Sample size determination for a binary response in a superiority clinical trial using a hybrid classical and Bayesian procedure

Maria M Ciarleglio,Christopher D Arendt

doi:10.1186/s13063-017-1791-0

Abstract

BackgroundWhen designing studies that have a binary outcome as the primary endpoint, the hypothesized proportion of patients in each population experiencing the endpoint of interest (i.e., π1,π2) plays an important role in sample size and power calculations. Point estimates for π1 and π2 are often calculated using historical data. However, the uncertainty in these estimates is rarely addressed.MethodsThis paper presents a hybrid classical and Bayesian procedure that formally integrates prior information on the distributions of π1 and π2 into the study’s power calculation. Conditional expected power (CEP), which averages the traditional power curve using the prior distributions of π1 and π2 as the averaging weight conditional on the presence of a positive treatment effect (i.e., π2>π1), is used, and the sample size is found that equates the pre-specified frequentist power (1−β) and the conditional expected power of the trial.ResultsNotional scenarios are evaluated to compare the probability of achieving a target value of power with a trial design based on traditional power and a design based on CEP. We show that if there is uncertainty in the study parameters and a distribution of plausible values for π1 and π2, the performance of the CEP design is more consistent and robust than traditional designs based on point estimates for the study parameters. Traditional sample size calculations based on point estimates for the hypothesized study parameters tend to underestimate the required sample size needed to account for the uncertainty in the parameters. The greatest marginal benefit of the proposed method is achieved when the uncertainty in the parameters is not large.ConclusionsThrough this procedure, we are able to formally integrate prior information on the uncertainty and variability of the study parameters into the design of the study while maintaining a frequentist framework for the final analysis. Solving for the sample size that is necessary to achieve a high level of CEP given the available prior information helps protect against misspecification of hypothesized treatment effect and provides a substantiated estimate that forms the basis for discussion about the study’s feasibility during the design phase.

Highlights

When designing studies that have a binary outcome as the primary endpoint, the hypothesized proportion of patients in each population experiencing the endpoint of interest (i.e., π1, π2) plays an important role in sample size and power calculations
We extend these methods to a binary endpoint by using a “hybrid classical and Bayesian” [7] technique based on conditional expected power (CEP) [8] to account for the uncertainty in study parameters π1 and π2 when determining the sample size of a superiority clinical trial
While sample size calculations based on traditional power assume no uncertainty in the study parameters, the hybrid classical and Bayesian procedure presented here formally accounts for the uncertainty in the study parameters by incorporating the prior distributions for π1 and π2 into the calculation of conditional expected power (CEP)

Summary

Introduction

When designing studies that have a binary outcome as the primary endpoint, the hypothesized proportion of patients in each population experiencing the endpoint of interest (i.e., π1, π2) plays an important role in sample size and power calculations. When designing a study that has a binary outcome as the primary endpoint, the hypothesized proportion of patients in each population experiencing the endpoint of interest (i.e., π1, π2) plays an important role in sample size determination. There is often uncertainty in these hypothesized proportions and, a distribution of plausible values that should be considered when determining sample size Misspecification of these hypothesized proportions in the sample size calculation may lead to an underpowered study, or one that has a low probability of detecting a smaller and potentially clinically relevant difference when such a difference exists [4]. A method for determining sample size that formally uses prior information on the distribution of study design parameters can mitigate the risk that the power calculation will be overly optimistic or overly conservative

Methods

Results

Discussion

Conclusion