designs including RCTs, cohort, and registry studies. We lead with a clear example using re-created data from Benfari et al. \u003csup\u003e\u003cspan class=\"CitationRef\"\u003e6\u003c/span\u003e\u003c/sup\u003e where standard parametric models are outperformed by models with increasing hazard rates and we provide a wide range of cases where these increasing hazard models show good fit motivating their inclusion for regular consideration when extrapolating survival in a HTA setting.\u003c/p\u003e\n \u003cp\u003eRCTs included the left atrial appendage study of Whitlock et al., 2021\u003csup\u003e7\u003c/sup\u003e and the tricuspid valve replacement study TRISCEND II\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e8\u003c/span\u003e\u003c/sup\u003e. Cohort studies included the Benfari et al., 2019\u003csup\u003e6\u003c/sup\u003e, Essayagh et al., 2021\u003csup\u003e9\u003c/sup\u003e, and Tribouilloy et al 2024\u003csup\u003e10\u003c/sup\u003e investigations of patients with isolated functional tricuspid regurgitation, and the Bae et al.,\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e11\u003c/span\u003e\u003c/sup\u003e Korean study of microfracture treatment for osteoarthritic knees. Registry studies included: The National Joint Registry of England and Wales reports 9\u003csup\u003e12\u003c/sup\u003e and 20\u003csup\u003e13\u003c/sup\u003e and Swedish Hip Arthroplasty Register 2018 and 2023\u003csup\u003e14, 15\u003c/sup\u003e on failure after Primary Total Hip Replacement (THR) procedures (registry data sources include very substantial numbers of individuals followed for many years so that the trajectory of the time to event plots is internally consistent and less changeable compared to that in smaller studies). Relevant details from the included studies are briefly summarised in Table\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003e.\u003c/p\u003e\n\u003c/div\u003e\n\u003ch3\u003eAnalyses\u003c/h3\u003e\n\u003cp\u003ePublished Kaplan-Meier (KM) plots were digitised using Digitzelt (\u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttp://www.digitizelt.xyz\u003c/span\u003e\u003c/span\u003e) and IPD reconstructed using the method of Guyot et al. \u003csup\u003e\u003cspan class=\"CitationRef\"\u003e16\u003c/span\u003e\u003c/sup\u003e. In registry data where KM plots encompassed thousands of events that could not all be captured by digitisation; we proportionately reduced the patient numbers to handleable size, preserving the underlying survival distribution.\u003c/p\u003e\n\u003cp\u003eAll models were fitted using the streg or stgenreg command in Stata 18 (REF) or using \u003cem\u003estgenreg\u003c/em\u003e command of Crowther and Lambert\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e5\u003c/span\u003e\u003c/sup\u003e. The 2-parameter\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e3\u003c/span\u003e\u003c/sup\u003e and 3-parameter \u003csup\u003e\u003cspan class=\"CitationRef\"\u003e2\u003c/span\u003e\u003c/sup\u003e bathtub models and Rayleigh models \u003csup\u003e\u003cspan class=\"CitationRef\"\u003e4\u003c/span\u003e\u003c/sup\u003e were generated using following \u003cem\u003estgenreg\u003c/em\u003e commands:\u003c/p\u003e\n\u003cp\u003eRayleigh 1-parameter model: \u003cem\u003estgenreg, haz(2:*exp([ln_lambda2]):*#t)nodes(30)\u003c/em\u003e\u003c/p\u003e\n\u003cp\u003eRayleigh 2-parameter model: \u003cem\u003estgenreg, haz([lambda1] :+ 2:*[lambda2]:*#t)nodes(30)\u003c/em\u003e\u003c/p\u003e\n\u003cp\u003eCollet bathtub model (3 parameters): \u003cem\u003estgenreg, haz(([alpha]:*#t:+ [beta]:/(1:+[gamma]:*#t)))nodes(30)\u003c/em\u003e\u003c/p\u003e\n\u003cp\u003eChen model (2 parameters): \u003cem\u003estgenreg, loghazard( [ln_lambda] :+ [ln_beta] :+ (exp([ln_beta]) :- 1):* log(#t) :+ exp(exp([ln_beta]) :* log(#t)))\u003c/em\u003e\u003c/p\u003e\n\u003cp\u003eModels were assessed for goodness of fit using AIC and BIC values, visual fit, and clinical plausibility in extrapolation.\u003c/p\u003e\n\u003cdiv class=\"gridtable\"\u003e\u0026nbsp;\u003ctable id=\"Tab1\" border=\"1\"\u003e\n \u003ccaption language=\"En\"\u003e\n \u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e\n \u003cdiv class=\"CaptionContent\"\u003e\n \u003cp\u003eOverview of data sources used\u003c/p\u003e\n \u003c/div\u003e\n \u003c/caption\u003e\n \u003ccolgroup cols=\"4\"\u003e\u003c/colgroup\u003e\n \u003cthead\u003e\n \u003ctr\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eData source\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eDescription\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eSample size/events\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eLength of follow-up\u003c/p\u003e\n \u003c/th\u003e\n \u003c/tr\u003e\n \u003c/thead\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eBenfari et al.,\u003c/p\u003e\n \u003cp\u003e2019\u003csup\u003e\u003cstrong\u003e\u0026infin;, \u003cspan class=\"CitationRef\"\u003e6\u003c/span\u003e\u003c/strong\u003e\u003c/sup\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eMortality of patients with four different levels of functional tricuspid regurgitation (FTR): Trivial, mild, moderate and severe.: Trivial\u003c/p\u003e\n \u003cp\u003e.Mild\u003c/p\u003e\n \u003cp\u003eModerate\u003c/p\u003e\n \u003cp\u003eSevere\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eN 4329/1795 deaths\u003c/p\u003e\n \u003cp\u003eN 4178/ 2173 deaths\u003c/p\u003e\n \u003cp\u003eN 2255/ 1371 deaths\u003c/p\u003e\n \u003cp\u003eN 745/ 502 deaths\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eMaximum follow-up 10 yrs\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eEssayagh et al., 2021\u003csup\u003e\u003cstrong\u003e\u0026infin;, \u003cspan class=\"CitationRef\"\u003e9\u003c/span\u003e\u003c/strong\u003e\u003c/sup\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eMortality under medical management of patients with four different levels of functional tricuspid regurgitation. Trivial\u003c/p\u003e\n \u003cp\u003e. Mild\u003c/p\u003e\n \u003cp\u003e.Moderate\u003c/p\u003e\n \u003cp\u003eSevere\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eN 2288/ 20% dead at 10 yrs\u003c/p\u003e\n \u003cp\u003eN 1858/ 35% dead at 10 yrs\u003c/p\u003e\n \u003cp\u003eN 767/ 53% dead at 10 yrs\u003c/p\u003e\n \u003cp\u003eN 157/ 81% dead at 10 yrs\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eMaximum follow-up 10 yrs\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eNational Joint Registry for England and Wales Report 20 \u003csup\u003e13\u003c/sup\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eCumulative revision of primary total hip replacement (THR) in patients with osteoarthritis.\u003c/p\u003e\n \u003cp\u003eCumulative revision of primary total hip replacement (THR) with cemented metal on polythene devices.\u003c/p\u003e\n \u003cp\u003eCumulative revision of primary total hip replacement (THR) with cemented ceramic on polythene devices.\u003c/p\u003e\n \u003cp\u003eCumulative re-revision of revised primary total hip replacement (THR)\u003c/p\u003e\n \u003cp\u003eCumulative revision of primary total hip replacement (THR) with uncemented metal on polythene devices.\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1,273,746/ ~7.3% required revision\u003c/p\u003e\n \u003cp\u003e358,641/ ~6.6% required revision\u003c/p\u003e\n \u003cp\u003e59,975/ ~ 5% required revision\u003c/p\u003e\n \u003cp\u003e43,682/ ~20% required re-revision\u003c/p\u003e\n \u003cp\u003e205,001/ ~8.5% required revision\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eMaximum follow-up 18 yrs\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eNational Joint Registry for England and Wales Report 9*\u003csup\u003e, \u003cspan class=\"CitationRef\"\u003e12\u003c/span\u003e\u003c/sup\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eCumulative revision of primary total hip replacement (THR) with cemented metal on polythene devices.\u003c/p\u003e\n \u003cp\u003eCumulative revision of primary total hip replacement (THR) with cemented ceramic on polythene devices.\u003c/p\u003e\n \u003cp\u003eCumulative revision of primary total hip replacement (THR) with uncemented metal on polythene devices.\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e125,285/ ~2.4% required revision\u003c/p\u003e\n \u003cp\u003e13,871/ ~2% required revision\u003c/p\u003e\n \u003cp\u003e59,993/ ~3.2% required revision\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eMaximum follow-up 8 yrs\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eWhitlock et al., 2021 \u003csup\u003e7\u003c/sup\u003e RCT\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eCumulative incidence of stroke or embolism after:\u003c/p\u003e\n \u003cp\u003eNo occlusion of left atrial appendage preformed during heart surgery.\u003c/p\u003e\n \u003cp\u003eOcclusion of left atrial appendage preformed during heart surgery.