Bayesian sample sizes for exploratory clinical trials comparing multiple experimental treatments with a control

Abstract

In this paper, a Bayesian approach is developed for simultaneously comparing multiple experimental treatments with a common control treatment in an exploratory clinical trial. The sample size is set to ensure that, at the end of the study, there will be at least one treatment for which the investigators have a strong belief that it is better than control, or else they have a strong belief that none of the experimental treatments are substantially better than control. This criterion bears a direct relationship with conventional frequentist power requirements, while allowing prior opinion to feature in the analysis with a consequent reduction in sample size. If it is concluded that at least one of the experimental treatments shows promise, then it is envisaged that one or more of these promising treatments will be developed further in a definitive phase III trial. The approach is developed in the context of normally distributed responses sharing a common standard deviation regardless of treatment. To begin with, the standard deviation will be assumed known when the sample size is calculated. The final analysis will not rely upon this assumption, although the intended properties of the design may not be achieved if the anticipated standard deviation turns out to be inappropriate. Methods that formally allow for uncertainty about the standard deviation, expressed in the form of a Bayesian prior, are then explored. Illustrations of the sample sizes computed from the new method are presented, and comparisons are made with frequentist methods devised for the same situation.

Evaluation of a multi-arm multi-stage Bayesian design for phase II drug selection trials – an example in hemato-oncology

“…Surprisingly, although several designs have used Bayesian adaptive allocation methods[17, 29], Bayesian adaptive designs in terms of sample size or treatment allocation have been proposed mainly in the early phases of cancer drug development, notably in the setting of seamless phase I/II trials [13]. In the MAMS setting, Bayesian adaptive phase II screening designs have been proposed only for selecting/dropping arms using normal outcome measures [11], and more frequently by modifying the allocation probabilities to each arm. For instance, to select among treatment combinations of multiple agents, patients were adaptively allocated to either one of the treatment combinations based on posterior probabilities of all hypotheses of superiority of each combination based on a continuous endpoint [29].…”

“…Indeed, Bayesian designs are an efficient way to achieve valid and reliable evidence in clinical trials, given that the interpretation of the data is unrelated to preplanned stopping rules and is independent of the number of interim views [9, 10]. Such Bayesian approaches for MAMS trials have been rarely used, notably with one proposal for normal outcomes [11]. To allow a direct and simple use of the Bayes approach, we focused on the probability of success in binomial trials, restricting our considerations to conjugate beta priors.…”

Development of drugs for severe malaria in children

“…Because of limited time and research capacity, innovative adaptive designs rather than conventional randomised controlled trials can be considered, which could accommodate testing several interventions in parallel. 20 These designs allow interventions in under-performing study arms be dropped in an early stage.…”

Bayesian sample‐size determination methods considering both worthwhileness and unpromisingness for exploratory two‐arm randomized clinical trials with binary endpoints

“…In the process of clinical research and development of an experimental treatment, a randomized exploratory clinical trial with a dichotomous or binary endpoint is often conducted to make a go or no‐go decision. Such an exploratory trial needs to have an adequate sample size to provide convincing evidence that the experimental treatment is either worthwhile or unpromising in comparison with a control treatment.…”