Group sequential designs for negative binomial outcomes

TL;DR

This paper develops and evaluates group sequential testing procedures for negative binomial outcomes in clinical trials, providing methods for planning, analysis, and error control, with implementation in an R package.

Contribution

It introduces a Wald-based group sequential testing method for negative binomial data, including finite sample properties and error control techniques, applicable to clinical trial planning.

Findings

Asymptotic normal theory applies to negative binomial outcomes with Wald statistics.

Two small-sample error control methods improve type I error rates.

Simulation studies demonstrate method effectiveness in realistic clinical trial scenarios.

Abstract

Count data and recurrent events in clinical trials, such as the number of lesions in magnetic resonance imaging in multiple sclerosis, the number of relapses in multiple sclerosis, the number of hospitalizations in heart failure, and the number of exacerbations in asthma or in chronic obstructive pulmonary disease (COPD) are often modeled by negative binomial distributions. In this manuscript we study planning and analyzing clinical trials with group sequential designs for negative binomial outcomes. We propose a group sequential testing procedure for negative binomial outcomes based on Wald statistics using maximum likelihood estimators. The asymptotic distribution of the proposed group sequential tests statistics are derived. The finite sample size properties of the proposed group sequential test for negative binomial outcomes and the methods for planning the respective clinical trials are assessed in a simulation study. The simulation scenarios are motivated by clinical trials in chronic heart failure and relapsing multiple sclerosis, which cover a wide range of practically relevant settings. Our research assures that the asymptotic normal theory of group sequential designs can be applied to negative binomial outcomes when the hypotheses are tested using Wald statistics and maximum likelihood estimators. We also propose two methods, one based on Student's t-distribution and one based on resampling, to improve type I error rate control in small samples. The statistical methods studied in this manuscript are implemented in the R package \textit{gscounts}, which is available for download on the Comprehensive R Archive Network (CRAN).