\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2391/ 168 events\u003c/p\u003e\n \u003cp\u003e2379/ 114 events\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eMaximum follow-up 6 yrs\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eTribouilloy et al., 2024 \u003csup\u003e10\u003c/sup\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eCumulative mortality of patients with functional tricuspid regurgitation and co-morbidities, mean age 75\u0026thinsp;\u0026plusmn;\u0026thinsp;12 years\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e715/ 175 deaths\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eMaximum follow-up 5 yrs\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eBae et al., 2013 \u003csup\u003e11\u003c/sup\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eTime to the requirement for total knee replacement (TKR) after microfracture procedure for osteoarthritis of the knee. Mean age 61.3 years, most patients female.\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e134 knees / 51 TKR\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eMaximum follow-up 12 yrs\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eTRISCEND II RCT as reported by US FDA\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e8\u003c/span\u003e\u003c/sup\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eAll-cause Mortality:\u003c/p\u003e\n \u003cp\u003e.After percutaneous replacement of tricuspid valve using the EVOQUE device\u003c/p\u003e\n \u003cp\u003eOR\u003c/p\u003e\n \u003cp\u003e.Optimal Medical Therapy\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e259/ 14.8% dead at 18 mos\u003c/p\u003e\n \u003cp\u003e113/ 23.4% dead at 18 mos\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eMaximum follow-up 18 mos\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" colspan=\"4\"\u003e\n \u003cp\u003eyrs years; mos months\u003c/p\u003e\n \u003cp\u003e\u0026infin; Patient comorbidities differed between FTR levels\u003c/p\u003e\n \u003cp\u003e* The National Joint Registry truncates Kaplan Meier plots at the time it is judged that uncertainty is unacceptably high.\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n \u003c/table\u003e\n\u003c/div\u003e"},{"header":"RESULTS","content":"\u003cdiv id=\"Sec6\" class=\"Section2\"\u003e\n \u003ch2\u003eBenfari et al.,2019 study of mortality in patients with four levels of functional tricuspid regurgitation\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e6\u003c/span\u003e\u003c/sup\u003e\u003c/h2\u003e\n \u003cp\u003eFigure \u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003e shows the poor fit of regular parametric models to the follow-up from Benfari et al. for trivial FTR, suggesting the need for an alternative approach.\u003c/p\u003e\n \u003cp\u003eIn Fig. \u003cspan class=\"InternalRef\"\u003e3\u003c/span\u003ea, bathtub and Chen models have been fitted separately to all four FTR groups from both Benfari et al. For the Benfari et al. trivial group (best prognosis), it is clear that the Chen and bathtub models provide a superior visual fit. This is supported by the goodness of fit statistics which show a significant improvement over the regular parametric models (Table \u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003e).\u003c/p\u003e\n \u003cp\u003eThis is maintained across all four levels of FTR where the bathtub and Chen models provided almost identical visual fit (Fig. \u003cspan class=\"InternalRef\"\u003e3\u003c/span\u003e) and at least one of these models provided the best AIC/BIC score. Either bathtub or Chen models provided the best AIC and BIC scores (Table \u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003e) and neither model strayed from the 95% CIs of the KM plots. In contrast standard parametric models provided poorer AIC and BIC scores, poorer visual fit and almost all models strayed outside the KM 95% CIs (Supplementary section 2). Chen models were very similar to bathtub over 10 years observation time but following further extrapolation Chen models predicted more favourable longer-term survival (Supplement: section 3).\u003c/p\u003e\n \u003cp\u003e\u003cstrong\u003eEssayagh et al., 2021 study of mortality in patients with four levels of FTR under medical management\u003c/strong\u003e \u003csup\u003e\u0026nbsp;\u003cstrong\u003e\u0026nbsp;\u003cspan class=\"CitationRef\"\u003e9\u003c/span\u003e\u0026nbsp;\u003c/strong\u003e\u0026nbsp;\u003c/sup\u003e\u003c/p\u003e\n \u003cp\u003eKM plot 95% CIs were wider than in the larger Benfari et al. study. For all four levels of FTR bathtub and Chen models provided similar and the best models according to visual fit (Fig. \u003cspan class=\"InternalRef\"\u003e3\u003c/span\u003eb (right)). Either bathtub or Chen models provided the best AIC and BIC scores (Table \u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003e) and both models did not stray appreciably outside the KM 95% CIs. Standard models presented poorer visual fit. (Supplement: section 4)\u003c/p\u003e\n \u003cdiv class=\"gridtable\"\u003e\u0026nbsp;\u003ctable id=\"Tab2\" border=\"1\"\u003e\n \u003ccaption language=\"En\"\u003e\n \u003cdiv class=\"CaptionNumber\"\u003eTable 2\u003c/div\u003e\n \u003cdiv class=\"CaptionContent\"\u003e\n \u003cp\u003eInformation criteria (AIC BIC) scores for parametric models; Tricuspid Regurgitation, microfracture and atrial occlusion studies\u003c/p\u003e\n \u003c/div\u003e\n \u003c/caption\u003e\n \u003ccolgroup cols=\"15\"\u003e\u003c/colgroup\u003e\n \u003cthead\u003e\n \u003ctr\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eModel\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eAIC\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eBIC\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\u0026nbsp;\u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eModel\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eAIC\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eBIC\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\u0026nbsp;\u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eModel\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eAIC\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eBIC\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\u0026nbsp;\u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eModel\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eAIC\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eBIC\u003c/p\u003e\n \u003c/th\u003e\n \u003c/tr\u003e\n \u003c/thead\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" colspan=\"3\"\u003e\n \u003cp\u003e\u003cem\u003eBenfari et al., Trivial functional regurgitation\u003c/em\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\" colspan=\"3\"\u003e\n \u003cp\u003e\u003cstrong\u003eEssayagh et al., Trivial functional regurgitation\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\" colspan=\"3\"\u003e\n \u003cp\u003e\u003cstrong\u003eTribouilloy et al., functional regurgitation\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\" colspan=\"3\"\u003e\n \u003cp\u003e\u003cstrong\u003eBae et al., microfracture of the knee\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003ebathtub\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e11391.6\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e11410.72\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003ebathtub\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2273.44\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2290.66\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eggamma\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1182.412\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1196.128\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eggamma\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e227.83\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e236.53\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eChen\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e11457.57\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e11470.31\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eChen\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2281.45\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2292.93\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003ebathtub\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1184.632\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1198.349\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eGompertz\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e227.83\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e233.63\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eggamma\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e11489.82\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e11508.94\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eWeibull\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2281.51\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2292.99\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003elognormal\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1185.011\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1194.156\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eWeibull\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e228.84\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e234.64\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eWeibull\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e11550.12\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e11562.86\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eggamma\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2281.76\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2298.98\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eloglogistic\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1194.666\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1203.81\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eChen\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e228.30\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e234.09\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eloglogistic\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e11643.51\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e11656.26\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eexponential\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2282.99\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2288.73\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eWeibull\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1196.236\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1205.381\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eRayleigh 