Multivariate group sequential tests for global summary statistics

TL;DR

This paper introduces a flexible multivariate group sequential testing framework that efficiently uses multiple endpoints for early stopping decisions, controlling error rates and accommodating complex summary statistics.

Contribution

It develops a novel error spending approach for multivariate interim analyses, including methods for implementation and comparison, enhancing early stopping procedures in clinical trials.

Findings

Numerical integration provided the most accurate error control.

The method accommodates non-linear functions of endpoints.

Sample size calculations are straightforward and reliable.

Abstract

We describe group sequential tests which efficiently incorporate information from multiple endpoints allowing for early stopping at pre-planned interim analyses. We formulate a testing procedure where several outcomes are examined, and interim decisions are based on a global summary statistic. An error spending approach to this problem is defined which allows for unpredictable group sizes and nuisance parameters such as the correlation between endpoints. We present and compare three methods for implementation of the testing procedure including numerical integration, the Delta approximation and Monte Carlo simulation. In our evaluation, numerical integration techniques performed best for implementation with error rate calculations accurate to five decimal places. Our proposed testing method is flexible and accommodates summary statistics derived from general, non-linear functions of endpoints informed by the statistical model. Type 1 error rates are controlled, and sample size calculations can easily be performed to satisfy power requirements.