Longitudinal studies frequently incorporate covariates that evolve over time, creating complex dependence structures between outcomes and predictors. When covariates are time dependent, standard power analysis tools--largely developed for generalized estimating equations (GEE)--can yield misleading results because they do not account for the moment based structure required for valid marginal inference. Generalized Method of Moments (GMM) provides a flexible and efficient framework for estimating marginal effects in the presence of time dependent covariates, yet no practical tools exist for conducting power analysis under GMM. This paper introduces a modern, implementable framework for power estimation in longitudinal studies with time dependent covariates using GMM. Two complementary approaches are developed: a Wald based method that leverages the asymptotic normality of GMM estimators, and a distance metric method based on quadratic forms of sample and population moment conditions. Both approaches require only limited distributional assumptions and rely on valid moment conditions rather than full likelihood specification. We outline the theoretical foundations, provide step by step implementation guidance, and illustrate the methods using data from the Osteoarthritis Initiative. A simulation framework is presented for evaluating empirical performance. These methods fill a critical gap in the longitudinal modeling literature by offering applied researchers a practical, distribution light approach to power estimation when time dependent covariates are present and GMM is the preferred estimation technique.

翻译：纵向研究常纳入随时间演变的协变量，由此在结局与预测变量间形成复杂依赖结构。当时变协变量存在时，主要基于广义估计方程（GEE）开发的经典统计功效分析工具可能产生误导性结果，因其未考虑实现有效边际推断所需的矩基结构。广义矩方法（GMM）为在时变协变量存在时估计边际效应提供了灵活高效的框架，但现有文献尚缺乏基于GMM进行统计功效分析的实用工具。本文提出一套现代化、可实施的统计功效估计框架，用于含时变协变量的纵向研究。我们开发了两种互补方法：基于Wald的渐进正态性方法，利用GMM估计量的渐近正态性；以及基于样本矩条件与总体矩条件二次型的距离度量方法。两种方法仅需有限分布假设，依赖有效矩条件而非完整似然规范。本文阐述理论基础，提供分步实施指南，并采用骨关节炎倡议数据库进行方法演示。我们提出仿真框架用于评估经验性能。这些方法为应用研究者提供了在时变协变量存在且GMM为优选估计技术时的实用、轻分布假设的统计功效估计工具，填补了纵向建模领域的关键空白。