Time to Failure Among Stroke Patients in Jigjiga, Ethiopia: An Application of Bayesian Accelerated Failure Time

Time to Failure Among Stroke Patients in Jigjiga, Ethiopia: An Application of Bayesian Accelerated Failure Time | 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 Time to Failure Among Stroke Patients in Jigjiga, Ethiopia: An Application of Bayesian Accelerated Failure Time Mustafe Abdi Ali, Abdisalan Ahmed Osman This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8290511/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract Stroke, a global health issue causing cerebrovascular conditions, affects millions annually, particularly in developing countries like Ethiopia, due to lifestyle changes, urbanization, and risk factors. The study examines the time to failure in stroke patients at Sheik Hassan Yabare Comprehensive Specialized Hospital in Ethiopia, highlighting the importance of understanding factors influencing survival times for improved patient outcomes. A retrospective study at Sheik Hassan Yabare Comprehensive Specialized Hospital analyzed stroke patients using Kaplan-Meier plots, the long-rank test, the Cox proportional hazards model, and the Accelerated Failure Time model. Akaike's Information Criterion was used to compare the effectiveness of models, and the Bayesian Accelerated Failure Time model was employed to identify factors affecting the time to failure of strokes. The study involved 353 stroke patients, with 26.6% female and 73.4% male. Male patients had a lower mortality rate of 26.3% compared to females at 42.6%. The majority of patients were from urban areas, with a mortality rate of 51.3% in rural areas and 19.8% in urban areas. The age distribution was categorized into three groups: 18–48, 49–65, and > 65, with corresponding death proportions of 21.6%, 18.9%, and 24.8%, respectively. Ischemic and hemorrhagic strokes had a combined mortality rate of 55.5%. A significant percentage of hypertension patients were censored, with 149 (80.5%) being censored and 36 (19.5%) experiencing death. The median estimated survival time for stroke patients was 48 days. Diabetes was the most effective variable related to patient survival, with a significant positive coefficient. Other factors, such as habit, hypertension, and cerebral vascularization failure, are less impactful. AFT Cerebrovascular Bayesian Jigjiga SHYCSH Stroke Figures Figure 1 Figure 2 1. Introduction Stroke is one of the main causes of mortality and acquired disability in the world ( 1 ); The Global Burden of Disease study reveals stroke as the second most common cause of mortality and the third most common cause of both mortality and disability globally ( 2 ). Stroke causes approximately 5.5 million deaths annually globally, resulting in over 116 million years of healthy life loss due to stroke-related mortality and disability ( 3 ). The World Health Organization defines stroke as sudden, clinical symptoms disrupting cerebral functioning, lasting over 24 hours, or causing death, primarily due to vascular origin ( 4 ). Strokes can be classified as ischemic or hemorrhagic, with disruptions or diminished cerebral blood flow ( 4 – 6 ). Currently, there is a global rise in the burden of stroke-related death, morbidity, and disability ( 7 , 8 ). Over 15 million people globally experience a stroke annually, with approximately five million experiencing physical impairment ( 9 ). Stroke is a severe health condition causing significant mortality, with tilting ischemic attacks having the best prognosis, followed by carotid stenosis and arterial obstruction. Stroke cases are categorized into two main types: ischemic stroke, where an artery in the cerebral vascular area becomes blocked, and hemorrhagic stroke, where a blood vessel ruptures, causing cerebral hypoxemia and brain cell damage ( 10 – 12 ). Metabolic hazards, such as high SBP, BMI, FPG, cholesterol, and glomerular filtration rate, account for 72.1% of stroke burden ( 3 ). The incidence of stroke is influenced by factors such as age, gender, ethnicity, and genetics ( 3 , 12 , 13 ). Stroke, a vascular illness, is the second leading cause of Disability-Adjusted Life Years (DALY) worldwide, causing millions of deaths due to lifestyle changes in low- and middle-income countries ( 14 ). A study in sub-Saharan Africa found a 40% case fatality rate over five years, with diabetes patients having a worse prognosis ( 15 ). Ethiopia's socio-economic impoverishment has led to a focus on communicable diseases, neglecting non-communicable ones like stroke, resulting in a significant public health issue ( 16 , 17 ). Multiple studies have been conducted on the topic of stroke in various locations in Ethiopia ( 18 – 20 ). The incidence of stroke in Ethiopia has been steadily rising, accounting for 7.5% to 19.3% of hospital admissions and resulting in about 11% to 42.8% mortality rates between 2014 and 2019 ( 21 , 22 ). The focus of the present investigation was the duration till the demise of individuals affected by stroke. Survival analysis is a statistical method that analyzes data from a certain starting point to the occurrence of a particular event or endpoint. It is a suitable tool for analyzing this sort of data ( 22 – 24 ). The study uses Bayesian Survival analysis to analyze stroke patient data, identifying factors associated with the duration until failure. This helps develop personalized treatment strategies and improve patient prognosis. The analysis evaluates prediction performance, investigates variations, and analyzes follow-up data, enhancing stroke patient prognosis and clinical decision-making. Bayesian survival analysis is gaining interest due to its adaptable outcomes. The aim is to analyze the risk factors of stroke patients at Sheik Hassan Yabare Comprehensive Specialized Hospital in Ethiopia from 2019 to 2023 using Bayesian survival analysis. 2. Methods 2.1 Study Area The study was conducted in Sh. Hassan Yabare Referral Hospital in Jigjiga city administration between January 1, 2019, and May 31, 2024. Jigjiga, situated in eastern Ethiopia, approximately 630km from Addis Ababa, serves as the capital city of the Somali Region. According to the 2007 data from the Central Statistical Agency, Jigjiga had a population of 125,876, with 67,128 males and 58,748 females. The city comprises four sub-cities and 22 kebeles. 2.2 Study Design and Population The study analyzed data on a Stroke patient from 2019 to 2023 at Sheikh Hassen Yabare Comprehensive Specialized Hospital in Jigjiga. The data was gathered from the patient's registration book and identity cards. A subset of data was selected from the patient's medical records from January 1, 2019, to May 31, 2024. The researcher used secondary data and a simple random sampling approach. The data on Stroke and the first dates of patient admission were obtained from the Stroke Centre at Sheikh Hassen Yabare Comprehensive Specialized Hospital. The investigation was conducted from January 1, 2019, to May 31, 2024. A retrospective study will gather data on 1,898 stroke patients at Sheikh Hassen Yabare Comprehensive Specialized Hospital in Ethiopia, meticulously examining registration logbooks and patient follow-up records. 2.3 Inclusion and Exclusion Criteria This study included all stroke patients who were registered and had complete information, as well as individuals who had at least one stroke therapy. Nevertheless, the study excluded patients who were under the age of 18, patients who did not initiate any stroke therapy, and those with insufficient medical data. 2.4 Study Variables Survival Time to Failure is a response variable measuring the difference between diagnosis and death, with 0 indicating censored and 1 indicating death. The factors of time to failure among stroke patients are sex, residency, Age, Stroke type, Habit, Cerebral vascularization failure, Atrial Fibrillation, Hypertension, and Diabetes. 2.5 Statistical Analysis Data analysis was conducted using both descriptive and inferential statistical methods. Kaplan–Meier survival curves and log-rank tests were employed to estimate and compare survival experiences across groups. A Bayesian Accelerated Failure Time (AFT) model was applied to identify predictors associated with time to failure among stroke patients. The model parameters were estimated using Markov Chain Monte Carlo (MCMC) simulation techniques, and posterior summaries were reported as posterior means with 95% credible intervals. Model comparison and goodness-of-fit were assessed using the Watanabe–Akaike Information Criterion (WAIC) and Leave-One-Out Cross-Validation (LOO-CV). All analyses were performed in R software. Accelerated Failure Time Model The Cox-PH model is commonly used for modeling survival data, whereas the AFT model is a parametric model that provides a better data fit. Both models differ in baseline hazard function and coefficient estimation methods ( 25 ). The AFT model measures the impact of explanatory factors on survival time through regression analysis of survival time against covariates, including Exponential, Weibull, Log-normal, and Log-logistic models ( 26 ). The AFT model can be written as follows:- $$\:log\left({T}_{i}\right)=\mu\:+{\beta\:}_{1}{X}_{1i}+,\dots\:,+{\beta\:}_{p}{X}_{pi}+\sigma\:{ϵ}_{i}$$ 1 2.6 Model Selection Criterion The Akaike Information Criterion was used to select the most suitable Accelerated Failure Time model from various models, comparing non-nested or varying parameter sets ( 27 ). AIC is obtained by: - $$\:AIC=2log\left(L\right)+kp$$ 2 The model with the least AIC value is regarded as the best-fitted model. The Bayesian Information Criteria (BIC) was employed to determine the optimal Accelerated Failure Time (AFT) model. The BIC is given by Schwarz ( 28 ). Bayesian Information Criteria is obtained by: - $$\:BIC=2log\left(L\right)+kp*log\left(n\right)$$ 3 2.7 Bayesian Analysis The Bayesian technique is preferred in survival analysis due to its powerful information. Bayesian analysis using Stan has gained popularity due to its efficiency and flexibility in parameter estimation and model comparison. Stan employs Hamiltonian Monte Carlo algorithms for full Bayesian inference, offering advantages over traditional maximum-likelihood methods ( 29 ). It allows for the straightforward implementation of custom distributions, making it suitable for cognitive modeling ( 30 ). The Bayesian approach is the most effective method for obtaining accurate estimates of the model ( 31 ). 2.8 Bayesian Accelerated Failure Time (AFT) Models Bayesian parametric models are fundamental in survival analysis due to their analytical tractability and flexibility in modeling time-to-event data. In this study, Bayesian Accelerated Failure Time (AFT) models were employed to analyze survival data with right censoring. The likelihood function was constructed by combining the density function \(\:f\left({t}_{i}|{x}_{i},\theta\:\right)\) for uncensored observations and the survival function \(\:S\left({t}_{i}|{x}_{i},\theta\:\right)\) for censored cases. The general log-likelihood function was formulated accordingly. Given the absence of a joint conjugate prior for both the regression coefficients \(\:\left(\beta\:\right)\) and the scale parameter ( \(\:{\sigma\:}^{2}\) ), the prior distributions were specified hierarchically. A multivariate normal prior was assumed for \(\:\beta\:|\:{\sigma\:}^{2}\:\sim\:{N}_{P}\left({\mu\:}_{0},\:{V}_{0}{\alpha\:}_{0}^{2}\right)\) , while an inverse gamma prior was placed on the variance term \(\:{\sigma\:}^{2}\sim\:IG\left(a,b\right)\) . The joint posterior distribution was then derived by combining the likelihood with these priors. Due to the lack of closed-form posterior solutions, Markov Chain Monte Carlo (MCMC) methods, particularly the Gibbs sampler, were used for posterior sampling. $$\:L\left(\theta\:|Data\right)=\prod\:_{i=1}^{n}\left[{f\left({t}_{i}|{X}_{i}\theta\:\right)}^{{\sigma\:}_{i}}*S{\left({t}_{i}|{X}_{i};\theta\:\right)}^{1-{\sigma\:}_{i}}\right]$$ 4 2.8.1 Log-normal AFT Model In the log-normal model, the logarithm of survival time is assumed to be normally distributed, such that \(\:T\sim\:LN\left({X}^{{\prime\:}}\beta\:,\frac{1}{\tau\:}\right)\) . The probability density function (PDF) and survival function were specified, and the joint posterior distribution of parameters was expressed using Bayes' theorem. The prior for β remained multivariate normal, and the variance component followed an inverse gamma distribution. The posterior distributions were sampled using MCMC, relying on the specification of full conditional distributions. 2.8.2 Log-logistic AFT Model The log-logistic distribution was also used, assuming \(\:T\sim\:LL\left({X}^{{\prime\:}}\beta\:,\sqrt{\tau\:}\right)\) . The density and survival functions were derived accordingly. The posterior distribution for \(\:\beta\:\) was expressed based on the combination of likelihood and prior information, with β again following a normal prior. MCMC sampling was employed to estimate the posterior distributions. Full conditional distributions for the parameters were specified, enabling Gibbs sampling. 2.8.3 Weibull AFT Model The Weibull distribution, one of the most widely used models in survival analysis, was also considered. Survival times \(\:{T}_{i}\) were assumed to follow a Weibull distribution with parameters \(\:\alpha\:\:and\:\lambda\:\) , where α > 0. The density function was parameterized as \(\:T\sim\:Weib\left(\sqrt{\tau\:},{e}^{-{X}^{{\prime\:}}\beta\:\sqrt{\tau\:}}\right)\) , with the survival function defined accordingly. The scale and shape parameters were assigned independent priors, with α\alpha following an inverse gamma distribution. As with the other models, the posterior distributions were obtained via MCMC sampling, given the complexity of the likelihood function and lack of analytical solutions. In all models, inference was based on the posterior distributions of the parameters. Convergence diagnostics and posterior summaries (mean, median, credible intervals) were assessed using standard Bayesian computational tools. 2.8.4 Log-normal AFT Model In the log-normal model, the logarithm of survival time is assumed to be normally distributed, such that \(\:T\sim\:LN\left({X}^{{\prime\:}}\beta\:,\frac{1}{\tau\:}\right)\) The probability density function (PDF) and survival function were specified, and the joint posterior distribution of parameters was expressed using Bayes' theorem. The prior for β remained multivariate normal, and the variance component followed an inverse gamma distribution. The posterior distributions were sampled using MCMC, relying on the specification of full conditional distributions. 