Robust Bayesian Inference for Small-Sample Clinical Trials

Thesis Abstract

Small-sample clinical trials frequently yield imprecise and biased inferences when conventional frequentist methods are applied, compromising decision-making in early-phase drug development and personalized medicine. The study addresses the methodological gap by developing and evaluating a robust Bayesian framework tailored for small-sample contexts, where prior information is deliberately integrated to stabilize estimates while controlling type I error and preserving calibration under model misspecification. The aim is to design, implement, and assess a Bayesian inference approach that remains reliable with sample sizes typical of Phase I/II trials (n ? 20–60 per arm) and heterogeneous patient populations. Specific objectives are (i) to formulate robust prior specifications, including power-regularized and heavy-tailed hyperpriors, that mitigate prior-data conflict; (ii) to implement hierarchical and shrinkage-based models for dose-response and time-to-event outcomes; (iii) to develop adaptive decision rules for early stopping and dose-ranging that maintain operating characteristics under misspecified models; (iv) to evaluate robustness through extensive simulation studies across scenarios of model misspecification, prior informativeness, and varying nuisance parameter structures; and (v) to demonstrate applicability via a real-world oncology trial dataset comprising 45 patients per arm with progression-free survival and objective response endpoints. Methodologically, the study adopts a design, implement, and evaluate research framework situated in a Bayesian statistics paradigm, integrating elements from decision-theoretic robustification and contemporary Bayesian computation. The population comprises adult cancer patients enrolled in early-phase trials, with a target sample of 120 subjects across three arms (two experimental doses and a control). Data collection instruments include patient-level outcomes such as time-to-progression, objective response rate, adverse event incidence, and biomarker measurements, captured through standardized case report forms and centralized data monitoring systems. The analytical methodology combines (a) robust Bayesian modeling with normal-inverse-gamma and t-distributed priors to accommodate outliers and prior-data conflict; (b) hierarchical models for pooling across cohorts and biomarkers; (c) skew-normal or heavy-tailed error structures for time-to-event and longitudinal endpoints; (d) Bayesian model averaging to address model uncertainty; and (e) adaptive Bayesian decision criteria implementing posterior probability-based stopping rules and dose selection guided by utility functions that balance efficacy and safety. Model fitting relies on Markov chain Monte Carlo (MCMC) methods, including Hamiltonian Monte Carlo (HMC) and sequential Monte Carlo (SMC) where appropriate, with rigorous convergence diagnostics and sensitivity analyses to prior specifications. Evaluation proceeds through comprehensive simulation experiments (1,000–5,000 replications per scenario) varying sample size, outcome type, dropout rates, and prior strength, to compare calibration, bias, mean squared error, and expected number of patients treated at suboptimal doses. The empirical analysis utilizes the collected trial dataset to illustrate posterior estimates of treatment effects, credible intervals, and probability of superiority, along with posterior predictive checks and calibration curves. Anticipated findings indicate that the robust Bayesian framework yields narrower and more reliable credible intervals than conventional Bayesian methods when true effects are modest and priors are informative yet non-conflicting. It is expected to demonstrate improved Type I error control and calibration across misspecified models, with lower bias in dose-response estimates and more accurate survival predictions in small samples. The study aims to show that adaptive decision rules based on posterior probabilities facilitate efficient dose selection and ethical trial conduct without sacrificing statistical integrity. The contribution to knowledge lies in providing a practically implementable inference blueprint for small-sample clinical trials that integrates robustness against prior-data conflict, model misspecification, and data sparsity, while delivering prespecified operating characteristics. The implications extend to regulatory science, offering a transparent framework for prior elicitation, sensitivity analysis, and decision-making that enhances reliability of early-phase conclusions. The main conclusion posits that robust Bayesian inference represents a viable and superior alternative for small-sample clinical trials, enabling credible estimation, ethically responsive adaptation, and informed progression decisions. Recommendations include standardizing prior-robustness diagnostics in trial protocols, integrating robust Bayesian methods into software toolchains for clinical statisticians, and extending the approach to multi-arm, multi-stage designs with complex endpoints.