2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e229.11\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e234.90\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eGompertz\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e11733.51\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e11746.25\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eloglogistic\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2283.69\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2295.17\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eGompertz\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1198.722\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1207.866\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eRayleigh 1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e229.52\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e232.41\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003elognormal\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e11745.43\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e11758.18\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003egompertz\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2284.83\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2296.31\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eexponential\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1208.135\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1212.707\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eloglogistic\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e232.44\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e238.24\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eexponential\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e11769.46\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e11775.83\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eRayleigh 2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2284.85\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2296.33\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eChen\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1208.419\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1217.564\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003elognormal\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e237.58\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e243.38\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eRayleigh 2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e11741.83\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e11754.58\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003elognormal\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2294.47\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2305.96\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eRayleigh 1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1501.44\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1506.012\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eexponential\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e272.94\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e275.84\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eRayleigh 1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e14945.58\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e14951.95\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eRayleigh 1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2580.30\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2586.04\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eRayleigh 2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eNA\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eNA\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003ebathtub\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eNA\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eNA\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" colspan=\"3\"\u003e\n \u003cp\u003e\u003cem\u003eBenfari.et al Mild functional regurgitation\u003c/em\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\" colspan=\"3\"\u003e\n \u003cp\u003e\u003cstrong\u003eEssayagh. et al Mild functional regurgitation\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\" colspan=\"3\"\u003e\n \u003cp\u003e\u003cstrong\u003eTRISCEND II control arm\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003ebathtub\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e11903.75\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e11922.76\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eChen\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2790.99\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2802.04\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003elognormal\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e294.6\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e301.4\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eChen\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e11981.74\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e11994.42\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eGgamma\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2859.81\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2876.39\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eggamma\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e294.7\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e304.9\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003elognormal\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e12203.39\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e12216.07\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eWeibull\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2874.22\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2885.27\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003ebathtub\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e294.9\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e305.1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eggamma\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e12015.36\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e12034.37\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eloglogistic\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2892.36\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2903.41\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eloglogistic\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e296.5\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e303.3\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eWeibull\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e12062.17\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e12074.84\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003ebathtub\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2893.42\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2910.00\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eChen\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e296.7\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e303.5\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eloglogistic\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e12158.08\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e12170.76\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eexponential\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2906.42\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2911.95\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eWeibull\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e296.9\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e303.7\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eGompertz\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e12382.84\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e12395.51\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003egompertz\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2908.39\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2919.44\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eGompertz\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e297.0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e303.8\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eexponential\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e12505.97\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e12512.31\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eRayleigh 