An improved sample size calculation method for score tests in generalized linear models

TL;DR

This paper introduces a modified sample size calculation method for score tests in generalized linear models, improving accuracy especially for large effect sizes and extending applicability to noninferiority trials.

Contribution

It proposes a variance-based modification of the Self-Mauritsen method and extends it to noninferiority trials, addressing limitations of previous approaches.

Findings

The modified method improves sample size accuracy for large effects.

It effectively applies to logistic and negative binomial regressions.

Numerical examples confirm the method's superior performance.

Abstract

Self and Mauritsen (1988) developed a sample size determination procedure for score tests in generalized linear models under contiguous alternatives. Its performance may deteriorate when the effect size is large. We propose a modification of the Self-Mauritsen method by taking into account of the variance of the score statistic under both the null and alternative hypotheses, and extend the method to noninferiority trials. The modified approach is employed to calculate the sample size for the logistic regression and negative binomial regression in superiority and noninferiority trials. We further explain why the formulae recently derived by Zhu and Lakkis tend to underestimate the required sample size for the negative binomial regression. Numerical examples are used to demonstrate the accuracy of the proposed method.