An Improved Sample Size Calculation Method for Score Tests in Generalized Linear Models

Self and Mauritsen 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.

Automated summary

Self and Mauritsen developed a sample size determination procedure for score tests in generalized linear models, which may deteriorate in performance when effect size is large. They proposed a modification to take into account the variance of the score statistic under null and alternative hypotheses, and extended the method to noninferiority trials. The modified approach was utilized to calculate sample size for logistic regression and negative binomial regression in superiority and noninferiority trials, while explaining why formulae by Zhu and Lakkis tend to underestimate sample size for the negative binomial regression.