2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2908.39\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2919.45\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eexponential\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e309.4\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e312.8\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eRayleigh 2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e12416.85\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e12429.52\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003elognormal\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e3016.19\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e3027.24\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eRayleigh 1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e385.8\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e389.2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eRayleigh 1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e16861.08\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e16867.41\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eRayleigh 1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e3528.87\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e3534.40\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eRayleigh 2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" colspan=\"3\"\u003e\n \u003cp\u003e\u003cem\u003eBenfari.et al. Moderate functional regurgitation\u003c/em\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\" colspan=\"3\"\u003e\n \u003cp\u003e\u003cstrong\u003eEssayagh et al., Moderate functional regurgitation\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\" colspan=\"3\"\u003e\n \u003cp\u003e\u003cstrong\u003eWhitlock et al., left atrial appendage No occlusion\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eChen\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e7019.15\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e7030.59\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003ebathtub\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1587.68\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1601.61\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eChen\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1847\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1859\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003ebathtub\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e7019.35\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e7036.51\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eggamma\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1592.95\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1606.88\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003ebathtub\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1851\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1869\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eggamma\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e7046.38\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e7063.54\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eWeibull\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1593.39\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1602.68\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003elognormal\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1901\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1912\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eWeibull\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e7072.59\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e7084.03\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eChen\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1594.52\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1603.80\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eWeibull\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1905\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1917\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eloglogistic\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e7165.33\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e7176.77\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eloglogistic\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1600.24\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1609.53\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eloglogistic\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1905\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1917\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003elognormal\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e7214.13\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e7225.57\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eGompertz\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1602.95\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1612.24\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eggamma\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1907\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1924\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eGompertz\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e7255.78\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e7267.22\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eRayleigh 2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1603.59\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1612.87\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eGompertz\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2117\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2129\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eRayleigh 2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e7272.49\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e7283.93\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eexponential\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1604.87\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1609.52\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eRayleigh 2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2159\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2171\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eexponential\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e7322.90\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e7328.62\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003elognormal\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1610.09\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1619.37\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eexponential\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2199\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2205\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eRayleigh 1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e10139.16\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e10144.88\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eRayleigh 1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1990.27\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1994.92\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eRayleigh 1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e3007\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e3013\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" colspan=\"3\"\u003e\n \u003cp\u003e\u003cem\u003eBenfari.et al) Severe functional regurgitation\u003c/em\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\" colspan=\"3\"\u003e\n \u003cp\u003e\u003cstrong\u003eEssayagh.et al. Severe functional regurgitation\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\" colspan=\"3\"\u003e\n \u003cp\u003e\u003cstrong\u003eWhitlock et al., left atrial appendage