Longitudinal causal inference is concerned with defining, identifying, and estimating the effect of a time-varying intervention on a time-varying outcome that is indexed by a follow-up time. In an observational study, Robins's generalized g-formula can identify causal effects induced by a broad class of time-varying interventions. Various methods for estimating the generalized g-formula have been posed for different outcome types, such as a failure event indicator by a specified time (e.g. mortality by 5 year follow-up), as well as continuous or dichotomous/multi-valued outcomes measures at a specified time (e.g. blood pressure in mm/hg or an indicator of high blood pressure at 5-year follow-up). Multiply-robust, data-adaptive estimators leverage flexible nonparametric estimation algorithms while allowing for statistical inference. However, extant methods do not accommodate time-smoothing when multiple outcomes are measured over time, which can lead to substantial loss of precision. We propose a novel multiply-robust estimator of the generalized g-formula that accommodates time-smoothing over numerous available outcome measures. Our approach accommodates any intervention that can be described as a Longitudinal Modified Treatment Policy, a flexible class suitable for binary, multi-valued, and continuous longitudinal treatments. Our method produces an estimate of the effect curve: the causal effect of the intervention on the outcome at each measurement time, taking into account censoring and non-monotonic outcome missingness patterns. In simulations we find that the proposed algorithm outperforms extant multiply-robust approaches for effect curve estimation in scenarios with high degrees of outcome missingness and when there is strong confounding. We apply the method to study longitudinal effects of union membership on wages.

翻译：纵向因果推断关注于定义、识别和估计随时间变化的干预措施对随时间变化的结局指标（按随访时间索引）所产生的影响。在观察性研究中，Robins的广义g公式能够识别由广泛类别的时变干预所诱导的因果效应。针对不同类型的结局指标，已有多种估计广义g公式的方法被提出，例如在特定时间前的失效事件指标（如5年随访内的死亡率），以及在特定时间点的连续或二分类/多分类结局测量值（如5年随访时以毫米汞柱计的血压或高血压指标）。多重稳健、数据自适应的估计器利用灵活的非参数估计算法，同时允许进行统计推断。然而，现有方法在随时间测量多个结局时未能纳入时间平滑处理，这可能导致显著的精度损失。我们提出了一种新颖的广义g公式多重稳健估计器，该估计器能够对大量可用的结局测量值进行时间平滑处理。我们的方法适用于任何可被描述为纵向修正治疗策略的干预措施，这是一类适用于二元、多值和连续纵向治疗的灵活类别。我们的方法能够生成效应曲线的估计：即干预措施在每个测量时间点上对结局的因果效应，同时考虑了删失和非单调的结局缺失模式。在模拟研究中，我们发现所提出的算法在结局缺失程度较高和存在强混杂的情况下，优于现有的效应曲线估计多重稳健方法。我们将该方法应用于研究工会会员身份对工资的纵向影响。