3. Result The data for this study were collected from 353 patients who received treatments for HF at least once at Sheikh Hassen Yabare Comprehensive Specialized Hospital between January 1, 2019 to May 31, 2024. The study analyzed 353 stroke patients, with 26.6% being female and 73.4% being male. The mortality rate for male patients was 26.3%, lower than that for female patients at 42.6%. Most of the patients were from rural areas, with 34.3% having a rural residence and 65.6% having an urban one. In rural areas, 51.3% of patients experienced death, while in urban areas, 19.8% experienced death. The age groups included 11.9% in the 18–48 age group, 31.7% in the 49–65 age group, and 56.4% in the > 65 age group. Table 1 Descriptive Summary for Patients of Stroke Variable Category Total Patients Status No of Censored No of Death Sex Male Female 259 (73.4%) 94 (26.6%) 191 (73.7%) 54 (57.4%) 68 (26.3%) 40 (42.6%) Residence Rural Urban 121 (34.3%) 232 (65.6%) 59 (48.7%) 186 (80.2%) 62 (51.3%) 46 (19.8%) Age 18–48 49–65 ≥ 65 42 (11.9%) 112 (31.7%) 199 (56.4%) 39 (92.8%) 96 (85.7%) 110 (55.2%) 3 (7.2%) 16 (14.3%) 89 (44.8%) Stroke Type Ischemic Hemorrhagic 227 (64.3%) 126 (35.7%) 170 (74.9%) 75 (59.5%) 57 (25.1%) 51 (40.5%) Habit No Smoking Alcohol Chat & Smoking 47 (13.3%) 61(17.3%) 115(32.6%) 130 (36.8%) 39 (82.9%) 42 (68.8%) 83 (72.2%) 81 (62.3%) 8 (17.1%) 19 (31.2%) 32(27.8%) 49 (37.7%) CRF No Yes 213 (60.3%) 140(39.7%) 144 (67.6%) 101 (72.1%) 69 (32.3%) 39 (27.9%) Hypertension No Yes 185 (52.4%) 168 (47.6%) 149 (80.5%) 96 (57.1%) 36 (19.5%) 72 (42.9%) Atrial Fibrillation No Yes 83 (23.5%) 270 (76.5%) 74 (89.1%) 171 (63.3%) 9 (10.9%) 99 (36.7%) Diabetes Yes No 68 (19.3%) 285 (80.7%) 11 (16.2%) 234 (82.1%) 57 (83.8%) 51 (17.9%) The stroke distribution among the patients is as follows: 64.3% of the patients have Ischemic stroke, and 35.7% have Haemorrhagic stroke. The mortality rate for ischemic stroke is 25.1%, while the mortality rate for hemorrhagic stroke is 40.5%. Together, these two types of stroke account for a total mortality rate of 55.5%. Among the patients included in the research, 38.8% were found to be chewing khat, 19.5% were smoking, and 9% were consuming alcohol. The other patients 32.3% were not engaged in any of these habits. The majority of stroke patients do not have Cerebral Revascularization Failure. Approximately 39.7% of individuals have Cerebral Revascularization Failure, whereas the remaining 60.3% do not. Among hypertension patients, 185 individuals (52.4%) were hypertension-free. Out of the hypertension-free group, 149 patients (80.5%) were censored, meaning that their follow-up was terminated before the occurrence of the event of interest, while 36 patients (19.5%) experienced death during the study period. On the other hand, there were 168 patients (47.6%) identified as having hypertension. Among this group, 96 patients (57.1%) were censored, indicating premature termination of follow-up, while the remaining patients' outcomes were not specified. Based on data the data on atrial fibrillation shows that 89.1% of cases are censored, with 74 out of 83 cases being censored. Death cases are also censored, with 9 out of 83 cases resulting in death. The data is interpreted based on the presence or absence of atrial fibrillation. In cases without atrial fibrillation, 74 cases are censored, while 99 cases (36.7%) have death. However, a significant portion of cases in both groups are censored, suggesting further analysis or additional information may be needed. The data on diabetes shows that 16.2% of cases are censored, representing 16.2% of total cases. 83.8% of cases have occurred, representing 57 cases. The data is categorized based on the presence or absence of diabetes. Out of 68 cases without diabetes, 11 cases are censored, while 57 cases have died. In contrast, 234 cases of diabetes have an unknown outcome, with 51 cases resulting in death. The data suggests that patients with diabetes have a lower percentage of deaths compared to those without diabetes. 3.1 Non-parametric Survival Kaplan-Meier Estimate of Time to Failure in Stroke The Kaplan-Meier Estimate and log-rank test are used in non-parametric survival analysis to compare the survival rates of stroke patients. The researcher used the Kaplan-Meier survival function graph and log-rank test to assess differences in diabetes patient survival outcomes among different variables. Kaplan-Meier survival estimates were plotted for each variable, and the study found that the category with a higher Kaplan-Meier curve had a higher survival level than the category with a lower curve. This study highlights the importance of non-parametric methods in patient survival analysis. The patient in the age category of 18–48 had a longer survival period than the other age categories. This is evident from the Kaplan-Meier plot, where the survival curve for this age group was higher than that of the other age groups. 3.2 Log-rank Test of Different Variables Here we begin the test to see if the probability is equal across several groups of a categorical variable using the Log Rank test. The null hypothesis being tested is that there is no significant difference in survival rates between the studied groups. Table 2 Log-rank tests of each Covariates Variables Categories Chi-square df P-values Sex Male Female 16.6 1 \(\:{5\text{e}}^{-05}\) Residence Rural Urban 29 1 \(\:{7e}^{-08}\) Age 18–48 49–65 ≥ 65 25.8 2 \(\:{3e}^{-06}\) Stroke Type Ischemic Hemorrhagic 7.9 1 0.005 Habit No Smoking Alcohol Chat & Smoking 12.7 3 0.005 CRF No Yes 18.2 1 \(\:{\:2e}^{-05}\) AF No Yes 3.2 1 0.07 Hypertension No Yes 11.3 1 \(\:{\:8e\:}^{-04}\) Diabetes No Yes 88.5 1 \(\:{<2e}^{-16}\) The log-rank test, as shown in Table 2 above, indicated a statistically significant difference in all covariate groups at a significance level of 5%. The KM plot and log-rank test for patient referral status indicated a significant difference between the covariates and time to failure. Accelerated Failure Time Model The assumption of proportionality in the Cox proportional hazard model was found to be violated in the stroke dataset. Therefore, parametric accelerated failure time (AFT) models were used instead. These models aimed to identify the covariates that are associated with the observed time to failure in patients with stroke. In the multivariable analysis, only variables with a p-value less than or equal to 25% in the univariable analysis were considered, following the approach described by ( 32 ). Different AFT models, such as exponential, Weibull, log-normal, and log-logistic distributions, were fitted to model the survival time of the Stroke dataset. These AFT models included all the covariates that showed significance in the univariate analysis at a 25% significance level. By employing this methodology, the researchers aimed to identify the significant predictors of patient survival while accounting for the time to failure (death) and adjusting for various covariates. Table 3 Comparison of Accelerated Failure Parametric Distribution Model Loglikelihood AIC BIC Exponential -507.4687 1024.9374 1044.270 Weibull -494.0729 998.1458 1017.478 Lognormal -490.5834 991.1668 1010.499 Loglogistic -489.3191 988.6383 1007.971 To assess the efficiency of different models, the AIC and BIC criteria were utilized. Table 3 presents the AIC and BIC values for all AFT models. Upon inspection, it is evident that the Weibull model exhibits the lowest AIC and BIC values among all the proposed AFT models. Thus, the Weibull AFT model (AIC = 988.6383 and BIC = 1007.971) is considered the most suitable fit for the stroke patients' survival time dataset. To identify significant covariates, a step-wise procedure was employed. Table 4 Summary of Weibull Accelerated Failure Time model Variables Categories Hazard Ratio Std Error Z P-Values Intercept 5.2075 0.5023 10.37 \(\:{<2\text{e}\:}^{-16}\) Sex Male Female --------- -0.7530 --------- 0.1533 --------- -4.91 --------- \(\:{9.0\text{e}\:}^{-07}\) Residence Rural Urban --------- 0.5931 --------- 0.1273 --------- 4.66 --------- 3.2e-06 Age 18–48 49–65 ≥ 65 --------- -1.2862 -1.2605 --------- 0.4018 0.3756 --------- -3.20 -3.36 --------- 0.00137 0.00079 Stroke Type Ischemic Hemorrhagic --------- -0.1850 --------- 0.1283 --------- -1.44 --------- 0.14940 Habit No Smoking Alcohol Chat & Smoking --------- -0.7686 -0.8171 -0.6214 --------- 0.2648 0.2721 0.2608 --------- -2.90 -3.00 -2.38 --------- 0.00370 0.00268 0.01719 CRF No Yes --------- 0.1640 --------- 0.1376 --------- 1.19 --------- 0.23308 AF No Yes --------- 0.0518 --------- 0.2343 --------- 0.22 --------- 0.82496 Hypertension No Yes --------- -0.3408 --------- 0.1319 --------- -2.58 --------- 0.00975 Diabetes No Yes --------- 1.0362 --------- 0.1461 --------- 7.09 --------- 1.3e-12 Log(scale) -0.4919 0.0728 -6.76 1.4e-11 From the above Table 4 result, it is observed that the test for the regression parameters equal to zero is rejected with a chi-square value of 163.71 for 12 df and a p-value of 9.2e-29. Diabetes is the most effective variable related to the survival of patients with p-value 1.3e-12 which is far below the common significance threshold of 0.05, indicating a very strong statistical significance. In male patients, survival rates significantly decrease with a p-value of 9.0e-07 and a negative coefficient of -0.7530. Survival rates for patients residing in rural areas significantly increase with a p-value of 3.2e-06 and a positive coefficient of 0.5931. Both age groups between 49 to 65 and above 65 show significant decreases in survival time with p-values below 0.01 and negative coefficients. Other factors like Habit, Hypertension, and Cerebral vascularization failure are significant but not as impactful as Diabetes in terms of p-values and effect sizes. The large positive coefficient suggests that having diabetes is associated with a significant increase in survival time in the context of this model. The loglikelihood (intercept only) is -571.2 for the Weibull distribution as a baseline. For other baseline distributions, the loglikelihood (intercept only) for the lognormal baseline is -569.7 and the log-logistic is -569.7. Among these three distributions, Weibull has the highest log-likelihood with a value of -571.2. 3.6 Bayesian Accelerated Failure Time Model A Bayesian Accelerated Failure Time (AFT) model was employed to identify factors influencing time to failure among stroke patients. The model was fitted using the Stan platform through the rstan package in R. A Weibull baseline distribution was assumed, parameterized in terms of a scale (λ) and shape (α) parameter to characterize the survival time distribution. Non-informative priors were assigned to the regression coefficients (β ∼ Normal(0, 10)) and weakly informative priors were used for the scale and shape parameters (λ, α ∼ Gamma(0.01, 0.01)) to ensure model stability. Posterior distributions were obtained using Markov Chain Monte Carlo (MCMC) sampling with four parallel chains, each running for 10,000 iterations after a 2,000-iteration warm-up. Convergence was assessed through the potential scale reduction factor (R̂) and visual inspection of trace plots. Model comparison and fit were evaluated using the Watanabe–Akaike Information Criterion (WAIC) and Leave-One-Out Cross-Validation (LOO-CV). Posterior summaries were reported as posterior means with corresponding 95% credible intervals (CrIs). Table 5 Bayesian Parametric Survival Model Comparison Distribution DIC WAIC LOOIC Weibull 1018.493 1020.739 1026.408 Lognormal 1035.369 1036.532 1036.677 Loglogistic 1022.310 1021.382 1021.404 Table 5 presents the comparison of Bayesian parametric survival models fitted under different distributional assumptions using the Deviance Information Criterion (DIC), Watanabe Akaike Information Criterion (WAIC), and Leave-One-Out Information Criterion (LOOIC). Lower values of these criteria indicate a better-fitting model. Among the three models considered, the Weibull AFT model yielded the lowest DIC (1018.493) and WAIC (1020.739), followed closely by the log-logistic model, while the log-normal model exhibited the highest values across all criteria. These results suggest that the Weibull AFT model provided the best fit to the data, indicating that it most appropriately captures the time-to-failure pattern among stroke patients. Consequently, the Weibull model was selected as the preferred model for further Bayesian inference and interpretation of covariate effects. 3.7 Bayesian Weibull AFT Model In accelerated failure time the stroke data in the SHYCSH from time to failure can be modelled as follows: Log( \(\:{T}_{i}\) ) = \(\:{\beta\:}_{1}+{\beta\:}_{2}Sex+{\beta\:}_{3}Residence+{\beta\:}_{4}{Age}_{2}+{\beta\:}_{5}{Age}_{3}+{\beta\:}_{6}Strok{e}_{t}ype+{\beta\:}_{7}{Habit}_{2}+{\beta\:}_{8}{Habit}_{3}+{\beta\:}_{9}{habit}_{4}+{\beta\:}_{10}CRF+{\beta\:}_{11}AF+{\beta\:}_{12}Diabetes+{\sigma\:}_{\in\:}\) Table 6 Posterior summary of the Bayesian Accelerated Failure Time Model Variables Categories Mean Se_mean sd 2.5% 50% 97.5% n_eff Rhat Intercept -0.597 0.021 1.122 -2.818 -0.581 1.541 2861 1.002 Sex Male Female 1.014 0.003 0.238 0.537 1.018 1.468 6911 1.000 Residence Rural Urban -0.855 0.002 0.207 -1.251 -0.854 -0.455 7254 1.001 Age 18–48 49–65 ≥ 65 1.862 1.953 0.012 0.012 0.692 0.648 0.658 0.836 1.806 1.888 3.364 3.368 3124 3025 1.002 1.001 Stroke Type Ischemic Hemorrhagic 0.282 0.002 0.212 -0.146 0.283 0.690 7648 1.000 Habit No Smoking Alcohol Chat & Smoking 1.045 1.212 1.041 0.007 0.008 0.008 0.432 0.433 0.415 0.223 0.412 0.273 1.035 1.195 1.032 1.927 2.100 1.893 3380 2959 2965 1.001 1.002 1.002 CRF No Yes -0.174 0.003 0.223 -0.610 -0.175 0.261 7089 1.000 AF No Yes -0.032 0.005 0.379 -0.744 -0.044 0.734 5905 1.000 Hypertension No Yes 0.521 0.003 0.209 0.117 0.520 0.935 6195 1.000 Diabetes No Yes -1.502 0.003 0.225 -1.944 -1.501 -1.062 5360 1.000 lambda 1.356 0.005 0.416 0.654 1.317 2.266 6637 1.000 alpha 1.091 0.004 0.332 0.542 1.051 1.862 7773 0.999 The summary provides the above Table 6 in Bayesian point estimates including the parameters' posterior mean estimate, standard error of the mean, standard deviation of the parameter's posterior distribution, 95% credible interval (2.5–97.5%), median of the posterior distribution (50%), effective sample size (n_eff), and potential scale reduction factor (Rhat). The 95% credible interval indicates that 95% of the posterior distribution lies, while the median measures the number of independent draws from the posterior distribution. A higher number indicates better sampling efficiency. Values close to 1 indicate convergence of chains. Female stroke patients have a mean of 1.014 with a standard error of 0.003 and a standard deviation of 0.238. The 95% credible interval for this parameter ranges from 0.537 to 1.468. With a high effective sample size of 6911 and a convergence statistic (Rhat) equal to 1, this parameter is likely associated with a covariate effect. The positive mean and the credible interval entirely above zero indicate a substantial positive impact on survival time. The urban residence of stroke patients has an average value of -0.855 with a standard error of 0.002 and a standard deviation of 0.207. The 95% credible interval for this parameter falls between − 1.251 and − 0.455. With a high effective sample size of 7254 and a convergence statistic (Rhat) close to 1, this parameter likely signifies the impact of another covariate. The negative mean and the credible interval entirely below zero indicate a substantial adverse effect on the survival time of urban is shortened; hence, the hazard rate is increasing. In the Bayesian Weibull AFT model, when considering the influence of other factors, the estimated acceleration factor for stroke patients in the age range of 49 to 65 years the coefficient of the variable age range of 49 to 65 is 1.862 which means there are prolonged life of patients, so the death (failure) will be delayed. In addition, it is evident that the 95% credible interval (0.658,3.364) that the coefficient of age grouped is statistically significant. The acceleration factor is \(\:{exp}^{1.862}\) = 6.4 for a patient age group 49–65, which is therefore, delayed by a multiple of about 6.6 than age group 18–48 stroke patients with an effective sample size of 3124 and a convergence statistic (Rhat) slightly above 1, this parameter is likely indicative of another covariate effect. The positive mean and the credible interval entirely above zero indicate a substantial positive impact on survival time. Furthermore, the patient age group above 65 has an average value of 1.953 with a standard error of 0.012 and a standard deviation of 0.648. Its 95% credible interval spans from 0.836 to 3.368. With an effective sample size of 3025 and a convergence statistic (Rhat) of 1.001, this parameter likely signifies another covariate effect. The positive mean and the credible interval entirely above zero indicate a substantial positive impact on survival time is lengthened hence the hazard rate is decreasing. The Hemorrhagic stroke has an average value of 0.282 with a standard error of 0.002 and a standard deviation of 0.212. The 95% credible