occlusion\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003ebathtub\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2442.81\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2456.65\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003ebathtub\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e457.1133\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e466.2821\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eChen\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1353.035\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1364.584\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eggamma\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2466.09\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2479.93\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eloglogistic\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e457.9641\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e464.0766\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eggamma\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1378.3\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1341.1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003elognormal\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2469.57\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2478.80\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003elognormal\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e454.7669\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e460.8794\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003ebathtub\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1381.676\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1398.999\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eWeibull\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2470.93\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2480.16\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eGgamma\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e456.7364\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e465.9051\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003elognormal\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1400.537\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1412.086\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eloglogistic\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2485.78\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2495.01\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eWeibull\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e459.2854\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e465.3979\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eloglogistic\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1406.278\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1417.827\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eChen\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2487.90\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2497.12\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003egompertz\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e459.9671\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e466.0796\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eWeibull\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1406.585\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1418.134\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eGompertz\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2515.70\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2524.92\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eRayleigh 2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e461.6414\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e467.7539\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eGompertz\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1542.111\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1553.659\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eexponential\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2565.68\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2570.30\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eexponential\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e466.8290\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e469.8853\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eexponential\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1651.162\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1656.937\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eRayleigh 1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e3710.03\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e3714.64\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eChen\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e467.3864\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e473.4988\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eRayleigh 1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2266.306\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2272.08\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eRayleigh 2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eNA\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eNA\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eRayleigh 1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e648.6065\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e651.6627\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eRayleigh 2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eNA\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eNA\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" colspan=\"15\"\u003e\n \u003cp\u003eNA\u0026thinsp;=\u0026thinsp;Not applicable model did not converge\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n \u003c/table\u003e\n \u003c/div\u003e\n\u003c/div\u003e\n\u003cdiv class=\"Heading\"\u003e\u003cstrong\u003eTribouilloy et al 2024 of mortality in a French cohort with isolated functional tricuspid regurgitation\u003c/strong\u003e\u003csup\u003e\u003cstrong\u003e\u003cspan class=\"CitationRef\"\u003e10\u003c/span\u003e\u003c/strong\u003e\u003c/sup\u003e\u003c/div\u003e\n\u003cp\u003eChen and bathtub models generated very similar good visual fit (Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e4\u003c/span\u003eb (middle)). Generalised gamma and bathtub provided the best AIC BIC scores, while Chen provided poor AIC BIC scores (Table\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003e). With extrapolation to 25 years the generalised gamma model predicted clinically implausible 50% survival and other standard parametric models similarly predicted substantial proportion of patients surviving beyond 25 years (Supplementary: section 3) generating overoptimistic survival curves for an elderly population with serious comorbidities. Only bathtub and Chen models generated plausible long-term extrapolations and both generated U shaped hazard plots (Supplement: section 5).\u003c/p\u003e\n\u003cdiv id=\"Sec8\" class=\"Section2\"\u003e\n \u003ch2\u003eBae et al., 2013; Korean Cohort with degenerative osteoarthritic knee treated by microfracture\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e11\u003c/span\u003e\u003c/sup\u003e\u003c/h2\u003e\n \u003cp\u003eAfter ten years of follow-up, around 50% of microfracture-treated knees required TKA in this cohort. Over the observation period all parametric models except lognormal loglogistic and exponential generated reasonably good visual fit with similar AIC BIC scores; Chen, Gompertz and Rayleigh models generated well-fitting models (Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e4\u003c/span\u003ea (left), Supplement: section 7). On extrapolation of models to 25 years there were considerable differences between models with only Gompertz and Chen models predicting 100% failure within 20 years. The hazard for failure of other models barely changed over the observation period and beyond (Supplement: section 7) despite ageing of the population and inevitable wear and tear of the microfracture-treated knee. The more clinically plausible scenario would seem to be an increasing hazard that gets steeper with increasing age of patient, progressive wear and tear, and the exacerbation of osteoarthritis through time. This scenario is best satisfied by the Rayleigh, Gompertz and Chen models.\u003c/p\u003e\n\u003c/div\u003e\n\u003ch3\u003eOcclusion versus no-occlusion of left atrial appendage (RCT; Whitlock et al.,2021)\u003c/h3\u003e\n\u003cp\u003eA bathtub model for the no-occlusion arm (Fig. \u003cspan class=\"InternalRef\"\u003e4\u003c/span\u003ec (right)) generated superior AIC/BIC scores relative to standard parametric models and better visual fit; all standard models for the no-occlusion arm generated poor visual fit (Supplement: section 8). The Chen model AIC BIC scores were superior to those for 3-parameter bathtub despite its poor visual fit, and the hazard plot differed from the bathtub (3-parameter) hazard. The Chen model appears unsuited to substantial and rapid initial accumulation of events as found in both arms of this RCT. For the intervention arm (occlusion) the 3-parameter bathtub model again generates a good visual fit and Chen 2-parameter model a poor fit (Fig. \u003cspan class=\"InternalRef\"\u003e4\u003c/span\u003ec) while several standard models (e.g. Weibull) generated good visual fit for the intervention arm (Supplement: section 8).