Effect modification occurs when the impact of the treatment on an outcome varies based on the levels of other covariates known as effect modifiers. Modeling of these effect differences is important for etiological goals and for purposes of optimizing treatment. Structural nested mean models (SNMMs) are useful causal models for estimating the potentially heterogeneous effect of a time-varying exposure on the mean of an outcome in the presence of time-varying confounding. In longitudinal health studies, information on many demographic, behavioural, biological, and clinical covariates may be available, among which some might cause heterogeneous treatment effects. A data-driven approach for selecting the effect modifiers of an exposure may be necessary if these effect modifiers are \textit{a priori} unknown and need to be identified. Although variable selection techniques are available in the context of estimating conditional average treatment effects using marginal structural models, or in the context of estimating optimal dynamic treatment regimens, all of these methods consider an outcome measured at a single point in time. In the context of an SNMM for repeated outcomes, we propose a doubly robust penalized G-estimator for the causal effect of a time-varying exposure with a simultaneous selection of effect modifiers and prove the oracle property of our estimator. We conduct a simulation study to evaluate the performance of the proposed estimator in finite samples and for verification of its double-robustness property. Our work is motivated by a study of hemodiafiltration for treating patients with end-stage renal disease at the Centre Hospitalier de l'Universit\'e de Montr\'eal.

翻译：效应修饰发生在治疗对结局的影响因其他协变量（称为效应修饰子）水平不同而变化时。对这些效应差异的建模对于病因学研究目标和优化治疗策略具有重要意义。结构化嵌套均值模型（SNMMs）是在存在时依性混杂因素的情况下，估计时依性暴露对结局均值的潜在异质性效应的有效因果模型。在纵向健康研究中，可能获取大量人口学、行为学、生物学和临床协变量信息，其中部分协变量可能导致异质性治疗效应。若效应修饰子先验未知且需被识别，则需采用数据驱动方法选择暴露的效应修饰子。尽管在利用边际结构模型估计条件平均处理效应或估计最优动态治疗方案的情境下已有变量选择技术，但这些方法均仅考虑单次时间点的结局测量。针对重复结局的SNMM框架，我们提出一种双稳健惩罚G估计量，用于同时选择效应修饰子并估计时依暴露的因果效应，同时证明该估计量的神谕性质。我们通过模拟研究评估所提估计量在有限样本下的性能并验证其双稳健性。本研究受蒙特利尔大学医院中心开展的血液透析滤过治疗终末期肾病患者研究的启发。