interval ranges from − 0.146 to 0.690. With a high effective sample size of 7648 and a convergence statistic (Rhat) at 1.000, this parameter likely reflects another covariate effect. However, since the credible interval encompasses zero, the effect may not be statistically significant. The stroke patients who smoke have an average value of 1.045, with a standard error of 0.007 and a standard deviation of 0.432. This indicates a significant positive impact on survival time and an increase in the chance of stroke damage to blood vessels. Patients who drink alcohol have an average value of 1.212, with a standard error of 0.008 and a standard deviation of 0.433. This indicates a substantial positive impact on survival time and a statistically significant increase in mortality related to ischemic stroke and cardiovascular disease. Patients who use chat and smoke have an average value of 1.041, with a standard error of 0.008 and a standard deviation of 0.415. This parameter is likely indicative of another covariate effect like chewing khat, with a positive mean and credible interval above zero indicating a substantial positive impact on survival time. Cerebral vascularization failure has an average value of -0.174 with a standard error of 0.003 and a standard deviation of 0.223. The 95% credible interval ranges from − 0.610 to 0.261. With a high effective sample size of 7089 and a convergence statistic (Rhat) at 1.000, this parameter likely signifies another covariate effect. However, since the credible interval encompasses zero, the effect may not be statistically significant. The impact of Atrial Fibrillation (AF) on stroke patients has an average value of -0.032 with a standard error of 0.005 and a standard deviation of 0.379. The 95% credible interval for this parameter is between − 0.744 and 0.734. With a substantial effective sample size of 5905 and a convergence statistic of 1.000, this parameter likely indicates another covariate effect. However, since the credible interval contains zero, the effect may not be statistically significant. When hypertension was examined while controlling for other variables, the estimated acceleration factor for stroke patients with hypertension had an average value of 0.521 with a standard error of 0.003 and a standard deviation of 0.209. Its 95% credible interval ranges from 0.117 to 0.935. With a notable effective sample size of 6195 and a convergence statistic of 1.000, this parameter probably reflects another covariate effect. The positive mean and the credible interval entirely above zero indicate a substantial positive impact on survival time. Examining the influence of Diabetes on stroke patients while controlling for other factors has an average value of -1.502 with a standard error of 0.003 and a standard deviation of 0.225. Its 95% credible interval spans from − 1.944 to -1.062. With a substantial effective sample size of 5360 and a convergence statistic of 1.000, this parameter is likely indicative of another covariate effect. The negative mean and the credible interval entirely below zero imply a considerable negative impact on survival time. 4. Discussion The purpose of this study is to identify the factors that influence the Bayesian survival analysis of time to failure in stroke patients using data collected from Sheikh Hassen Yabare Comprehensive Specialized Hospital. Similarly, Bayesian survival analysis offers advantages over classical methods in stroke outcome prediction, particularly for smaller sample sizes or rare events ( 33 ). A Weibull accelerated failure time model identified additional prognostic factors such as atrial fibrillation, alcohol consumption, and diabetes mellitus ( 34 ). Bayesian network models have shown promise in predicting post-stroke outcomes, achieving high accuracy with a reduced set of risk variables ( 35 ). The interpretability of Bayesian models, combined with their predictive power, makes them valuable tools for analyzing stroke patient outcomes and identifying crucial risk factors. In this research, about 69.3% of the stroke patients were censored, with the remaining 30.7% having died the Variables that caused higher mortality are sex, residency, Age, Stroke type, Habit, Cerebral vascularization failure, Atrial Fibrillation, Hypertension, and Diabetes. These results also coincide with four studies done on stroke patient survival and mortality. Stroke mortality rates varied across studies, with one reporting 15.2% mortality over 51 months ( 36 ), while another found 18% one-year mortality ( 37 ). A large-scale study in China reported 35.8% mortality over four years (Wu et al., 2014). Factors associated with increased mortality risk included advanced age, elevated body temperature, abnormal potassium, and creatinine levels ( 36 ), and discontinuation of statin therapy ( 37 , 38 ), identified additional risk factors such as gender, education level, hospital quality, hypertension, and stroke type. Survival rates differed by stroke type, with cerebral infarction patients having better outcomes than those with intracerebral hemorrhage ( 38 , 39 ), highlighted the importance of considering medication types and stroke locations in future studies to better understand long-term outcomes. The results of the Bayesian Weibull AFT model using the INLA method indicate that various factors significantly affect the survival time of stroke patients. These factors include Sex, Residence, Age, stroke type, Habit, CHF, Hypertension, Diabetes, and atrial fibrillation. Specifically, the study findings highlight that age, hypertension, and atrial fibrillation have a notable impact on the survival time of stroke patients. The results come from previous studies on stroke and hypertension survival analysis. Multiple factors significantly affect stroke patients' survival time, including age, sex, hypertension, diabetes, atrial fibrillation, and stroke type ( 34 , 40 ). Hypertension patients' survival is influenced by age, gender, family history, tobacco use, alcohol consumption, khat intake, blood cholesterol levels, disease stage, treatment adherence, and comorbidities ( 41 ). The Weibull accelerated failure time model effectively describes stroke patients' survival data ( 34 , 42 ). Bayesian estimation approaches, particularly the Bayesian Weibull model, demonstrated superior performance in analyzing hypertension patient data compared to classical approaches ( 41 ). These studies highlight the importance of considering multiple risk factors in managing stroke and hypertension patients and emphasize the need for lifestyle modifications and thorough patient follow-up by healthcare professionals. The age greater than 65 of the patients was one of the risk factors that affected the survival time to failure of stroke patients. This means that older patients had a higher hazard rate. Similar studies have investigated risk factors affecting survival time in stroke patients. Age greater than 65 was consistently identified as a significant predictor of mortality, with older patients having a higher hazard rate ( 36 , 43 , 44 ). Other important risk factors included hypertension, diabetes, structural heart disease, and a history of previous stroke ( 43 ). Additional factors associated with decreased survival time included elevated body temperature, abnormal potassium levels, and creatinine levels ( 36 ). These findings highlight the importance of early management and targeted interventions for high-risk stroke patients to improve survival outcomes. Furthermore, apart from the aforementioned variables, the specific diagnosis of stroke disease also exerts a substantial impact on the duration between diagnosis and mortality among stroke patients. The findings elucidate that individuals afflicted with the hemorrhagic type of stroke disease exhibit an elevated risk of fatality in comparison to patients who have been diagnosed with the ischemic type of stroke. Research consistently shows that hemorrhagic stroke (HS) is associated with higher mortality rates compared to ischemic stroke (IS), particularly in the short term. Studies report 30-day survival rates of 78.3% for HS versus 91.8% for IS (Della, 2020), with HS carrying a 4-fold higher mortality risk initially, decreasing to 1.5-fold after three weeks (Andersen et al., 2009). However, long-term survival rates tend to equalize after one month (Henriksson et al., 2012). HS patients are generally younger but experience more severe strokes (Andersen et al., 2009). Risk factors differ between stroke types, with diabetes, atrial fibrillation, and previous cardiovascular events favoring IS, while smoking and alcohol consumption are more associated with HS (Andersen et al., 2009; Bilić et al., 2009). Hypertension is prevalent in both types but more common in IS (Bilić et al., 2009). These findings highlight the importance of considering stroke type when assessing patient prognosis and tailoring treatment approaches. The study's findings indicated that diabetes mellitus was recognized as a significant risk factor impacting the time to failure in stroke patients. Diabetes mellitus is a significant risk factor for stroke, associated with increased mortality and poorer outcomes. Studies have shown that diabetic stroke patients have a higher burden of traditional risk factors, including hypertension and myocardial infarction ( 45 ). These findings underscore the importance of diabetes management in stroke prevention and highlight the need for targeted interventions in diabetic stroke patients. 5. Conclusion The study used a Bayesian survival analysis to study stroke patients in Ethiopia. It identified factors affecting survival time, such as age, gender, comorbidities, and treatment interventions. Results showed older age, male gender, and comorbidities were associated with shorter survival time. Treatment interventions like early thrombolytic therapy and rehabilitation were positively correlated with longer survival time. Other risk factors included hypertension, age, atrial fibrillation, stroke type, and diabetes. The study highlights the importance of early intervention, ongoing monitoring, and comprehensive post-stroke care for stroke patients. Future research should increase sample sizes, use longitudinal analysis techniques, explore additional risk factors, and investigate the long-term impact of interventions on stroke survival outcomes. Limitation The study's limitations were addressed by utilizing secondary data and a checklist. Retrospective cohort research designs can potentially introduce information bias during data collection, particularly when examining registration log books, cards, and patient follow-up records. Declarations Ethical Approval The study was approved by the Statistics Department of Jigjiga University and the Ethics Committee of Sheik Hassan Yabare Comprehensive Specialized Hospital. The ethics committee approved the letter (Ref: JJU/CNCS/Stat/16/2014) and authorized the collection of data from patients' records. To ensure anonymity, no connections were established with specific patients, and all data were devoid of personal identifiers, exempting the patient from the requirement of informed consent. Conflicts of interest The authors declare no conflict of interest in this work. Contributions Conceptualization, M.A.A.; methodology, M.A.A.; data extraction, M.A.A and A.A.O.; analysis and interpretation, M.A.A and A.A.O.; drafting the manuscript, M.A.A and A.A.O.; Supervision A.A.O. ; All authors have read and agreed to the published version of the manuscript. Consent for publication Not applicable. Funding No funding Author Contribution Conceptualization, M.A.A.; methodology, M.A.A.; data extraction, M.A.A and A.A.O.; analysis and interpretation, M.A.A and A.A.O.; drafting the manuscript, M.A.A and A.A.O.; Supervision A.A.O.; All authors have read and agreed to the published version of the manuscript. Data Availability Data is available from the corresponding author upon reasonable request. 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Unsectioned Paragraphs 1 Department of Statistics, Jigjiga University, P.O. Box 1020, Jigjiga, Ethiopia; Email: [email protected] , [email protected] * Correspondence : Abdisalan Ahmed Osman; Email: [email protected] Additional Declarations No competing interests reported. Cite Share Download PDF Status: Posted Version 1 posted 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-8290511","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":559896866,"identity":"7c4e2e24-8ef6-452e-9802-09128d7f00c8","order_by":0,"name":"Mustafe Abdi Ali","email":"","orcid":"","institution":"Jigjiga University","correspondingAuthor":false,"prefix":"","firstName":"Mustafe","middleName":"Abdi","lastName":"Ali","suffix":""},{"id":559896867,"identity":"99754fd2-7976-4821-9369-866f92a6daa3","order_by":1,"name":"Abdisalan Ahmed Osman","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA/0lEQVRIiWNgGAWjYBACNgkGgwMMDBZAJg8QVQBpZuYGvFr4IVokoFrOgLQw4tciOYPBgAGuhbcNJEZAi8Ht5o0Hf9RIyJuznz264e282mj+dqCWHxXbcGu5c6zgMM8xCcOdPXlpN+duO5474zBjA2PPmdu4tdzIMTgMDATGDQdyzG7zbjuW2wDUwszYhluLPVDLwR//JOw3nH8D1DLnWO58QlpAthzgbZNI3HADZEtDTe4GglpAfuHtk0jecOON2c05xw7kbgRqOYjXL7ebN3/88c3GdsP5HLMbb2rqcuedP3zwwY8K3FrQwWEweYBo9UBQR4riUTAKRsEoGCEAAGb5ZtBU7Uk0AAAAAElFTkSuQmCC","orcid":"","institution":"Jigjiga University","correspondingAuthor":true,"prefix":"","firstName":"Abdisalan","middleName":"Ahmed","lastName":"Osman","suffix":""}],"badges":[],"createdAt":"2025-12-05 19:53:18","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-8290511/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-8290511/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":98387820,"identity":"f718655d-4748-425c-9ffc-3edc2871a5ca","added_by":"auto","created_at":"2025-12-17 09:00:59","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":16464,"visible":true,"origin":"","legend":"\u003cp\u003eOverall Survival Function of Stroke Patient at SHYCSH\u003c/p\u003e","description":"","filename":"1.png","url":"https://assets-eu.researchsquare.com/files/rs-8290511/v1/f79801632b6a03ae53b3a49e.png"},{"id":98387823,"identity":"c58cd1de-de14-41a1-8833-883cf453806e","added_by":"auto","created_at":"2025-12-17 09:00:59","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":244421,"visible":true,"origin":"","legend":"\u003cp\u003eKaplan-Meier Plot of Age and Stroke\u003c/p\u003e","description":"","filename":"2.png","url":"https://assets-eu.researchsquare.com/files/rs-8290511/v1/37746cf0b537520140ca63da.png"},{"id":98440558,"identity":"7c6e4ef7-1b4c-498e-9f4e-13cdad41ce0f","added_by":"auto","created_at":"2025-12-17 17:04:00","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1343043,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8290511/v1/35160608-296b-4353-a0a3-2e862efbf70f.