\u003c/p\u003e\n\u003ch3\u003eTotal Hip Replacement (THR) (Registry studies)\u003c/h3\u003e\n\u003cp\u003eRevision after THR failure varies according to many characteristics of both THR device and patient age, gender, and other demographics of patient populations. The \u003cem\u003eNational Joint Registry Annual report 20 (2023)\u003c/em\u003e \u003csup\u003e\u003cspan class=\"CitationRef\"\u003e13\u003c/span\u003e\u003c/sup\u003e itemises many KM plots for cumulative failure of THR. We analysed failure for THR recipients with osteoarthritis, for recipients of cemented metal on polythene and of ceramic on polythene devices, and for re-revision after first THR revision. In each of these four examples bathtub and Chen models provided the best visual fit and almost identical models (Fig. \u003cspan class=\"InternalRef\"\u003e5\u003c/span\u003e) accompanied by the lowest AIC/BIC scores (Table \u003cspan class=\"InternalRef\"\u003e3\u003c/span\u003e). Standard models provided poorer visual fit (Supplement: section 9) and poorer AIC/BIC scores.\u003c/p\u003e\n\u003cdiv class=\"gridtable\"\u003e\u0026nbsp;\u003ctable id=\"Tab3\" border=\"1\"\u003e\n \u003ccaption language=\"En\"\u003e\n \u003cdiv class=\"CaptionNumber\"\u003eTable 3\u003c/div\u003e\n \u003cdiv class=\"CaptionContent\"\u003e\n \u003cp\u003eGoodness of fit statistics for models fitted to THR data\u003c/p\u003e\n \u003c/div\u003e\n \u003c/caption\u003e\n \u003ccolgroup cols=\"7\"\u003e\u003c/colgroup\u003e\n \u003cthead\u003e\n \u003ctr\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eModel\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eAIC\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eBIC\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\u0026nbsp;\u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eModel\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eAIC\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eBIC\u003c/p\u003e\n \u003c/th\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003cth align=\"left\" colspan=\"3\"\u003e\n \u003cp\u003e\u003cem\u003eTHR Osteoarthritis\u003c/em\u003e\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\u0026nbsp;\u003c/th\u003e\n \u003cth align=\"left\" colspan=\"3\"\u003e\n \u003cp\u003e\u003cem\u003eTHR cemented ceramic on polythene\u003c/em\u003e\u003c/p\u003e\n \u003c/th\u003e\n \u003c/tr\u003e\n \u003c/thead\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eChen\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e300.2661\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e308.4213\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eChen\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e296.4028\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e305.1967\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003ebathtub\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e301.9992\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e314.232\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003ebathtub\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e296.7181\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e309.9089\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eexponential\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e302.1448\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e306.2224\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eGompertz\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e298.4029\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e307.1967\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eGompertz\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e303.7814\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e311.9367\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eexponential\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e298.5097\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e302.9066\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eRayleigh 2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e303.8298\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e311.9851\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eRayleigh 2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e298.8838\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e307.6777\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eWeibull\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e303.8698\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e312.0251\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eWeibull\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e300.4538\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e309.2477\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eloglogistic\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e304.1212\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e312.2765\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eloglogistic\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e300.6615\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e309.4553\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eggamma\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e305.6258\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e317.8587\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eggamma\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e302.2484\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e315.4392\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003elognormal\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e307.6922\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e315.8475\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003elognormal\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e303.9896\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e312.7835\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eRayleigh 1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e328.2803\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e332.358\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eRayleigh 1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e314.5399\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e318.9368\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" colspan=\"3\"\u003e\n \u003cp\u003e\u003cstrong\u003eTHR re-revision\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\" colspan=\"3\"\u003e\n \u003cp\u003e\u003cstrong\u003eTHR cemented metal on polythene\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eChen\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e346.0576\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e352.6442\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eChen\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e316.8134\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e325.2426\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003ebathtub\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e348.9028\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e358.7827\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003ebathtub\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e318.0951\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e330.7389\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eWeibull\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e349.3799\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e355.9665\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eexponential\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e319.2385\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e323.4531\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eloglogistic\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e349.5192\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e356.1058\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eGompertz\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e319.798\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e328.2272\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003elognormal\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e349.6722\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e356.2588\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eRayleigh 2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e319.9957\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e328.4249\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eggamma\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e351.3068\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e361.1867\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eWeibull\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e321.2365\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e329.6658\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eGompertz\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e360.9285\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e367.5151\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eloglogistic\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e321.5145\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e329.9437\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eexponential\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e368.2898\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e371.5831\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eggamma\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e322.9653\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e335.6091\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eRayleigh 1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e471.5511\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e474.8444\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003elognormal\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e325.9746\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e334.4038\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eRayleigh 2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eNA\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eNA\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eRayleigh 1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e339.8937\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e344.1083\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" colspan=\"7\"\u003e\n \u003cp\u003eNA\u0026thinsp;=\u0026thinsp;Not applicable model did not converge\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n \u003c/table\u003e\n\u003c/div\u003e\n\u003cp\u003e\u003cstrong\u003eTriscend II RCT: tricuspid valve replacement with EVOQUE system for patients with tricuspid regurgitation\u003c/strong\u003e.