Power and sample size for generalized linear models

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PROJECT SUMMARY / ABSTRACT This project responds to FOA PA-21-235. A variety of well-characterized and valid methods for power and sam- ple size (PSS) estimation in generalized linear models (GLM) have been developed. These are primarily in the area of linear models for continuous data and logistic regression for binary data. By and large, methods that are more general require a prior specification of several study-specific details in order to be implemented in a par- ticular application, and this can pose challenges for applied statisticians and non-statistical collaborators. These challenges have impeded the study design of translational mental health research, randomized clinical trials in psychiatric populations, and other investigations that involve GLM in ways that linear models do not. To overcome these challenges, the overarching goal of this project is to develop methods for estimating power, needed sample size, or minimally-detectable effect size in study designs involving GLMs. To be broadly useful, such methods should be accurate, interpretable, and, importantly, easily-specified. This project offers, in the framework of GLMs, a general formulation with the aim to recapture, to close approx- imation, features of the common approach to PSS for linear models, namely the use of partial multiple R-squared as a general measure of effect size. This is accomplished by introducing two GLM analogues of R-squared. Local and more distal alternative hypotheses are considered, the latter requiring more attention to yield accurate re- sults as the alternative hypothesis moves further from the null. Both Wald and score tests (which coincide under linear models) are also considered. This project has three specific aims: Using novel GLM analogues of multiple partial R-squared for linear models, develop approaches to estimate power, needed sample size, or minimally detectable effect size for Wald (Aim 1) and score (Aim 2) tests to be conducted in the framework of GLMs. Aim 3 is to develop, test, document and disseminate software implementing the new methods. The developed methods are guided by and applied to two collaborative projects in translational mental health. The expectation is a new and general suite of applicable and usable approaches to power and sample size es- timation for the “bread-and-butter” class of generalized linear models forming the foundation of so many analysis methods in modern biomedical and public health investigation.