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Time to Failure Among Stroke Patients in Jigjiga, Ethiopia: An Application of Bayesian Accelerated Failure Time","fulltext":[{"header":"1. Introduction","content":"\u003cp\u003eStroke is one of the main causes of mortality and acquired disability in the world (\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e); The Global Burden of Disease study reveals stroke as the second most common cause of mortality and the third most common cause of both mortality and disability globally (\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e). Stroke causes approximately 5.5\u0026nbsp;million deaths annually globally, resulting in over 116\u0026nbsp;million years of healthy life loss due to stroke-related mortality and disability (\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e). The World Health Organization defines stroke as sudden, clinical symptoms disrupting cerebral functioning, lasting over 24 hours, or causing death, primarily due to vascular origin (\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e). Strokes can be classified as ischemic or hemorrhagic, with disruptions or diminished cerebral blood flow (\u003cspan additionalcitationids=\"CR5\" citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e). Currently, there is a global rise in the burden of stroke-related death, morbidity, and disability (\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e, \u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e). Over 15\u0026nbsp;million people globally experience a stroke annually, with approximately five million experiencing physical impairment (\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e). Stroke is a severe health condition causing significant mortality, with tilting ischemic attacks having the best prognosis, followed by carotid stenosis and arterial obstruction. Stroke cases are categorized into two main types: ischemic stroke, where an artery in the cerebral vascular area becomes blocked, and hemorrhagic stroke, where a blood vessel ruptures, causing cerebral hypoxemia and brain cell damage (\u003cspan additionalcitationids=\"CR11\" citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e). Metabolic hazards, such as high SBP, BMI, FPG, cholesterol, and glomerular filtration rate, account for 72.1% of stroke burden (\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e). The incidence of stroke is influenced by factors such as age, gender, ethnicity, and genetics (\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e, \u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e, \u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eStroke, a vascular illness, is the second leading cause of Disability-Adjusted Life Years (DALY) worldwide, causing millions of deaths due to lifestyle changes in low- and middle-income countries (\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e). A study in sub-Saharan Africa found a 40% case fatality rate over five years, with diabetes patients having a worse prognosis (\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e). Ethiopia's socio-economic impoverishment has led to a focus on communicable diseases, neglecting non-communicable ones like stroke, resulting in a significant public health issue (\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e, \u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e). Multiple studies have been conducted on the topic of stroke in various locations in Ethiopia (\u003cspan additionalcitationids=\"CR19\" citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e). The incidence of stroke in Ethiopia has been steadily rising, accounting for 7.5% to 19.3% of hospital admissions and resulting in about 11% to 42.8% mortality rates between 2014 and 2019 (\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e, \u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e). The focus of the present investigation was the duration till the demise of individuals affected by stroke. Survival analysis is a statistical method that analyzes data from a certain starting point to the occurrence of a particular event or endpoint. It is a suitable tool for analyzing this sort of data (\u003cspan additionalcitationids=\"CR23\" citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eThe study uses Bayesian Survival analysis to analyze stroke patient data, identifying factors associated with the duration until failure. This helps develop personalized treatment strategies and improve patient prognosis. The analysis evaluates prediction performance, investigates variations, and analyzes follow-up data, enhancing stroke patient prognosis and clinical decision-making. Bayesian survival analysis is gaining interest due to its adaptable outcomes. The aim is to analyze the risk factors of stroke patients at Sheik Hassan Yabare Comprehensive Specialized Hospital in Ethiopia from 2019 to 2023 using Bayesian survival analysis.\u003c/p\u003e"},{"header":"2. Methods","content":"\u003cdiv id=\"Sec3\" class=\"Section2\"\u003e \u003ch2\u003e2.1 Study Area\u003c/h2\u003e \u003cp\u003eThe study was conducted in Sh. Hassan Yabare Referral Hospital in Jigjiga city administration between January 1, 2019, and May 31, 2024. Jigjiga, situated in eastern Ethiopia, approximately 630km from Addis Ababa, serves as the capital city of the Somali Region. According to the 2007 data from the Central Statistical Agency, Jigjiga had a population of 125,876, with 67,128 males and 58,748 females. The city comprises four sub-cities and 22 kebeles.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec4\" class=\"Section2\"\u003e \u003ch2\u003e2.2 Study Design and Population\u003c/h2\u003e \u003cp\u003eThe study analyzed data on a Stroke patient from 2019 to 2023 at Sheikh Hassen Yabare Comprehensive Specialized Hospital in Jigjiga. The data was gathered from the patient's registration book and identity cards. A subset of data was selected from the patient's medical records from January 1, 2019, to May 31, 2024. The researcher used secondary data and a simple random sampling approach. The data on Stroke and the first dates of patient admission were obtained from the Stroke Centre at Sheikh Hassen Yabare Comprehensive Specialized Hospital. The investigation was conducted from January 1, 2019, to May 31, 2024. A retrospective study will gather data on 1,898 stroke patients at Sheikh Hassen Yabare Comprehensive Specialized Hospital in Ethiopia, meticulously examining registration logbooks and patient follow-up records.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec5\" class=\"Section2\"\u003e \u003ch2\u003e2.3 Inclusion and Exclusion Criteria\u003c/h2\u003e \u003cp\u003eThis study included all stroke patients who were registered and had complete information, as well as individuals who had at least one stroke therapy. Nevertheless, the study excluded patients who were under the age of 18, patients who did not initiate any stroke therapy, and those with insufficient medical data.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec6\" class=\"Section2\"\u003e \u003ch2\u003e2.4 Study Variables\u003c/h2\u003e \u003cp\u003eSurvival Time to Failure is a response variable measuring the difference between diagnosis and death, with 0 indicating censored and 1 indicating death. The factors of time to failure among stroke patients are sex, residency, Age, Stroke type, Habit, Cerebral vascularization failure, Atrial Fibrillation, Hypertension, and Diabetes.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec7\" class=\"Section2\"\u003e \u003ch2\u003e2.5 Statistical Analysis\u003c/h2\u003e \u003cp\u003eData analysis was conducted using both descriptive and inferential statistical methods. Kaplan\u0026ndash;Meier survival curves and log-rank tests were employed to estimate and compare survival experiences across groups. A Bayesian Accelerated Failure Time (AFT) model was applied to identify predictors associated with time to failure among stroke patients. The model parameters were estimated using Markov Chain Monte Carlo (MCMC) simulation techniques, and posterior summaries were reported as posterior means with 95% credible intervals. Model comparison and goodness-of-fit were assessed using the Watanabe\u0026ndash;Akaike Information Criterion (WAIC) and Leave-One-Out Cross-Validation (LOO-CV). All analyses were performed in R software.\u003c/p\u003e \u003cp\u003e \u003cb\u003eAccelerated Failure Time Model\u003c/b\u003e \u003c/p\u003e \u003cp\u003eThe Cox-PH model is commonly used for modeling survival data, whereas the AFT model is a parametric model that provides a better data fit. Both models differ in baseline hazard function and coefficient estimation methods (\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e). The AFT model measures the impact of explanatory factors on survival time through regression analysis of survival time against covariates, including Exponential, Weibull, Log-normal, and Log-logistic models (\u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e26\u003c/span\u003e). The AFT model can be written as follows:-\u003cdiv id=\"Equ1\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ1\" name=\"EquationSource\"\u003e\n$$\\:log\\left({T}_{i}\\right)=\\mu\\:+{\\beta\\:}_{1}{X}_{1i}+,\\dots\\:,+{\\beta\\:}_{p}{X}_{pi}+\\sigma\\:{ϵ}_{i}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e1\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec8\" class=\"Section2\"\u003e \u003ch2\u003e2.6 Model Selection Criterion\u003c/h2\u003e \u003cp\u003eThe Akaike Information Criterion was used to select the most suitable Accelerated Failure Time model from various models, comparing non-nested or varying parameter sets (\u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e27\u003c/span\u003e). AIC is obtained by: -\u003cdiv id=\"Equ2\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ2\" name=\"EquationSource\"\u003e\n$$\\:AIC=2log\\left(L\\right)+kp$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e2\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eThe model with the least AIC value is regarded as the best-fitted model. The Bayesian Information Criteria (BIC) was employed to determine the optimal Accelerated Failure Time (AFT) model. The BIC is given by Schwarz (\u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e28\u003c/span\u003e). Bayesian Information Criteria is obtained by: -\u003cdiv id=\"Equ3\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ3\" name=\"EquationSource\"\u003e\n$$\\:BIC=2log\\left(L\\right)+kp*log\\left(n\\right)$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e3\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec9\" class=\"Section2\"\u003e \u003ch2\u003e2.7 Bayesian Analysis\u003c/h2\u003e \u003cp\u003eThe Bayesian technique is preferred in survival analysis due to its powerful information. Bayesian analysis using Stan has gained popularity due to its efficiency and flexibility in parameter estimation and model comparison. Stan employs Hamiltonian Monte Carlo algorithms for full Bayesian inference, offering advantages over traditional maximum-likelihood methods (\u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e). It allows for the straightforward implementation of custom distributions, making it suitable for cognitive modeling (\u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e30\u003c/span\u003e). The Bayesian approach is the most effective method for obtaining accurate estimates of the model (\u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e31\u003c/span\u003e).\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec10\" class=\"Section2\"\u003e \u003ch2\u003e2.8 Bayesian Accelerated Failure Time (AFT) Models\u003c/h2\u003e \u003cp\u003eBayesian parametric models are fundamental in survival analysis due to their analytical tractability and flexibility in modeling time-to-event data. In this study, Bayesian Accelerated Failure Time (AFT) models were employed to analyze survival data with right censoring. The likelihood function was constructed by combining the density function \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:f\\left({t}_{i}|{x}_{i},\\theta\\:\\right)\\)\u003c/span\u003e\u003c/span\u003efor uncensored observations and the survival function \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:S\\left({t}_{i}|{x}_{i},\\theta\\:\\right)\\)\u003c/span\u003e\u003c/span\u003e for censored cases. The general log-likelihood function was formulated accordingly. Given the absence of a joint conjugate prior for both the regression coefficients \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\left(\\beta\\:\\right)\\)\u003c/span\u003e\u003c/span\u003e and the scale parameter (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\sigma\\:}^{2}\\)\u003c/span\u003e\u003c/span\u003e), the prior distributions were specified hierarchically. A multivariate normal prior was assumed for \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\beta\\:|\\:{\\sigma\\:}^{2}\\:\\sim\\:{N}_{P}\\left({\\mu\\:}_{0},\\:{V}_{0}{\\alpha\\:}_{0}^{2}\\right)\\)\u003c/span\u003e\u003c/span\u003e, while an inverse gamma prior was placed on the variance term \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\sigma\\:}^{2}\\sim\\:IG\\left(a,b\\right)\\)\u003c/span\u003e\u003c/span\u003e. The joint posterior distribution was then derived by combining the likelihood with these priors. Due to the lack of closed-form posterior solutions, Markov Chain Monte Carlo (MCMC) methods, particularly the Gibbs sampler, were used for posterior sampling.\u003cdiv id=\"Equ4\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ4\" name=\"EquationSource\"\u003e\n$$\\:L\\left(\\theta\\:|Data\\right)=\\prod\\:_{i=1}^{n}\\left[{f\\left({t}_{i}|{X}_{i}\\theta\\:\\right)}^{{\\sigma\\:}_{i}}*S{\\left({t}_{i}|{X}_{i};\\theta\\:\\right)}^{1-{\\sigma\\:}_{i}}\\right]$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e4\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cdiv id=\"Sec11\" class=\"Section3\"\u003e \u003ch2\u003e2.8.1 Log-normal AFT Model\u003c/h2\u003e \u003cp\u003eIn the log-normal model, the logarithm of survival time is assumed to be normally distributed, such that \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:T\\sim\\:LN\\left({X}^{{\\prime\\:}}\\beta\\:,\\frac{1}{\\tau\\:}\\right)\\)\u003c/span\u003e\u003c/span\u003e. The probability density function (PDF) and survival function were specified, and the joint posterior distribution of parameters was expressed using Bayes' theorem. The prior for β remained multivariate normal, and the variance component followed an inverse gamma distribution. The posterior distributions were sampled using MCMC, relying on the specification of full conditional distributions.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec12\" class=\"Section3\"\u003e \u003ch2\u003e2.8.2 Log-logistic AFT Model\u003c/h2\u003e \u003cp\u003eThe log-logistic distribution was also used, assuming \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:T\\sim\\:LL\\left({X}^{{\\prime\\:}}\\beta\\:,\\sqrt{\\tau\\:}\\right)\\)\u003c/span\u003e\u003c/span\u003e. The density and survival functions were derived accordingly. The posterior distribution for \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\beta\\:\\)\u003c/span\u003e\u003c/span\u003e was expressed based on the combination of likelihood and prior information, with β again following a normal prior. MCMC sampling was employed to estimate the posterior distributions. Full conditional distributions for the parameters were specified, enabling Gibbs sampling.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec13\" class=\"Section3\"\u003e \u003ch2\u003e2.8.3 Weibull AFT Model\u003c/h2\u003e \u003cp\u003eThe Weibull distribution, one of the most widely used models in survival analysis, was also considered. Survival times \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{T}_{i}\\)\u003c/span\u003e\u003c/span\u003e were assumed to follow a Weibull distribution with parameters \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\alpha\\:\\:and\\:\\lambda\\:\\)\u003c/span\u003e\u003c/span\u003e, where α\u0026thinsp;\u0026gt;\u0026thinsp;0. The density function was parameterized as \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:T\\sim\\:Weib\\left(\\sqrt{\\tau\\:},{e}^{-{X}^{{\\prime\\:}}\\beta\\:\\sqrt{\\tau\\:}}\\right)\\)\u003c/span\u003e\u003c/span\u003e, with the survival function defined accordingly. The scale and shape parameters were assigned independent priors, with α\\alpha following an inverse gamma distribution. As with the other models, the posterior distributions were obtained via MCMC sampling, given the complexity of the likelihood function and lack of analytical solutions. In all models, inference was based on the posterior distributions of the parameters. Convergence diagnostics and posterior summaries (mean, median, credible intervals) were assessed using standard Bayesian computational tools.