Sequential tests and estimates after overrunning based on $p$-value combination

TL;DR

This paper introduces a method to incorporate additional data from overrunning in sequential trials using p-value combination, providing exact and approximate inference techniques, with applications to clinical trial data.

Contribution

It develops a novel approach for combining overrunning data in sequential tests using weighted Zs, enhancing inference accuracy in clinical trial analysis.

Findings

Exact inference methods for proportional overrunning information.

Approximate methods evaluated for non-proportional overrunning.

Application demonstrated with clinical trial data.

Abstract

Often in sequential trials additional data become available after a stopping boundary has been reached. A method of incorporating such information from overrunning is developed, based on the ``adding weighted Zs'' method of combining $p$-values. This yields a combined $p$-value for the primary test and a median-unbiased estimate and confidence bounds for the parameter under test. When the amount of overrunning information is proportional to the amount available upon terminating the sequential test, exact inference methods are provided; otherwise, approximate methods are given and evaluated. The context is that of observing a Brownian motion with drift, with either linear stopping boundaries in continuous time or discrete-time group-sequential boundaries. The method is compared with other available methods and is exemplified with data from two sequential clinical trials.