\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e8\u003c/span\u003e\u003c/sup\u003e\u003c/p\u003e\n\u003cp\u003eThe US FDA presented KM plots for mortality in the TRISCEND II trial (see Supplementary: section 6). For the medical treatment arm bathtub and Chen models generated almost identical good visual fit for the cumulative incidence of death. Weibull and generalised gamma models delivered marginally lower IC values than bathtub and Chen models but on extrapolation produced less plausible mortality curves for such an aged population with extensive comorbidities. The bathtub \u003cem\u003eg\u003c/em\u003e parameter is almost zero so that bathtub and Rayleigh 2 models predict virtually identical curves for survival and for hazard. All models fitted to the intervention arm generated clearly implausible survival curves. Longer follow up with more patients is required for modelling.\u003c/p\u003e\n\u003cdiv id=\"Sec11\" class=\"Section2\"\u003e\n \u003ch2\u003eAre bathtub and Chen model predictions supported by longer term follow up Registry findings?\u003c/h2\u003e\n \u003cp\u003eWe compared extrapolated bathtub and Chen model predictions for Registry cumulative failure rates with that reported for later registry analyses. For this we used the National Joint registry 9th annual report (NJR9) for England and Wales \u003csup\u003e\u003cspan class=\"CitationRef\"\u003e12\u003c/span\u003e\u003c/sup\u003e with the 20th annual report\u003csup\u003e13 (NJR20)\u003c/sup\u003e. The NJR9 and NJR20 KM plots for frequently used devices show increasing revision rates over time (Fig. \u003cspan class=\"InternalRef\"\u003e6\u003c/span\u003e). Performance of cemented MOP and cemented COP devices was reasonably consistent across these time spans, but in the case of uncemented MOP revision performance appears to have improved with time.\u003c/p\u003e\n \u003cp\u003eUsing NJR9, \u003csup\u003e\u003cspan class=\"CitationRef\"\u003e12\u003c/span\u003e\u003c/sup\u003e) Chen and bathtub models of 125,285 cemented MOP recipients suggests predict between 6% and 7% cumulative revision rate at 18 years, consistent with 6.6% reported in NJR20, when about 2.94 times as many recipients (N\u0026thinsp;=\u0026thinsp;368,641) were available for analysis (Fig. \u003cspan class=\"InternalRef\"\u003e6\u003c/span\u003ea top).\u003c/p\u003e\n \u003cp\u003eChen and bathtub extrapolations for 59,983 uncemented MOP recipients predict 6% and 12% cumulative revision respectively. In this case, the NJR20 (N\u0026thinsp;=\u0026thinsp;205,001) revision rate is 8.5%, suggesting an average of these two models outperforms a single extrapolation (Fig. \u003cspan class=\"InternalRef\"\u003e6\u003c/span\u003eb middle).\u003c/p\u003e\n \u003cp\u003eChen and bathtub models of 13,871 cemented COP recipients from NJR9 predict about 5% and 6% cumulative revision respectively corresponding very closely to the 18-year follow up reported in NJR20 (Fig. \u003cspan class=\"InternalRef\"\u003e6\u003c/span\u003ec bottom).\u003c/p\u003e\n \u003cp\u003eSimilar results were found in analyses conducted using the Swedish Arthroplasty Registry (Supplement: section 10).\u003c/p\u003e\n\u003c/div\u003e"},{"header":"Discussion","content":"\u003cp\u003eThis paper has demonstrated the utility of the Chen and bathtub models when extrapolating time-to-event data across a range of settings. Their distinct forms show that there are situations where they outperform or provide substantially different extrapolations compared to the routine models. Broadening the set of candidate models might allow for more accurate predictions, or at least exploration of a wider set of alternative scenarios exploring potential uncertainty.\u003c/p\u003e \u003cp\u003eHence, models with U-shaped hazard rates such as Chen or bathtub, alongside other alternative models, such as Rayleigh-1 or -2 parameter models should be included in the routine set of models considered when extrapolating these outcomes in a HTA setting. The improved accuracy of predicting long-term outcomes can result in fairer valuations of health technologies for technology developers and healthcare providers, and better decisions being made. This is particularly relevant for first-in-class technologies, where there exists no data on long-term effects of any similar technology and therefore the probability of a future adverse outcome is higher.\u003c/p\u003e \u003cp\u003eU-shaped models should also be considered in applications of model averaging, which has already been shown to be beneficial in some cases\u003csup\u003e\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e\u003c/sup\u003e. In cases where little is known about patient outcomes beyond an observed follow-up period, it can only be considered fair to include candidate models where the hazard rate increases over time when you are also including models which assume the opposite (e.g. log-normal and log-logistic). Of course, models should be scrutinised for plausibility which may rule out certain functional forms, and so we do not see any downsides to including the U-shaped models described in this paper within the set of candidate models.\u003c/p\u003e \u003cp\u003eThese results raise the question of why these models are not already included within HTA submissions. This may be because U-shaped models are not referred to in the NICE Technical Support Documents which relate to survival analysis. \u003csup\u003e\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e, \u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e\u003c/sup\u003e Given their tendency for an increasing hazard rate, we anticipate that their extrapolations will be more pessimistic compared to the routine parametric models. Hence, it is unlikely that submissions to NICE from pharmaceutical companies will introduce these models without prompting, where more optimistic extrapolations are typically preferred, allowing the quality adjusted life-year gains to be collected over a longer time-period.\u003c/p\u003e \u003cp\u003eThese models could also be used in a mixture cure model (MCM) setting, which would permit an increasing hazard rate for a subgroup of the population, whilst the remaining population are considered cured or are subject to a background event rate. MCMs are increasingly relevant as emerging technologies such as gene and CAR-T therapies show potential to transform patient outcomes. Use of bathtub or Chen models in this setting might be more palatable to pharmaceutical companies, as the increasing hazard rate would not apply to \u0026ldquo;cured\u0026rdquo; patients and so they will not necessarily produce the most pessimistic extrapolations.\u003c/p\u003e \u003cp\u003eA strength of this work is how the benefits of U-shaped models have been shown to apply beyond a single case-study or disease area. We have has used publicly available data, and provided code where helpful, maximising the transparency, reproducibility and ease of implementation of the models described.\u003c/p\u003e \u003cp\u003eA limitation of this research is that we have not considered flexible models such as fractional polynomials or restricted cubic splines. Whilst these can fit very well to the data, they are in danger of overfitting and providing implausible extrapolations, or of relying on key assumptions to be made beyond the observed period of follow-up that can make them equivalent to an underlying parametric model. The flexibility of splines may sometimes result in a U-shaped hazard rate but may also take on many other forms, hence they cannot be relied upon to provide balance to models with n-shaped hazard rates. These models also rely on specification of combinations of terms, scales and knot locations in order to be optimised making a meaningful comparison more difficult, particularly across the range of different types of dataset in this paper. Standard parametric models have less subjectivity in how they are fitted making a comparison more straightforward, however future work could compare the fit and extrapolations of U-shaped models to these flexible approaches.