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec14\" class=\"Section3\"\u003e \u003ch2\u003e2.8.4 Log-normal AFT Model\u003c/h2\u003e \u003cp\u003eIn the log-normal model, the logarithm of survival time is assumed to be normally distributed, such that \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:T\\sim\\:LN\\left({X}^{{\\prime\\:}}\\beta\\:,\\frac{1}{\\tau\\:}\\right)\\)\u003c/span\u003e\u003c/span\u003e The probability density function (PDF) and survival function were specified, and the joint posterior distribution of parameters was expressed using Bayes' theorem. The prior for β remained multivariate normal, and the variance component followed an inverse gamma distribution. The posterior distributions were sampled using MCMC, relying on the specification of full conditional distributions.\u003c/p\u003e \u003c/div\u003e \u003c/div\u003e"},{"header":"3. Result","content":"\u003cp\u003eThe data for this study were collected from 353 patients who received treatments for HF at least once at Sheikh Hassen Yabare Comprehensive Specialized Hospital between January 1, 2019 to May 31, 2024. The study analyzed 353 stroke patients, with 26.6% being female and 73.4% being male. The mortality rate for male patients was 26.3%, lower than that for female patients at 42.6%. Most of the patients were from rural areas, with 34.3% having a rural residence and 65.6% having an urban one. In rural areas, 51.3% of patients experienced death, while in urban areas, 19.8% experienced death. The age groups included 11.9% in the 18\u0026ndash;48 age group, 31.7% in the 49\u0026ndash;65 age group, and 56.4% in the \u0026gt;\u0026thinsp;65 age group.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab1\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eDescriptive Summary for Patients of Stroke\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"5\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eVariable\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eCategory\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eTotal\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colspan=\"2\" nameend=\"c5\" namest=\"c4\"\u003e \u003cp\u003ePatients Status\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eNo of Censored\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eNo of Death\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSex\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eMale\u003c/p\u003e \u003cp\u003eFemale\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e259 (73.4%)\u003c/p\u003e \u003cp\u003e94 (26.6%)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e191 (73.7%)\u003c/p\u003e \u003cp\u003e54 (57.4%)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e68 (26.3%)\u003c/p\u003e \u003cp\u003e40 (42.6%)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eResidence\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eRural\u003c/p\u003e \u003cp\u003eUrban\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e121 (34.3%)\u003c/p\u003e \u003cp\u003e232 (65.6%)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e59 (48.7%)\u003c/p\u003e \u003cp\u003e186 (80.2%)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e62 (51.3%)\u003c/p\u003e \u003cp\u003e46 (19.8%)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eAge\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e18\u0026ndash;48\u003c/p\u003e \u003cp\u003e49\u0026ndash;65\u003c/p\u003e \u003cp\u003e\u0026ge;\u0026thinsp;65\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e42 (11.9%)\u003c/p\u003e \u003cp\u003e112 (31.7%)\u003c/p\u003e \u003cp\u003e199 (56.4%)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e39 (92.8%)\u003c/p\u003e \u003cp\u003e96 (85.7%)\u003c/p\u003e \u003cp\u003e110 (55.2%)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e3 (7.2%)\u003c/p\u003e \u003cp\u003e16 (14.3%)\u003c/p\u003e \u003cp\u003e89 (44.8%)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eStroke Type\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eIschemic\u003c/p\u003e \u003cp\u003eHemorrhagic\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e227 (64.3%)\u003c/p\u003e \u003cp\u003e126 (35.7%)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e170 (74.9%)\u003c/p\u003e \u003cp\u003e75 (59.5%)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e57 (25.1%)\u003c/p\u003e \u003cp\u003e51 (40.5%)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eHabit\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eNo\u003c/p\u003e \u003cp\u003eSmoking\u003c/p\u003e \u003cp\u003eAlcohol\u003c/p\u003e \u003cp\u003eChat \u0026amp; Smoking\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e47 (13.3%)\u003c/p\u003e \u003cp\u003e61(17.3%)\u003c/p\u003e \u003cp\u003e115(32.6%)\u003c/p\u003e \u003cp\u003e130 (36.8%)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e39 (82.9%)\u003c/p\u003e \u003cp\u003e42 (68.8%)\u003c/p\u003e \u003cp\u003e83 (72.2%)\u003c/p\u003e \u003cp\u003e81 (62.3%)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e8 (17.1%)\u003c/p\u003e \u003cp\u003e19 (31.2%)\u003c/p\u003e \u003cp\u003e32(27.8%)\u003c/p\u003e \u003cp\u003e49 (37.7%)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eCRF\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eNo\u003c/p\u003e \u003cp\u003eYes\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e213 (60.3%)\u003c/p\u003e \u003cp\u003e140(39.7%)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e144 (67.6%)\u003c/p\u003e \u003cp\u003e101 (72.1%)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e69 (32.3%)\u003c/p\u003e \u003cp\u003e39 (27.9%)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eHypertension\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eNo\u003c/p\u003e \u003cp\u003eYes\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e185 (52.4%)\u003c/p\u003e \u003cp\u003e168 (47.6%)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e149 (80.5%)\u003c/p\u003e \u003cp\u003e96 (57.1%)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e36 (19.5%)\u003c/p\u003e \u003cp\u003e72 (42.9%)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eAtrial Fibrillation\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eNo\u003c/p\u003e \u003cp\u003eYes\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e83 (23.5%)\u003c/p\u003e \u003cp\u003e270 (76.5%)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e74 (89.1%)\u003c/p\u003e \u003cp\u003e171 (63.3%)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e9 (10.9%)\u003c/p\u003e \u003cp\u003e99 (36.7%)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eDiabetes\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eYes\u003c/p\u003e \u003cp\u003eNo\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e68 (19.3%)\u003c/p\u003e \u003cp\u003e285 (80.7%)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e11 (16.2%)\u003c/p\u003e \u003cp\u003e234 (82.1%)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e57 (83.8%)\u003c/p\u003e \u003cp\u003e51 (17.9%)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eThe stroke distribution among the patients is as follows: 64.3% of the patients have Ischemic stroke, and 35.7% have Haemorrhagic stroke. The mortality rate for ischemic stroke is 25.1%, while the mortality rate for hemorrhagic stroke is 40.5%. Together, these two types of stroke account for a total mortality rate of 55.5%. Among the patients included in the research, 38.8% were found to be chewing khat, 19.5% were smoking, and 9% were consuming alcohol. The other patients 32.3% were not engaged in any of these habits. The majority of stroke patients do not have Cerebral Revascularization Failure. Approximately 39.7% of individuals have Cerebral Revascularization Failure, whereas the remaining 60.3% do not. Among hypertension patients, 185 individuals (52.4%) were hypertension-free. Out of the hypertension-free group, 149 patients (80.5%) were censored, meaning that their follow-up was terminated before the occurrence of the event of interest, while 36 patients (19.5%) experienced death during the study period. On the other hand, there were 168 patients (47.6%) identified as having hypertension. Among this group, 96 patients (57.1%) were censored, indicating premature termination of follow-up, while the remaining patients' outcomes were not specified. Based on data the data on atrial fibrillation shows that 89.1% of cases are censored, with 74 out of 83 cases being censored. Death cases are also censored, with 9 out of 83 cases resulting in death. The data is interpreted based on the presence or absence of atrial fibrillation. In cases without atrial fibrillation, 74 cases are censored, while 99 cases (36.7%) have death. However, a significant portion of cases in both groups are censored, suggesting further analysis or additional information may be needed. The data on diabetes shows that 16.2% of cases are censored, representing 16.2% of total cases. 83.8% of cases have occurred, representing 57 cases. The data is categorized based on the presence or absence of diabetes. Out of 68 cases without diabetes, 11 cases are censored, while 57 cases have died. In contrast, 234 cases of diabetes have an unknown outcome, with 51 cases resulting in death. The data suggests that patients with diabetes have a lower percentage of deaths compared to those without diabetes.\u003c/p\u003e \u003cdiv id=\"Sec16\" class=\"Section2\"\u003e \u003ch2\u003e3.1 Non-parametric Survival\u003c/h2\u003e \u003cp\u003e \u003cb\u003eKaplan-Meier Estimate of Time to Failure in Stroke\u003c/b\u003e \u003c/p\u003e \u003cp\u003eThe Kaplan-Meier Estimate and log-rank test are used in non-parametric survival analysis to compare the survival rates of stroke patients. The researcher used the Kaplan-Meier survival function graph and log-rank test to assess differences in diabetes patient survival outcomes among different variables. Kaplan-Meier survival estimates were plotted for each variable, and the study found that the category with a higher Kaplan-Meier curve had a higher survival level than the category with a lower curve. This study highlights the importance of non-parametric methods in patient survival analysis.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eThe patient in the age category of 18\u0026ndash;48 had a longer survival period than the other age categories. This is evident from the Kaplan-Meier plot, where the survival curve for this age group was higher than that of the other age groups.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec17\" class=\"Section2\"\u003e \u003ch2\u003e3.2 Log-rank Test of Different Variables\u003c/h2\u003e \u003cp\u003eHere we begin the test to see if the probability is equal across several groups of a categorical variable using the Log Rank test. The null hypothesis being tested is that there is no significant difference in survival rates between the studied groups.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab2\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 2\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eLog-rank tests of each Covariates\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"5\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eVariables\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eCategories\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eChi-square\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003edf\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eP-values\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSex\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eMale\u003c/p\u003e \u003cp\u003eFemale\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e16.6\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{5\\text{e}}^{-05}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eResidence\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eRural\u003c/p\u003e \u003cp\u003eUrban\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e29\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{7e}^{-08}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eAge\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e18\u0026ndash;48\u003c/p\u003e \u003cp\u003e49\u0026ndash;65\u003c/p\u003e \u003cp\u003e\u0026ge;\u0026thinsp;65\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e25.8\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{3e}^{-06}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eStroke Type\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eIschemic\u003c/p\u003e \u003cp\u003eHemorrhagic\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e7.9\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.005\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eHabit\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eNo\u003c/p\u003e \u003cp\u003eSmoking\u003c/p\u003e \u003cp\u003eAlcohol\u003c/p\u003e \u003cp\u003eChat \u0026amp; Smoking\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e12.7\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.005\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eCRF\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eNo\u003c/p\u003e \u003cp\u003eYes\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e18.2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\:2e}^{-05}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eAF\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eNo\u003c/p\u003e \u003cp\u003eYes\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e3.2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.07\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eHypertension\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eNo\u003c/p\u003e \u003cp\u003eYes\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e11.3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\:8e\\:}^{-04}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eDiabetes\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eNo\u003c/p\u003e \u003cp\u003eYes\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e88.5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\u0026lt;2e}^{-16}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eThe log-rank test, as shown in Table\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e above, indicated a statistically significant difference in all covariate groups at a significance level of 5%. The KM plot and log-rank test for patient referral status indicated a significant difference between the covariates and time to failure.\u003c/p\u003e \u003cp\u003e \u003cb\u003eAccelerated Failure Time Model\u003c/b\u003e \u003c/p\u003e \u003cp\u003eThe assumption of proportionality in the Cox proportional hazard model was found to be violated in the stroke dataset. Therefore, parametric accelerated failure time (AFT) models were used instead. These models aimed to identify the covariates that are associated with the observed time to failure in patients with stroke. In the multivariable analysis, only variables with a p-value less than or equal to 25% in the univariable analysis were considered, following the approach described by (\u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e32\u003c/span\u003e). Different AFT models, such as exponential, Weibull, log-normal, and log-logistic distributions, were fitted to model the survival time of the Stroke dataset. These AFT models included all the covariates that showed significance in the univariate analysis at a 25% significance level. By employing this methodology, the researchers aimed to identify the significant predictors of patient survival while accounting for the time to failure (death) and adjusting for various covariates.