General Measures of Effect Size for Generalized Linear Models

Thomas M. Menino Convention & Exhibition Center 

Power and sample size calculations for generalized linear models (GLMs) are, somewhat surprisingly, still largely ad hoc. Beyond linear regression, applied statisticians typically have to use methods tailored to a specific GLM, predictor, or distribution — what Paul Rathouz called "bespoke" solutions. Paul recognized an opportunity to define effect sizes that are general enough for routine study planning yet simple enough to be practical for applied investigators. He proposed two such measures, which he affectionately named 2SLiP and P2R2. In joint work with Paul and Shijie Yuan, we present these measures as a general framework for power and sample size calculations across GLMs. The framework accommodates arbitrary predictors and adjusters while requiring only limited information at the planning stage. We justify the framework theoretically and show its practical value through simulations and applied examples. This work grew out of Paul's gift for finding general solutions to the practical problems that emerge through collaboration.

Generalized Linear Model

Hypothesis testing

Logistic regression

Poisson regression

Research design