Modern Techniques in Design and Analysis of Bayesian Adaptive Clinical Trials

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Adaptive designs are considered an efficient and ethical alternative to conventional randomized clinical trials. Planned adjustments to the design are allowed through the course of the trial to address ethical, feasibility and scientific issues. Specifically, in response adaptive designs intermediate results are used to adapt arm allocation ratios or make stopping decisions. Bayesian methods have become the default approach for design and analysis of response adaptive trials due to the following reasons: sequentially updating the results is facilitated in the Bayesian framework; multiplicity arising from multiple interim looks as well as multi-arm trial settings is naturally dealt with in Bayesian significance tests; uncertainty quantification is easily addressed; and prior knowledge can be readily incorporated through Bayesian models. However, currently, Bayesian analyses for adaptive clinical trials are restricted to simple models with closed form posteriors, and utilities of Bayesian inference for innovative and efficient design and analysis of clinical trials are yet to be explored. In Bayesian adaptive trials, decision making relies on Bayesian posterior or predictive probabilities. However, the main design operating characteristics (DOC) remain frequentist measures, namely power and type I error rate. A crucial step in planning the trial is, therefore, specifying the stopping/adaptation rules that meet DOC requirements. Given that the sampling distributions of Bayesian test statistics are not generally known, the "optimal" Bayesian rules cannot be obtained analytically. Currently, decision criteria are specified by means of extensive, exploratory simulation studies. The proposed research program is focused on a comprehensive decision theoretic approach for optimal design of Bayesian adaptive clinical trials. The goal is to develop rigorous methodology, computational techniques and accessible software that can be used regardless of complexity of the model. More specifically, I propose emulating the DOC by Gaussian process surrogate models built upon simulations of the trial for a small number of decision criteria. Promising development avenues include methods for incorporating known DOC behaviour in the surrogate model, refinement steps through a sequential design framework, multivariate surrogate modelling and uncertainty quantification. Furthermore, optimization procedures tailored to the present problem will be developed. The proposal lays out a Bayesian sequential optimization approach in which prior information about the behaviour of DOC are leveraged to inform the search while mitigating uncertainty adaptively. The completion of the proposed program will remove major roadblocks in design of efficient and ethical clinical trials by providing investigators with a complete set of methodology and accessible tools for adaptive trial design and will lead to HQP with an exceptionally diverse and specialized skill set.