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab3\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 3\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eComparison of Accelerated Failure Parametric Distribution\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"4\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eModel\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eLoglikelihood\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eAIC\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eBIC\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eExponential\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e-507.4687\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e1024.9374\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e1044.270\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eWeibull\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e-494.0729\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e998.1458\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e1017.478\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eLognormal\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e-490.5834\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e991.1668\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e1010.499\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eLoglogistic\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e-489.3191\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e988.6383\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e1007.971\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eTo assess the efficiency of different models, the AIC and BIC criteria were utilized. Table\u0026nbsp;\u003cspan refid=\"Tab3\" class=\"InternalRef\"\u003e3\u003c/span\u003e presents the AIC and BIC values for all AFT models. Upon inspection, it is evident that the Weibull model exhibits the lowest AIC and BIC values among all the proposed AFT models. Thus, the Weibull AFT model (AIC\u0026thinsp;=\u0026thinsp;988.6383 and BIC\u0026thinsp;=\u0026thinsp;1007.971) is considered the most suitable fit for the stroke patients' survival time dataset. To identify significant covariates, a step-wise procedure was employed.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab4\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 4\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eSummary of Weibull Accelerated Failure Time model\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"6\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eVariables\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eCategories\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eHazard\u003c/p\u003e \u003cp\u003eRatio\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eStd Error\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eZ\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003eP-Values\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c2\" namest=\"c1\"\u003e \u003cp\u003e\u003cb\u003eIntercept\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e5.2075\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.5023\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e10.37\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\u0026lt;2\\text{e}\\:}^{-16}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSex\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cb\u003eMale\u003c/b\u003e\u003c/p\u003e \u003cp\u003eFemale\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e---------\u003c/p\u003e \u003cp\u003e-0.7530\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e---------\u003c/p\u003e \u003cp\u003e0.1533\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e---------\u003c/p\u003e \u003cp\u003e-4.91\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e---------\u003c/p\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{9.0\\text{e}\\:}^{-07}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eResidence\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cb\u003eRural\u003c/b\u003e\u003c/p\u003e \u003cp\u003eUrban\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e---------\u003c/p\u003e \u003cp\u003e0.5931\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e---------\u003c/p\u003e \u003cp\u003e0.1273\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e---------\u003c/p\u003e \u003cp\u003e4.66\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e---------\u003c/p\u003e \u003cp\u003e3.2e-06\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eAge\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cb\u003e18\u0026ndash;48\u003c/b\u003e\u003c/p\u003e \u003cp\u003e49\u0026ndash;65\u003c/p\u003e \u003cp\u003e\u0026ge;\u0026thinsp;65\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e---------\u003c/p\u003e \u003cp\u003e-1.2862\u003c/p\u003e \u003cp\u003e-1.2605\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e---------\u003c/p\u003e \u003cp\u003e0.4018\u003c/p\u003e \u003cp\u003e0.3756\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e---------\u003c/p\u003e \u003cp\u003e-3.20\u003c/p\u003e \u003cp\u003e-3.36\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e---------\u003c/p\u003e \u003cp\u003e0.00137\u003c/p\u003e \u003cp\u003e0.00079\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eStroke Type\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cb\u003eIschemic\u003c/b\u003e\u003c/p\u003e \u003cp\u003eHemorrhagic\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e---------\u003c/p\u003e \u003cp\u003e-0.1850\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e---------\u003c/p\u003e \u003cp\u003e0.1283\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e---------\u003c/p\u003e \u003cp\u003e-1.44\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e---------\u003c/p\u003e \u003cp\u003e0.14940\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eHabit\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cb\u003eNo\u003c/b\u003e\u003c/p\u003e \u003cp\u003eSmoking\u003c/p\u003e \u003cp\u003eAlcohol\u003c/p\u003e \u003cp\u003eChat \u0026amp; Smoking\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e---------\u003c/p\u003e \u003cp\u003e-0.7686\u003c/p\u003e \u003cp\u003e-0.8171\u003c/p\u003e \u003cp\u003e-0.6214\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e---------\u003c/p\u003e \u003cp\u003e0.2648\u003c/p\u003e \u003cp\u003e0.2721\u003c/p\u003e \u003cp\u003e0.2608\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e---------\u003c/p\u003e \u003cp\u003e-2.90\u003c/p\u003e \u003cp\u003e-3.00\u003c/p\u003e \u003cp\u003e-2.38\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e---------\u003c/p\u003e \u003cp\u003e0.00370\u003c/p\u003e \u003cp\u003e0.00268\u003c/p\u003e \u003cp\u003e0.01719\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eCRF\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cb\u003eNo\u003c/b\u003e\u003c/p\u003e \u003cp\u003eYes\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e---------\u003c/p\u003e \u003cp\u003e0.1640\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e---------\u003c/p\u003e \u003cp\u003e0.1376\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e---------\u003c/p\u003e \u003cp\u003e1.19\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e---------\u003c/p\u003e \u003cp\u003e0.23308\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eAF\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cb\u003eNo\u003c/b\u003e\u003c/p\u003e \u003cp\u003eYes\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e---------\u003c/p\u003e \u003cp\u003e0.0518\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e---------\u003c/p\u003e \u003cp\u003e0.2343\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e---------\u003c/p\u003e \u003cp\u003e0.22\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e---------\u003c/p\u003e \u003cp\u003e0.82496\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eHypertension\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cb\u003eNo\u003c/b\u003e\u003c/p\u003e \u003cp\u003eYes\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e---------\u003c/p\u003e \u003cp\u003e-0.3408\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e---------\u003c/p\u003e \u003cp\u003e0.1319\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e---------\u003c/p\u003e \u003cp\u003e-2.58\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e---------\u003c/p\u003e \u003cp\u003e0.00975\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eDiabetes\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cb\u003eNo\u003c/b\u003e\u003c/p\u003e \u003cp\u003eYes\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e---------\u003c/p\u003e \u003cp\u003e1.0362\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e---------\u003c/p\u003e \u003cp\u003e0.1461\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e---------\u003c/p\u003e \u003cp\u003e7.09\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e---------\u003c/p\u003e \u003cp\u003e1.3e-12\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c2\" namest=\"c1\"\u003e \u003cp\u003eLog(scale)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e-0.4919\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.0728\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e-6.76\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e1.4e-11\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eFrom the above Table\u0026nbsp;\u003cspan refid=\"Tab4\" class=\"InternalRef\"\u003e4\u003c/span\u003e result, it is observed that the test for the regression parameters equal to zero is rejected with a chi-square value of 163.71 for 12 df and a p-value of 9.2e-29. Diabetes is the most effective variable related to the survival of patients with p-value 1.3e-12 which is far below the common significance threshold of 0.05, indicating a very strong statistical significance. In male patients, survival rates significantly decrease with a p-value of 9.0e-07 and a negative coefficient of -0.7530. Survival rates for patients residing in rural areas significantly increase with a p-value of 3.2e-06 and a positive coefficient of 0.5931. Both age groups between 49 to 65 and above 65 show significant decreases in survival time with p-values below 0.01 and negative coefficients. Other factors like Habit, Hypertension, and Cerebral vascularization failure are significant but not as impactful as Diabetes in terms of p-values and effect sizes. The large positive coefficient suggests that having diabetes is associated with a significant increase in survival time in the context of this model. The loglikelihood (intercept only) is -571.2 for the Weibull distribution as a baseline. For other baseline distributions, the loglikelihood (intercept only) for the lognormal baseline is -569.7 and the log-logistic is -569.7. Among these three distributions, Weibull has the highest log-likelihood with a value of -571.2.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec18\" class=\"Section2\"\u003e \u003ch2\u003e3.6 Bayesian Accelerated Failure Time Model\u003c/h2\u003e \u003cp\u003eA Bayesian Accelerated Failure Time (AFT) model was employed to identify factors influencing time to failure among stroke patients. The model was fitted using the Stan platform through the rstan package in R. A Weibull baseline distribution was assumed, parameterized in terms of a scale (λ) and shape (α) parameter to characterize the survival time distribution. Non-informative priors were assigned to the regression coefficients (β \u0026sim; Normal(0, 10)) and weakly informative priors were used for the scale and shape parameters (λ, α \u0026sim; Gamma(0.01, 0.01)) to ensure model stability. Posterior distributions were obtained using Markov Chain Monte Carlo (MCMC) sampling with four parallel chains, each running for 10,000 iterations after a 2,000-iteration warm-up. Convergence was assessed through the potential scale reduction factor (R̂) and visual inspection of trace plots. Model comparison and fit were evaluated using the Watanabe\u0026ndash;Akaike Information Criterion (WAIC) and Leave-One-Out Cross-Validation (LOO-CV). Posterior summaries were reported as posterior means with corresponding 95% credible intervals (CrIs).\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab5\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 5\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eBayesian Parametric Survival Model Comparison\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"4\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eDistribution\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eDIC\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eWAIC\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eLOOIC\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eWeibull\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e1018.493\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e1020.739\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e1026.408\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eLognormal\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e1035.369\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e1036.532\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e1036.677\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eLoglogistic\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e1022.310\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e1021.382\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e1021.404\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eTable\u0026nbsp;\u003cspan refid=\"Tab5\" class=\"InternalRef\"\u003e5\u003c/span\u003e presents the comparison of Bayesian parametric survival models fitted under different distributional assumptions using the Deviance Information Criterion (DIC), Watanabe Akaike Information Criterion (WAIC), and Leave-One-Out Information Criterion (LOOIC). Lower values of these criteria indicate a better-fitting model. Among the three models considered, the Weibull AFT model yielded the lowest DIC (1018.493) and WAIC (1020.739), followed closely by the log-logistic model, while the log-normal model exhibited the highest values across all criteria. These results suggest that the Weibull AFT model provided the best fit to the data, indicating that it most appropriately captures the time-to-failure pattern among stroke patients. Consequently, the Weibull model was selected as the preferred model for further Bayesian inference and interpretation of covariate effects.