Comparative Analysis of Bayesian and Frequentist Interventions in Survival Data

Thesis Abstract

In survival analysis, researchers face the challenge of selecting inferential frameworks that balance prior information incorporation with data-driven evidence, particularly when both Bayesian and frequentist approaches yield divergent conclusions in real-world censoring patterns. This study aims to compare Bayesian and frequentist interventions in survival data to elucidate how methodological choices influence parameter estimates, predictive accuracy, and decision-making in clinical prognosis. The objectives are to (i) evaluate estimation bias, variance, and interval coverage for comparative hazards and survival functions under both paradigms; (ii) assess predictive performance using time-to-event predictions via Brier scores and concordance indices; (iii) examine robustness to model misspecification through simulation studies varying censoring rates, sample sizes, and prior informativeness; (iv) analyze computational efficiency and convergence diagnostics for common implementations; and (v) synthesize practical guidelines for practitioners on method selection under different data contexts. A mixed-methods design is employed, combining extensive simulation experiments with an empirical analysis of a cancer survival dataset. The population consists of adult patients diagnosed with colorectal cancer from a national registry, comprising 2,500 observations with right-censoring proportions ranging from 15% to 40% across subgroups. For the empirical component, survival times are modeled using the Cox proportional hazards framework as the baseline, with Bayesian models incorporating informative priors on regression coefficients and baseline hazard, and frequentist models using partial likelihood and robust standard errors. Data collection instruments include clinical registry records, extractable covariates such as age, sex, tumor stage, treatment modality, comorbidity index, and follow-up status, along with mortality verification from national death indices. Sample sizes for simulation scenarios are set at n = 200, 500, and 1,000 with varying censoring rates to reflect realistic study designs. The Bayesian analyses utilize Markov chain Monte Carlo sampling via Hamiltonian Monte Carlo implemented in Stan, with priors calibrated through elicitation from clinical experts and sensitivity analyses for weakly informative versus strongly informative settings. Frequentist analyses apply iterative reweighted least squares for baseline hazards and stratified Cox models where appropriate. Validity and reliability are addressed through convergence diagnostics (R-hat, effective sample size) for Bayesian models and diagnostic checks for proportional hazards in frequentist models. Internal validity is further supported by performing repeated simulation runs (n = 1,000 per scenario) to assess estimator bias, mean squared error, and interval coverage under correctly specified and misspecified models. Data analysis methods include (i) parametric and semi-parametric survival modeling, (ii) time-dependent ROC and concordance index evaluations, (iii) Bayesian model comparison using Bayes factors and posterior predictive checks, and (iv) frequentist model selection via Akaike and Bayesian information criteria equivalents and likelihood ratio tests. Additionally, calibration plots and decision-curve analysis are used to translate statistical performance into clinical utility. Key expected findings indicate that Bayesian interventions provide improved interval coverage and robust uncertainty quantification in small-to-moderate samples with informative priors, while frequentist methods offer faster computation and comparable point estimates under correctly specified models. In scenarios with weak or non-existent prior information, results from both paradigms converge, but Bayesian methods demonstrate greater resilience to censoring-induced bias when priors reflect domain knowledge. The empirical analysis is anticipated to show comparable hazard ratio estimates across methods for strong covariates (e.g., advanced tumor stage) but divergent estimates for less certain predictors, with predictive accuracy differing modestly between approaches depending on prior strength and censoring. The study contributes to knowledge by offering a systematic, theory-informed comparison of Bayesian and frequentist interventions in survival data, clarifying when each framework yields superior inference and prediction, and providing actionable guidelines for method selection in oncologic prognosis research. The main conclusion is that neither framework universally outperforms the other; instead, a context-driven approach that leverages prior information and explicit uncertainty quantification, complemented by rigorous diagnostic checks, yields the most reliable survival inferences. Recommendations include adopting Bayesian priors informed by clinical expertise in data-poor settings, using robust frequentist diagnostics in large samples, and integrating model-agnostic evaluation metrics to support evidence-based decision-making in survival analysis.