Abstract
BackgroundBayesian adaptive methods are increasingly being used to design clinical trials and offer several advantages over traditional approaches. Decisions at analysis points are usually based on the posterior distribution of the treatment effect. However, there is some confusion as to whether control of type I error is required for Bayesian designs as this is a frequentist concept.MethodsWe discuss the arguments for and against adjusting for multiplicities in Bayesian trials with interim analyses. With two case studies we illustrate the effect of including interim analyses on type I/II error rates in Bayesian clinical trials where no adjustments for multiplicities are made. We propose several approaches to control type I error, and also alternative methods for decision-making in Bayesian clinical trials.ResultsIn both case studies we demonstrated that the type I error was inflated in the Bayesian adaptive designs through incorporation of interim analyses that allowed early stopping for efficacy and without adjustments to account for multiplicity. Incorporation of early stopping for efficacy also increased the power in some instances. An increase in the number of interim analyses that only allowed early stopping for futility decreased the type I error, but also decreased power. An increase in the number of interim analyses that allowed for either early stopping for efficacy or futility generally increased type I error and decreased power.ConclusionsCurrently, regulators require demonstration of control of type I error for both frequentist and Bayesian adaptive designs, particularly for late-phase trials. To demonstrate control of type I error in Bayesian adaptive designs, adjustments to the stopping boundaries are usually required for designs that allow for early stopping for efficacy as the number of analyses increase. If the designs only allow for early stopping for futility then adjustments to the stopping boundaries are not needed to control type I error. If one instead uses a strict Bayesian approach, which is currently more accepted in the design and analysis of exploratory trials, then type I errors could be ignored and the designs could instead focus on the posterior probabilities of treatment effects of clinically-relevant values.
Highlights
Bayesian adaptive methods are increasingly being used to design clinical trials and offer several advantages over traditional approaches
If we allow stopping for efficacy at the interim analysis if Pr(HR < 1| Data) > 0.95 and use this criteria at the final analysis for declaring the trial to be successful, the type I error decreases to 9.8%
Without adjustment of the stopping boundaries, the type I error increased above the desired level of 2.5% as more interim analyses were included that allowed early stopping for efficacy only (Fig. 3a); the power had little variation with the number of interim analyses for these designs (Fig. 3b)
Summary
Bayesian adaptive methods are increasingly being used to design clinical trials and offer several advantages over traditional approaches. Multiplicities can arise in RCTs by testing multiple hypotheses (e.g., multiple endpoints, treatment group comparisons, or subgroup analyses) or from repeatedly testing the same hypothesis over time (e.g., sequential designs). Demonstration of the control of type I error at a prespecified level is generally a prerequisite for a clinical trial design to be accepted by regulators, for late phase trials. Frequentist adaptive designs, such as group sequential designs, typically perform corrections to the stopping boundaries to ensure that the overall type I error rate is maintained at some specific level, e.g., 5% (see [1, 2]). The statistical theory is well developed to control the type I error rate for frequentist adaptive designs
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