Comparison of Bayesian and frequentist group-sequential clinical trial designs

Nigel Stallard,Susan Todd,Simon Gates,Elizabeth G Ryan

doi:10.1186/s12874-019-0892-8

Abstract

BackgroundThere is a growing interest in the use of Bayesian adaptive designs in late-phase clinical trials. This includes the use of stopping rules based on Bayesian analyses in which the frequentist type I error rate is controlled as in frequentist group-sequential designs.MethodsThis paper presents a practical comparison of Bayesian and frequentist group-sequential tests. Focussing on the setting in which data can be summarised by normally distributed test statistics, we evaluate and compare boundary values and operating characteristics.ResultsAlthough Bayesian and frequentist group-sequential approaches are based on fundamentally different paradigms, in a single arm trial or two-arm comparative trial with a prior distribution specified for the treatment difference, Bayesian and frequentist group-sequential tests can have identical stopping rules if particular critical values with which the posterior probability is compared or particular spending function values are chosen. If the Bayesian critical values at different looks are restricted to be equal, O’Brien and Fleming’s design corresponds to a Bayesian design with an exceptionally informative negative prior, Pocock’s design to a Bayesian design with a non-informative prior and frequentist designs with a linear alpha spending function are very similar to Bayesian designs with slightly informative priors.This contrasts with the setting of a comparative trial with independent prior distributions specified for treatment effects in different groups. In this case Bayesian and frequentist group-sequential tests cannot have the same stopping rule as the Bayesian stopping rule depends on the observed means in the two groups and not just on their difference. In this setting the Bayesian test can only be guaranteed to control the type I error for a specified range of values of the control group treatment effect.ConclusionsComparison of frequentist and Bayesian designs can encourage careful thought about design parameters and help to ensure appropriate design choices are made.

Highlights

There is a growing interest in the use of Bayesian adaptive designs in late-phase clinical trials
Some have suggested that the stopping rules for Bayesian group sequential designs should be chosen in such a way that the frequentist type I error rate is controlled [2, 5, 6], in the setting of phase III or late phase II clinical trials, when it is often considered desirable to control the risk of a false positive result, that is an erroneous conclusion that a new treatment is efficacious
In the two-parameter setting we show that the frequentist and Bayesian designs cannot correspond, and show that in this case the Bayesian group-sequential designs can only control the type I error rate for specified values of the control group treatment effect

Summary

Introduction

There is a growing interest in the use of Bayesian adaptive designs in late-phase clinical trials. This includes the use of stopping rules based on Bayesian analyses in which the frequentist type I error rate is controlled as in frequentist group-sequential designs. Some have suggested that the stopping rules for Bayesian group sequential designs should be chosen in such a way that the frequentist type I error rate is controlled [2, 5, 6], in the setting of phase III or late phase II clinical trials, when it is often considered desirable to control the risk of a false positive result, that is an erroneous conclusion that a new treatment is efficacious.

Methods

Results

Discussion

Conclusion