Power and sample size calculations for Wald tests in generalized linear models (GLMs) are often limited to specific cases like logistic regression. More general methods typically require detailed study parameters that are difficult to obtain during planning. We introduce two new effect size measures for estimating power and sample size in studies using Wald tests across any GLM. These measures accommodate any number of predictors or adjusters and require only basic study information. We provide practical guidance for interpreting and applying these measures to approximate a key parameter in power calculations. We also derive asymptotic bounds on the relative error of these approximations, showing that accuracy depends on features of the GLM such as the nonlinearity of the link function. To complement this analysis, we conduct simulation studies across common model specifications, identifying best use cases and opportunities for improvement. Finally, we test the methods in finite samples to confirm their practical utility, using a case study on the relationship between education and receipt of mental health treatment.

翻译：广义线性模型（GLM）中Wald检验的功效与样本量计算通常局限于逻辑回归等特定情形。更通用的方法往往需要规划阶段难以获取的详细研究参数。本文针对使用Wald检验的任意GLM研究，提出了两种用于估计功效与样本量的新型效应量度量方法。这些度量可适应任意数量的预测变量或调整变量，且仅需基础研究信息。我们为解释和应用这些度量以近似功效计算中的关键参数提供了实践指导，并推导了这些近似值相对误差的渐近界，证明其精度取决于GLM的特征（如连接函数的非线性程度）。为完善分析，我们在常见模型设定下进行了模拟研究，确定了最佳适用场景与改进空间。最后，通过教育程度与心理健康治疗接受度关系的案例研究，我们在有限样本中验证了这些方法的实际效用。