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec19\" class=\"Section2\"\u003e \u003ch2\u003e3.7 Bayesian Weibull AFT Model\u003c/h2\u003e \u003cp\u003eIn accelerated failure time the stroke data in the SHYCSH from time to failure can be modelled as follows:\u003c/p\u003e \u003cp\u003eLog(\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{T}_{i}\\)\u003c/span\u003e\u003c/span\u003e) = \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\beta\\:}_{1}+{\\beta\\:}_{2}Sex+{\\beta\\:}_{3}Residence+{\\beta\\:}_{4}{Age}_{2}+{\\beta\\:}_{5}{Age}_{3}+{\\beta\\:}_{6}Strok{e}_{t}ype+{\\beta\\:}_{7}{Habit}_{2}+{\\beta\\:}_{8}{Habit}_{3}+{\\beta\\:}_{9}{habit}_{4}+{\\beta\\:}_{10}CRF+{\\beta\\:}_{11}AF+{\\beta\\:}_{12}Diabetes+{\\sigma\\:}_{\\in\\:}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab6\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 6\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003ePosterior summary of the Bayesian Accelerated Failure Time Model\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"10\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c8\" colnum=\"8\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c9\" colnum=\"9\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c10\" colnum=\"10\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eVariables\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eCategories\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eMean\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eSe_mean\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003esd\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003e2.5%\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c7\"\u003e \u003cp\u003e50%\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c8\"\u003e \u003cp\u003e97.5%\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c9\"\u003e \u003cp\u003en_eff\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c10\"\u003e \u003cp\u003eRhat\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c2\" namest=\"c1\"\u003e \u003cp\u003eIntercept\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e-0.597\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.021\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e1.122\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e-2.818\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e-0.581\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e1.541\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e2861\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e1.002\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSex\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cb\u003eMale\u003c/b\u003e\u003c/p\u003e \u003cp\u003eFemale\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e1.014\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.003\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.238\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.537\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e1.018\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e1.468\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e6911\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e1.000\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eResidence\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cb\u003eRural\u003c/b\u003e\u003c/p\u003e \u003cp\u003eUrban\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e-0.855\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.002\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.207\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e-1.251\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e-0.854\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e-0.455\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e7254\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e1.001\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eAge\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cb\u003e18\u0026ndash;48\u003c/b\u003e\u003c/p\u003e \u003cp\u003e49\u0026ndash;65\u003c/p\u003e \u003cp\u003e\u0026ge;\u0026thinsp;65\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e1.862\u003c/p\u003e \u003cp\u003e1.953\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.012\u003c/p\u003e \u003cp\u003e0.012\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.692\u003c/p\u003e \u003cp\u003e0.648\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.658\u003c/p\u003e \u003cp\u003e0.836\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e1.806\u003c/p\u003e \u003cp\u003e1.888\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e3.364\u003c/p\u003e \u003cp\u003e3.368\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e3124\u003c/p\u003e \u003cp\u003e3025\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e1.002\u003c/p\u003e \u003cp\u003e1.001\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eStroke Type\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cb\u003eIschemic\u003c/b\u003e\u003c/p\u003e \u003cp\u003eHemorrhagic\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.282\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.002\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.212\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e-0.146\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0.283\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0.690\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e7648\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e1.000\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eHabit\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cb\u003eNo\u003c/b\u003e\u003c/p\u003e \u003cp\u003eSmoking\u003c/p\u003e \u003cp\u003eAlcohol\u003c/p\u003e \u003cp\u003eChat \u0026amp; Smoking\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e1.045\u003c/p\u003e \u003cp\u003e1.212\u003c/p\u003e \u003cp\u003e1.041\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.007\u003c/p\u003e \u003cp\u003e0.008\u003c/p\u003e \u003cp\u003e0.008\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.432\u003c/p\u003e \u003cp\u003e0.433\u003c/p\u003e \u003cp\u003e0.415\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.223\u003c/p\u003e \u003cp\u003e0.412\u003c/p\u003e \u003cp\u003e0.273\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e1.035\u003c/p\u003e \u003cp\u003e1.195\u003c/p\u003e \u003cp\u003e1.032\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e1.927\u003c/p\u003e \u003cp\u003e2.100\u003c/p\u003e \u003cp\u003e1.893\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e3380\u003c/p\u003e \u003cp\u003e2959\u003c/p\u003e \u003cp\u003e2965\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e1.001\u003c/p\u003e \u003cp\u003e1.002\u003c/p\u003e \u003cp\u003e1.002\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eCRF\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cb\u003eNo\u003c/b\u003e\u003c/p\u003e \u003cp\u003eYes\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e-0.174\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.003\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.223\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e-0.610\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e-0.175\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0.261\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e7089\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e1.000\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eAF\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cb\u003eNo\u003c/b\u003e\u003c/p\u003e \u003cp\u003eYes\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e-0.032\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.005\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.379\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e-0.744\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e-0.044\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0.734\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e5905\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e1.000\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eHypertension\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cb\u003eNo\u003c/b\u003e\u003c/p\u003e \u003cp\u003eYes\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.521\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.003\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.209\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.117\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0.520\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0.935\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e6195\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e1.000\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eDiabetes\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cb\u003eNo\u003c/b\u003e\u003c/p\u003e \u003cp\u003eYes\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e-1.502\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.003\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.225\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e-1.944\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e-1.501\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e-1.062\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e5360\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e1.000\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c2\" namest=\"c1\"\u003e \u003cp\u003elambda\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e1.356\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.005\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.416\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.654\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e1.317\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e2.266\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e6637\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e1.000\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c2\" namest=\"c1\"\u003e \u003cp\u003ealpha\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e1.091\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.004\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.332\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.542\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e1.051\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e1.862\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e7773\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e0.999\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eThe summary provides the above Table\u0026nbsp;\u003cspan refid=\"Tab6\" class=\"InternalRef\"\u003e6\u003c/span\u003e in Bayesian point estimates including the parameters' posterior mean estimate, standard error of the mean, standard deviation of the parameter's posterior distribution, 95% credible interval (2.5\u0026ndash;97.5%), median of the posterior distribution (50%), effective sample size (n_eff), and potential scale reduction factor (Rhat). The 95% credible interval indicates that 95% of the posterior distribution lies, while the median measures the number of independent draws from the posterior distribution. A higher number indicates better sampling efficiency. Values close to 1 indicate convergence of chains. Female stroke patients have a mean of 1.014 with a standard error of 0.003 and a standard deviation of 0.238. The 95% credible interval for this parameter ranges from 0.537 to 1.468. With a high effective sample size of 6911 and a convergence statistic (Rhat) equal to 1, this parameter is likely associated with a covariate effect. The positive mean and the credible interval entirely above zero indicate a substantial positive impact on survival time.\u003c/p\u003e \u003cp\u003eThe urban residence of stroke patients has an average value of -0.855 with a standard error of 0.002 and a standard deviation of 0.207. The 95% credible interval for this parameter falls between \u0026minus;\u0026thinsp;1.251 and \u0026minus;\u0026thinsp;0.455. With a high effective sample size of 7254 and a convergence statistic (Rhat) close to 1, this parameter likely signifies the impact of another covariate. The negative mean and the credible interval entirely below zero indicate a substantial adverse effect on the survival time of urban is shortened; hence, the hazard rate is increasing.\u003c/p\u003e \u003cp\u003eIn the Bayesian Weibull AFT model, when considering the influence of other factors, the estimated acceleration factor for stroke patients in the age range of 49 to 65 years the coefficient of the variable age range of 49 to 65 is 1.862 which means there are prolonged life of patients, so the death (failure) will be delayed. In addition, it is evident that the 95% credible interval (0.658,3.364) that the coefficient of age grouped is statistically significant. The acceleration factor is \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{exp}^{1.862}\\)\u003c/span\u003e\u003c/span\u003e = 6.4 for a patient age group 49\u0026ndash;65, which is therefore, delayed by a multiple of about 6.6 than age group 18\u0026ndash;48 stroke patients with an effective sample size of 3124 and a convergence statistic (Rhat) slightly above 1, this parameter is likely indicative of another covariate effect. The positive mean and the credible interval entirely above zero indicate a substantial positive impact on survival time. Furthermore, the patient age group above 65 has an average value of 1.953 with a standard error of 0.012 and a standard deviation of 0.648. Its 95% credible interval spans from 0.836 to 3.368. With an effective sample size of 3025 and a convergence statistic (Rhat) of 1.001, this parameter likely signifies another covariate effect. The positive mean and the credible interval entirely above zero indicate a substantial positive impact on survival time is lengthened hence the hazard rate is decreasing.\u003c/p\u003e \u003cp\u003eThe Hemorrhagic stroke has an average value of 0.282 with a standard error of 0.002 and a standard deviation of 0.212. The 95% credible interval ranges from \u0026minus;\u0026thinsp;0.146 to 0.690. With a high effective sample size of 7648 and a convergence statistic (Rhat) at 1.000, this parameter likely reflects another covariate effect. However, since the credible interval encompasses zero, the effect may not be statistically significant. The stroke patients who smoke have an average value of 1.045, with a standard error of 0.007 and a standard deviation of 0.432. This indicates a significant positive impact on survival time and an increase in the chance of stroke damage to blood vessels. Patients who drink alcohol have an average value of 1.212, with a standard error of 0.008 and a standard deviation of 0.433. This indicates a substantial positive impact on survival time and a statistically significant increase in mortality related to ischemic stroke and cardiovascular disease. Patients who use chat and smoke have an average value of 1.041, with a standard error of 0.008 and a standard deviation of 0.415. This parameter is likely indicative of another covariate effect like chewing khat, with a positive mean and credible interval above zero indicating a substantial positive impact on survival time.\u003c/p\u003e \u003cp\u003eCerebral vascularization failure has an average value of -0.174 with a standard error of 0.003 and a standard deviation of 0.223. The 95% credible interval ranges from \u0026minus;\u0026thinsp;0.610 to 0.261. With a high effective sample size of 7089 and a convergence statistic (Rhat) at 1.000, this parameter likely signifies another covariate effect. However, since the credible interval encompasses zero, the effect may not be statistically significant. The impact of Atrial Fibrillation (AF) on stroke patients has an average value of -0.032 with a standard error of 0.005 and a standard deviation of 0.379. The 95% credible interval for this parameter is between \u0026minus;\u0026thinsp;0.744 and 0.734. With a substantial effective sample size of 5905 and a convergence statistic of 1.000, this parameter likely indicates another covariate effect. However, since the credible interval contains zero, the effect may not be statistically significant. When hypertension was examined while controlling for other variables, the estimated acceleration factor for stroke patients with hypertension had an average value of 0.521 with a standard error of 0.003 and a standard deviation of 0.209. Its 95% credible interval ranges from 0.117 to 0.935. With a notable effective sample size of 6195 and a convergence statistic of 1.000, this parameter probably reflects another covariate effect. The positive mean and the credible interval entirely above zero indicate a substantial positive impact on survival time.\u003c/p\u003e \u003cp\u003eExamining the influence of Diabetes on stroke patients while controlling for other factors has an average value of -1.502 with a standard error of 0.003 and a standard deviation of 0.225. Its 95% credible interval spans from \u0026minus;\u0026thinsp;1.944 to -1.062. With a substantial effective sample size of 5360 and a convergence statistic of 1.000, this parameter is likely indicative of another covariate effect. The negative mean and the credible interval entirely below zero imply a considerable negative impact on survival time.\u003c/p\u003e \u003c/div\u003e"},{"header":"4. Discussion","content":"\u003cp\u003eThe purpose of this study is to identify the factors that influence the Bayesian survival analysis of time to failure in stroke patients using data collected from Sheikh Hassen Yabare Comprehensive Specialized Hospital. Similarly, Bayesian survival analysis offers advantages over classical methods in stroke outcome prediction, particularly for smaller sample sizes or rare events (\u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e33\u003c/span\u003e). A Weibull accelerated failure time model identified additional prognostic factors such as atrial fibrillation, alcohol consumption, and diabetes mellitus (\u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e34\u003c/span\u003e). Bayesian network models have shown promise in predicting post-stroke outcomes, achieving high accuracy with a reduced set of risk variables (\u003cspan citationid=\"CR35\" class=\"CitationRef\"\u003e35\u003c/span\u003e). The interpretability of Bayesian models, combined with their predictive power, makes them valuable tools for analyzing stroke patient outcomes and identifying crucial risk factors.