Methods and Applications of Statistics in Clinical Trials, Volume 2: Planning, Analysis, and Inferential Methods

Chapter 7

Conditional Power in Clinical Trial Monitoring

Ming T. Tan

7.1 Introduction

For ethical, economical, and scientific reasons, clinical trials may be terminated early for a pronounced treatment benefit or the lack thereof. In addition to group sequential tests and type I error-spending functions, another approach is to address the question more directly by asking whether the accumulated evidence is sufficiently convincing for efficacy. Or, if evidence is lacking, one should ask whether the trial should continue to the planned end and whether the conventional (reference) nonsequential test (RNST) should be employed. Conditional power is one way to quantify this evidence. It is simply the usual statistical power of RNST conditional on the current data. Thus, it is the conditional probability that the RNST will reject the null hypothesis on completion of the trial given the data currently available at a given parameter value of the alternative hypothesis. Therefore, if the conditional power is too low or exceedingly high, then the trial may be terminated early for futility or for efficacy, respectively. The early stopping procedure derived based on conditional power is referred to as stochastic curtailing, by which an ongoing trial is curtailed as soon as the trend based on current data becomes highly convincing [1]. Therefore, conditional power serves two closely related purposes: (1) as a measure of trend reversal (e.g., futility index) and (2) as an interim analysis procedure ...