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.

翻译：在准似然模型（该模型将广义线性模型扩展至结果变量完全分布未指定的场景）的研究设计中，精确的统计功效与样本量计算至关重要。传统的PSS方法通常依赖于严格的分布假设，当响应变量呈现非标准分布、方差函数设定错误或预测变量存在复杂依赖结构时，其适用性受到限制。基于近期以可解释性为目标开发的PSS效应量度量方法——特别是线性预测器中2个标准差与伪偏R²——本研究在QL框架下对这些效应量度量进行了扩展与评估，重点考察其在PSS中的实用性。我们通过Wald检验评估了这些方法的实证性能，随后通过涵盖多种结果类型、连接函数和方差结构的广泛模拟，将其扩展至得分检验。为说明实际应用价值，我们将这些效应量度量应用于\citet{cahill2022occupational}关于一线医护人员调查数据，在调整协变量后量化了COVID-19大流行期间感知个人防护装备充足性与心理健康结果之间的关联。研究结果表明，2SLiP与P2R2均能作为传统方法的稳健且可解释的替代方案，在最小化分布假设的前提下保持计算准确性，并增强了实际研究设计中PSS的灵活性。