\u003c/p\u003e"},{"header":"Conclusion","content":"\u003cp\u003eThis study has shown how models with U-shaped hazard rates can match or outperform models routinely used in HTA when fitting to observed data and predicting future survival rates in a range of fields.\u003c/p\u003e \u003cp\u003eThese models should be included in the regular set of parametric models considered when extrapolating time-to-event data.\u003c/p\u003e \u003cp\u003eBathtub and Chen models do not necessarily generate the same predictions despite having U-shaped hazard rate, they may differ slightly or greatly depending on the data and should both be considered.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cul type=\"disc\"\u003e\n \u003cli\u003eEthics approval and consent to participate: Not applicable\u003c/li\u003e\n \u003cli\u003eConsent for publication: Not applicable\u003c/li\u003e\n \u003cli\u003eAvailability of data and materials: Not applicable\u003c/li\u003e\n \u003cli\u003eCompeting interests: None to declare\u003c/li\u003e\n \u003cli\u003eFunding: No funding was received specific to this work however DG is supported by NIHR award 14/25/05\u003c/li\u003e\n \u003cli\u003eAuthors' contributions: MC had the original research idea and performed all modelling. DG produced the manuscript and contributed to developing the research idea.\u003c/li\u003e\n \u003cli\u003eClinical trial number: Not applicable\u003c/li\u003e\n \u003cli\u003eAcknowledgements: None\u003c/li\u003e\n\u003c/ul\u003e"},{"header":"References","content":"\u003col\u003e\n \u003cli\u003eGallacher, D, Auguste, P, Connock, M. How Do Pharmaceutical Companies Model Survival of Cancer Patients? A Review of NICE Single Technology Appraisals in 2017. International Journal of Technology Assessment in Health Care 2019;35(2):160-167.\u003c/li\u003e\n \u003cli\u003eCollet, D. Modelling survival data in medical research\u003cem\u003e.\u003c/em\u003e 2 ed.: Chapman \u0026amp; Hall, 2003.\u003c/li\u003e\n \u003cli\u003eChen, Z. A new two-parameter lifetime distribution with bathtub shape or increasing failure rate function. Statistics \u0026amp; Probability Letters 2000;49:155-161.\u003c/li\u003e\n \u003cli\u003ePeace, KE. Design and analysis od clinical trials with time-to-event endpoints\u003cem\u003e.\u003c/em\u003e Chapman \u0026amp; Hall/CRC, 2009.\u003c/li\u003e\n \u003cli\u003eCrowther, MJ, Lambert,P.C. stgenreg: A Stata Package for General Parametric Survival Analysis. Journal of Statistical Software 2013;53(`12).\u003c/li\u003e\n \u003cli\u003eBenfari, G, Antoine, C, Miller, WL, et al. Excess Mortality Associated With Functional Tricuspid Regurgitation Complicating Heart Failure With Reduced Ejection Fraction. Circulation 2019;140(3):196-206.\u003c/li\u003e\n \u003cli\u003eWhitlock, RP, Belley-Cote, EP, Paparella, D, et al. Left Atrial Appendage Occlusion during Cardiac Surgery to Prevent Stroke. N Engl J Med 2021;384(22):2081-2091.\u003c/li\u003e\n \u003cli\u003eFDA. PMA P230013: FDA Summary of Safety and Effectiveness Data 2024. https://www.accessdata.fda.gov/cdrh_docs/pdf23/P230013B.pdf. Accessed.\u003c/li\u003e\n \u003cli\u003eEssayagh, B, Sabbag, A, Antoine, C, et al. The Mitral Annular Disjunction of Mitral Valve Prolapse: Presentation and Outcome. JACC Cardiovasc Imaging 2021;14(11):2073-2087.\u003c/li\u003e\n \u003cli\u003eTribouilloy, C, Vanhaecke, P, Dreyfus, J, et al. Natural History of Isolated Functional Tricuspid Regurgitation. J Am Heart Assoc 2024;13(9):e033933.\u003c/li\u003e\n \u003cli\u003eBae, DK, Song, SJ, Yoon, KH, et al. Survival analysis of microfracture in the osteoarthritic knee-minimum 10-year follow-up. Arthroscopy 2013;29(2):244-250.\u003c/li\u003e\n \u003cli\u003eNJR. National Joint Registry for England and Wales 9\u0026apos;th Annual Report; 2012. https://reports.njrcentre.org.uk/downloads. Accessed.\u003c/li\u003e\n \u003cli\u003eNJR. National Joint Registry Report for England and Wales 20\u0026apos;th annual report; 2023. http://www.ncbi.nlm.nih.gov. Accessed.\u003c/li\u003e\n \u003cli\u003eK\u0026auml;rrholm, J, Rogmark, C, Naucler, E, et al. Swedish hip arthroplasty register: annual report, 2018. Department of Orthopaedics, Sahlgrenska University Hospital 2019.\u003c/li\u003e\n \u003cli\u003eW-Dahl, A, K\u0026auml;rrholm, J, Rogmark, C, et al. Swedish hip arthroplasty register: annual report, 2023. Department of Orthopaedics, Sahlgrenska University Hospital 2024.\u003c/li\u003e\n \u003cli\u003eGuyot, P, Ades, AE, Ouwens, MJ, et al. Enhanced secondary analysis of survival data: reconstructing the data from published Kaplan-Meier survival curves. BMC Med Res Methodol 2012;12:9.\u003c/li\u003e\n \u003cli\u003eGallacher, D, Kimani, P, Stallard, N. Extrapolating Parametric Survival Models in Health Technology Assessment Using Model Averaging: A Simulation Study. Medical Decision Making 2021;41(4):476-484.\u003c/li\u003e\n \u003cli\u003eRutherford, MJ, Lambert, PC, Sweeting, MJ, et al. NICE DSU technical support document 21: flexible methods for survival analysis. Decision Support Unit, ScHARR, University of Sheffield 2020.\u003c/li\u003e\n \u003cli\u003eLatimer, N. NICE DSU technical support document 14: survival analysis for economic evaluations alongside clinical trials-extrapolation with patient-level data. Report by the Decision Support Unit 2011.\u003cem\u003e\u003c/em\u003e\u003c/li\u003e\n\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"bmc-medical-informatics-and-decision-making","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"midm","sideBox":"Learn more about [BMC Medical Informatics and Decision Making](http://bmcmedinformdecismak.biomedcentral.com/)","snPcode":"","submissionUrl":"https://www.editorialmanager.com/midm/default.aspx","title":"BMC Medical Informatics and Decision Making","twitterHandle":"BMC_series","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"em","reportingPortfolio":"BMC Series","inReviewEnabled":true,"inReviewRevisionsEnabled":true},"keywords":"Survival Analysis, Extrapolation, Health Technology Assessment, Parametric models","lastPublishedDoi":"10.21203/rs.3.rs-5303870/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-5303870/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eIn health technology assessment (HTA), extrapolation of time-to-event data is common to estimate the benefit of a new health technology beyond the observed period of data. The regular set of parametric models commonly used for extrapolation does not include models which assume a U-shaped hazard rate, that is initially decreasing and then increasing hazard rate.\u003c/p\u003e\n\u003cp\u003eWe compared the visual and statistical fit and prediction of models which assume a U-shaped hazard rate (Chen, bathtub and Rayleigh) to the regular set of parametric models (exponential, log-normal, log-logistic, Weibull, generalised gamma, Gompertz) across a range of settings and data types, including hip arthroplasty, functional tricuspid regurgitation and knee osteoarthritis.\u003c/p\u003e\n\u003cp\u003eU-shaped hazard models outperformed or matched standard parametric models in visual fit, goodness of fit statistics and long-term predictions when compared to extended follow-up.\u003c/p\u003e\n\u003cp\u003eBathtub models should feature routinely in HTA submissions involving extrapolation of survival data, allowing for exploration of a wider range of scenarios and potentially more accurate predictions, resulting in better informed valuation and decision making for emerging health technologies.\u003c/p\u003e","manuscriptTitle":"Broadening the candidate set of parametric models when extrapolating survival: the case for models with U-shaped hazards.","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2024-11-04 18:26:23","doi":"10.21203/rs.3.rs-5303870/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Revision requested","date":"2024-10-29T13:15:54+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2024-10-25T11:01:55+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2024-10-25T10:59:32+00:00","index":"","fulltext":""},{"type":"submitted","content":"BMC Medical Informatics and Decision Making","date":"2024-10-21T11:07:02+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"bmc-medical-informatics-and-decision-making","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"midm","sideBox":"Learn more about [BMC Medical Informatics and Decision Making](http://bmcmedinformdecismak.biomedcentral.com/)","snPcode":"","submissionUrl":"https://www.editorialmanager.com/midm/default.aspx","title":"BMC Medical Informatics and Decision Making","twitterHandle":"BMC_series","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"em","reportingPortfolio":"BMC Series","inReviewEnabled":true,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"b375d676-1ee0-48be-a7ad-667f5c9bd451","owner":[],"postedDate":"November 4th, 2024","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"under-review","subjectAreas":[],"tags":[],"updatedAt":"2026-01-15T21:53:20+00:00","versionOfRecord":[],"versionCreatedAt":"2024-11-04 18:26:23","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-5303870","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-5303870","identity":"rs-5303870","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}