General measures of effect size to calculate power and sample size for Wald tests with generalized linear models

TL;DR

This paper introduces two new effect size measures for power and sample size calculations in Wald tests for generalized linear models, applicable across various models with minimal parameter requirements.

Contribution

It provides general effect size measures for GLMs, along with practical guidance, asymptotic error bounds, and validation through simulations and a case study.

Findings

Effect size measures are effective across different GLMs.

Accuracy depends on link function nonlinearity.

Simulation studies identify optimal use cases.

Abstract

Power and sample size calculations for Wald tests in generalized linear models (GLMs) are often limited to specific cases like logistic regression. More general methods typically require detailed study parameters that are difficult to obtain during planning. We introduce two new effect size measures for estimating power and sample size in studies using Wald tests across any GLM. These measures accommodate any number of predictors or adjusters and require only basic study information. We provide practical guidance for interpreting and applying these measures to approximate a key parameter in power calculations. We also derive asymptotic bounds on the relative error of these approximations, showing that accuracy depends on features of the GLM such as the nonlinearity of the link function. To complement this analysis, we conduct simulation studies across common model specifications, identifying best use cases and opportunities for improvement. Finally, we test the methods in finite samples to confirm their practical utility, using a case study on the relationship between education and receipt of mental health treatment.