Robust power and sample size calculations in quasi-likelihood models: methods and practice

Accurate power and sample size calculations are essential in study planning, yet they are often difficult to carry out for quasi-likelihood (QL) models. Traditional power and sample size (PSS) approaches often rely on restrictive distributional assumptions, limiting their applicability when responses have non-standard distributions, variance functions are misspecified, or when covariates exhibit complex dependence structures.

We examine whether two effect size measures-2 Standard Deviations in the Linear Predictor (2SLiP) and Pseudo-Partial [Formula: see text] (P2R2)-originally developed for Wald tests involving generalized linear models, are effective at power and sample size calculations in the QL framework. Through extensive simulations across diverse outcome types, link functions, and variance structures, we assess their performance under Wald tests and explore whether they remain useful for score tests. To illustrate practical utility, we apply these effect size measures to survey data on frontline health care workers to quantify the association between perceived personal protective equipment (PPE) adequacy and burnout risk during the COVID-19 pandemic, adjusting for covariates.

We show that the two generalized linear model (GLM)-based effect sizes are fundamentally moment-based objects, and therefore extend directly to QL models. Across all simulation settings, both measures remained accurate, with sample size and power estimates within 3% and 2% of the target, respectively. In the case study, the estimated effect sizes for perceived PPE adequacy (2SLiP = 0.096 and P2R2 = 0.020) correspond to small but meaningful associations with burnout risk after adjustment for demographic and occupational covariates; both yielded accurate recommendations for sample size.

Both 2SLiP and P2R2 offer robust alternatives for power and sample size calculation in QL settings. By requiring minimal distributional assumptions, these measures enhance the flexibility and reliability of power and sample size calculations for realistic study designs commonly encountered in medical and public health research.