Robust Power and Sample Size Calculations in Quasi-likelihood Models: Methods and Practice

TL;DR

This paper introduces robust effect size measures, 2SLiP and P2R2, for power and sample size calculations in quasi-likelihood models, improving flexibility and accuracy in diverse, real-world study settings.

Contribution

It extends and evaluates effect size measures 2SLiP and P2R2 within the quasi-likelihood framework, demonstrating their robustness and interpretability for practical PSS applications.

Findings

Both measures perform well across diverse outcome types and link functions.

They provide accurate PSS estimates with minimal distributional assumptions.

Application to health data illustrates their practical utility.

Abstract

Accurate power and sample size (PSS) calculations are essential for designing studies that use quasi-likelihood (QL) models, which extend generalized linear models (GLMs) to settings where the full distribution of the outcome is not specified. Traditional PSS approaches often rely on restrictive distributional assumptions, limiting their applicability when responses have non-standard distributions, variance functions are misspecified, or when predictors exhibit complex dependence structures. Building on recent advances in effect size measures for PSS - specifically, 2 Standard Deviations in the Linear Predictor (2SLiP) and Pseudo-Partial $R^2$ (P2R2) - developed with interpretability in mind, this paper extends and evaluates these effect size measures in the QL framework, keying in particular on their utility in PSS. We assess their empirical performance for the Wald test and then extend to the score test through extensive simulations across diverse outcome types, link functions, and variance structures. To illustrate practical utility, we applied these effect size measures to survey data on frontline health care workers from \citet{cahill2022occupational} to quantify the association between perceived personal protective equipment adequacy and mental health outcomes during the COVID-19 pandemic, adjusting for covariates. Our findings demonstrate that both 2SLiP and P2R2 provide robust and interpretable alternatives to traditional methods, maintaining accuracy with minimal distributional assumptions and enhancing the flexibility of PSS for realistic study designs.