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

2026-02-28

AI Summary

This study addresses the limitations of conventional power and sample size calculations in quasi-likelihood models, which rely on strong distributional assumptions and struggle with real-world complexities such as nonstandard distributions, misspecified variance structures, or intricate covariate dependencies. To overcome these challenges, the authors extend the interpretable effect size metrics 2SLiP and P2R2 into the quasi-likelihood framework, developing a robust approach that avoids stringent distributional requirements. The proposed method is evaluated under Wald and Score tests across diverse link functions, variance specifications, and outcome types. Validation via Monte Carlo simulations and an empirical analysis of healthcare workers’ mental health data demonstrates that the approach offers strong interpretability, accuracy, and robustness, substantially enhancing the flexibility and reliability of sample size planning in complex applied research settings.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Reasoning under Uncertainty: Other Foundations of Reasoning under Uncertainty
• Natural Language Processing: Safety and Robustness

Application Category

• User Modeling, Personalization and Recommendation: Metrics for user behavior and evaluating success
• Security and Privacy: Large-scale security measurements
• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics

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.

Problem

• power and sample size
• quasi-likelihood models
• distributional assumptions
• effect size
• study design

Innovation

• Quasi-likelihood
• Power and Sample Size
• 2SLiP
• P2R2
• Robust inference