\u003c/p\u003e \u003cp\u003eIn this research, about 69.3% of the stroke patients were censored, with the remaining 30.7% having died the Variables that caused higher mortality are sex, residency, Age, Stroke type, Habit, Cerebral vascularization failure, Atrial Fibrillation, Hypertension, and Diabetes. These results also coincide with four studies done on stroke patient survival and mortality. Stroke mortality rates varied across studies, with one reporting 15.2% mortality over 51 months (\u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e36\u003c/span\u003e), while another found 18% one-year mortality (\u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e37\u003c/span\u003e). A large-scale study in China reported 35.8% mortality over four years (Wu et al., 2014). Factors associated with increased mortality risk included advanced age, elevated body temperature, abnormal potassium, and creatinine levels (\u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e36\u003c/span\u003e), and discontinuation of statin therapy (\u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e37\u003c/span\u003e, \u003cspan citationid=\"CR38\" class=\"CitationRef\"\u003e38\u003c/span\u003e), identified additional risk factors such as gender, education level, hospital quality, hypertension, and stroke type. Survival rates differed by stroke type, with cerebral infarction patients having better outcomes than those with intracerebral hemorrhage (\u003cspan citationid=\"CR38\" class=\"CitationRef\"\u003e38\u003c/span\u003e, \u003cspan citationid=\"CR39\" class=\"CitationRef\"\u003e39\u003c/span\u003e), highlighted the importance of considering medication types and stroke locations in future studies to better understand long-term outcomes.\u003c/p\u003e \u003cp\u003eThe results of the Bayesian Weibull AFT model using the INLA method indicate that various factors significantly affect the survival time of stroke patients. These factors include Sex, Residence, Age, stroke type, Habit, CHF, Hypertension, Diabetes, and atrial fibrillation. Specifically, the study findings highlight that age, hypertension, and atrial fibrillation have a notable impact on the survival time of stroke patients. The results come from previous studies on stroke and hypertension survival analysis. Multiple factors significantly affect stroke patients' survival time, including age, sex, hypertension, diabetes, atrial fibrillation, and stroke type (\u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e34\u003c/span\u003e, \u003cspan citationid=\"CR40\" class=\"CitationRef\"\u003e40\u003c/span\u003e). Hypertension patients' survival is influenced by age, gender, family history, tobacco use, alcohol consumption, khat intake, blood cholesterol levels, disease stage, treatment adherence, and comorbidities (\u003cspan citationid=\"CR41\" class=\"CitationRef\"\u003e41\u003c/span\u003e). The Weibull accelerated failure time model effectively describes stroke patients' survival data (\u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e34\u003c/span\u003e, \u003cspan citationid=\"CR42\" class=\"CitationRef\"\u003e42\u003c/span\u003e). Bayesian estimation approaches, particularly the Bayesian Weibull model, demonstrated superior performance in analyzing hypertension patient data compared to classical approaches (\u003cspan citationid=\"CR41\" class=\"CitationRef\"\u003e41\u003c/span\u003e). These studies highlight the importance of considering multiple risk factors in managing stroke and hypertension patients and emphasize the need for lifestyle modifications and thorough patient follow-up by healthcare professionals.\u003c/p\u003e \u003cp\u003eThe age greater than 65 of the patients was one of the risk factors that affected the survival time to failure of stroke patients. This means that older patients had a higher hazard rate. Similar studies have investigated risk factors affecting survival time in stroke patients. Age greater than 65 was consistently identified as a significant predictor of mortality, with older patients having a higher hazard rate (\u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e36\u003c/span\u003e, \u003cspan citationid=\"CR43\" class=\"CitationRef\"\u003e43\u003c/span\u003e, \u003cspan citationid=\"CR44\" class=\"CitationRef\"\u003e44\u003c/span\u003e). Other important risk factors included hypertension, diabetes, structural heart disease, and a history of previous stroke (\u003cspan citationid=\"CR43\" class=\"CitationRef\"\u003e43\u003c/span\u003e). Additional factors associated with decreased survival time included elevated body temperature, abnormal potassium levels, and creatinine levels (\u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e36\u003c/span\u003e). These findings highlight the importance of early management and targeted interventions for high-risk stroke patients to improve survival outcomes. Furthermore, apart from the aforementioned variables, the specific diagnosis of stroke disease also exerts a substantial impact on the duration between diagnosis and mortality among stroke patients. The findings elucidate that individuals afflicted with the hemorrhagic type of stroke disease exhibit an elevated risk of fatality in comparison to patients who have been diagnosed with the ischemic type of stroke.\u003c/p\u003e \u003cp\u003eResearch consistently shows that hemorrhagic stroke (HS) is associated with higher mortality rates compared to ischemic stroke (IS), particularly in the short term. Studies report 30-day survival rates of 78.3% for HS versus 91.8% for IS (Della, 2020), with HS carrying a 4-fold higher mortality risk initially, decreasing to 1.5-fold after three weeks (Andersen et al., 2009). However, long-term survival rates tend to equalize after one month (Henriksson et al., 2012). HS patients are generally younger but experience more severe strokes (Andersen et al., 2009). Risk factors differ between stroke types, with diabetes, atrial fibrillation, and previous cardiovascular events favoring IS, while smoking and alcohol consumption are more associated with HS (Andersen et al., 2009; Bilić et al., 2009). Hypertension is prevalent in both types but more common in IS (Bilić et al., 2009). These findings highlight the importance of considering stroke type when assessing patient prognosis and tailoring treatment approaches.\u003c/p\u003e \u003cp\u003eThe study's findings indicated that diabetes mellitus was recognized as a significant risk factor impacting the time to failure in stroke patients. Diabetes mellitus is a significant risk factor for stroke, associated with increased mortality and poorer outcomes. Studies have shown that diabetic stroke patients have a higher burden of traditional risk factors, including hypertension and myocardial infarction (\u003cspan citationid=\"CR45\" class=\"CitationRef\"\u003e45\u003c/span\u003e). These findings underscore the importance of diabetes management in stroke prevention and highlight the need for targeted interventions in diabetic stroke patients.\u003c/p\u003e"},{"header":"5. Conclusion","content":"\u003cp\u003eThe study used a Bayesian survival analysis to study stroke patients in Ethiopia. It identified factors affecting survival time, such as age, gender, comorbidities, and treatment interventions. Results showed older age, male gender, and comorbidities were associated with shorter survival time. Treatment interventions like early thrombolytic therapy and rehabilitation were positively correlated with longer survival time. Other risk factors included hypertension, age, atrial fibrillation, stroke type, and diabetes. The study highlights the importance of early intervention, ongoing monitoring, and comprehensive post-stroke care for stroke patients. Future research should increase sample sizes, use longitudinal analysis techniques, explore additional risk factors, and investigate the long-term impact of interventions on stroke survival outcomes.\u003c/p\u003e \u003cp\u003e \u003cb\u003eLimitation\u003c/b\u003e \u003c/p\u003e \u003cp\u003eThe study's limitations were addressed by utilizing secondary data and a checklist. Retrospective cohort research designs can potentially introduce information bias during data collection, particularly when examining registration log books, cards, and patient follow-up records.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e \u003ch2\u003eEthical Approval\u003c/h2\u003e \u003cp\u003e The study was approved by the Statistics Department of Jigjiga University and the Ethics Committee of Sheik Hassan Yabare Comprehensive Specialized Hospital. The ethics committee approved the letter (Ref: JJU/CNCS/Stat/16/2014) and authorized the collection of data from patients' records. To ensure anonymity, no connections were established with specific patients, and all data were devoid of personal identifiers, exempting the patient from the requirement of informed consent.\u003c/p\u003e \u003c/p\u003e\u003cp\u003e \u003ch2\u003eConflicts of interest\u003c/h2\u003e \u003cp\u003eThe authors declare no conflict of interest in this work.\u003c/p\u003e \u003c/p\u003e\u003cp\u003e \u003ch2\u003eContributions\u003c/h2\u003e \u003cp\u003eConceptualization, M.A.A.; methodology, M.A.A.; data extraction, M.A.A and A.A.O.; analysis and interpretation, M.A.A and A.A.O.; drafting the manuscript, M.A.A and A.A.O.; Supervision A.A.O. ; All authors have read and agreed to the published version of the manuscript.\u003c/p\u003e \u003c/p\u003e\u003cp\u003e \u003ch2\u003eConsent for publication\u003c/h2\u003e \u003cp\u003eNot applicable.\u003c/p\u003e \u003c/p\u003e\u003ch2\u003eFunding\u003c/h2\u003e \u003cp\u003eNo funding\u003c/p\u003e\u003ch2\u003eAuthor Contribution\u003c/h2\u003e\u003cp\u003eConceptualization, M.A.A.; methodology, M.A.A.; data extraction, M.A.A and A.A.O.; analysis and interpretation, M.A.A and A.A.O.; drafting the manuscript, M.A.A and A.A.O.; Supervision A.A.O.; All authors have read and agreed to the published version of the manuscript.\u003c/p\u003e\u003ch2\u003eData Availability\u003c/h2\u003e\u003cp\u003eData is available from the corresponding author upon reasonable request.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\u003cli\u003e\u003cspan\u003eSarikaya H, Ferro J, Arnold M. 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Global, regional, and national age-sex specific all-cause and cause-specific mortality for 240 causes of death, 1990\u0026ndash;2013: a systematic analysis for the Global Burden of Disease Study 2013. Lancet (British Ed. 2015;385(9963):117\u0026ndash;71.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eFeigin VL, Norrving B, Mensah GA. Global burden of stroke. Circ Res. 2017;120(3):439\u0026ndash;48.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eMonta\u0026ntilde;o A, Hanley DF, Hemphill JC III. Hemorrhagic stroke. Handb Clin Neurol. 2021;176:229\u0026ndash;48.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eTaylor A, Ntusi NAB. Guest editorial: Evolving concepts of stroke and stroke management in South Africa: Quo vadis? South Afr Med J. 2019;109(2):69\u0026ndash;71.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eDembelu M, Wosenyeleh T, Gezimu W, Kumara D. 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Stroke Res Treat. 2020;2020.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eZewdie A, Debebe F, Kebede S, Azazh A, Laytin A, Pashmforoosh G, et al. Prospective assessment of patients with stroke in Tikur Anbessa specialised hospital, Addis Ababa, Ethiopia. Afr J Emerg Med. 2018;8(1):21\u0026ndash;4.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eMulatu G. Types and Associated Factor of Stroke at Selected Public Referral Hospitals in Addis Ababa; Ethiopia. Addis Ababa University; 2017.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eMulat B, Mohammed J, Yeseni M, Alamirew M, Dermello M, Asemahagn MA. Magnitude of stroke and associated factors among patients who attended the medical ward of Felege Hiwot Referral Hospital, Bahir Dar town, Northwest Ethiopia. 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J Res Diabetes. 2015;2015:1\u0026ndash;12.\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e"},{"header":"Unsectioned Paragraphs","content":"\u003cp\u003e\u003csup\u003e1\u003c/sup\u003e Department of Statistics, Jigjiga University, P.O. Box 1020, Jigjiga, Ethiopia; Email: [email protected], [email protected]\u003c/p\u003e\u003cp\u003e\u003cb\u003e* Correspondence\u003c/b\u003e: Abdisalan Ahmed Osman; Email: [email protected]\u003c/p\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":true,"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":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"AFT, Cerebrovascular, Bayesian, Jigjiga, SHYCSH, Stroke","lastPublishedDoi":"10.21203/rs.3.rs-8290511/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-8290511/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eStroke, a global health issue causing cerebrovascular conditions, affects millions annually, particularly in developing countries like Ethiopia, due to lifestyle changes, urbanization, and risk factors. The study examines the time to failure in stroke patients at Sheik Hassan Yabare Comprehensive Specialized Hospital in Ethiopia, highlighting the importance of understanding factors influencing survival times for improved patient outcomes. A retrospective study at Sheik Hassan Yabare Comprehensive Specialized Hospital analyzed stroke patients using Kaplan-Meier plots, the long-rank test, the Cox proportional hazards model, and the Accelerated Failure Time model. Akaike's Information Criterion was used to compare the effectiveness of models, and the Bayesian Accelerated Failure Time model was employed to identify factors affecting the time to failure of strokes. The study involved 353 stroke patients, with 26.6% female and 73.4% male. Male patients had a lower mortality rate of 26.3% compared to females at 42.6%. The majority of patients were from urban areas, with a mortality rate of 51.3% in rural areas and 19.8% in urban areas. The age distribution was categorized into three groups: 18\u0026ndash;48, 49\u0026ndash;65, and \u0026gt;\u0026thinsp;65, with corresponding death proportions of 21.6%, 18.9%, and 24.8%, respectively. Ischemic and hemorrhagic strokes had a combined mortality rate of 55.5%. A significant percentage of hypertension patients were censored, with 149 (80.5%) being censored and 36 (19.5%) experiencing death. The median estimated survival time for stroke patients was 48 days. Diabetes was the most effective variable related to patient survival, with a significant positive coefficient. Other factors, such as habit, hypertension, and cerebral vascularization failure, are less impactful.\u003c/p\u003e","manuscriptTitle":"Time to Failure Among Stroke Patients in Jigjiga, Ethiopia: An Application of Bayesian Accelerated Failure Time","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-12-17 09:00:51","doi":"10.21203/rs.3.rs-8290511/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"6d5a7651-56d2-49fc-91f8-2cb6a44e4db3","owner":[],"postedDate":"December 17th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[],"tags":[],"updatedAt":"2025-12-17T09:00:51+00:00","versionOfRecord":[],"versionCreatedAt":"2025-12-17 09:00:51","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-8290511","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-8290511","identity":"rs-8290511","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}