The front-door criterion is an identification strategy for the intervention-specific mean outcome in settings where the standard back-door criterion fails due to unmeasured exposure-outcome confounders, but an intermediate variable exists that completely mediates the effect of exposure on the outcome and is not affected by unmeasured confounding. The front-door criterion has been extended to the longitudinal setting, where exposure and mediator vary over time. However, with the exception of a simple plug-in estimator, no suitable estimation techniques have been proposed. In this work, we derive nonparametric efficient estimators of the longitudinal front-door functional. The estimators accommodate high-dimensional mediators, are multiply robust, and allow for the use of data-adaptive methods for estimating nuisance functions while still providing valid inference. The theoretical properties of the estimators are illustrated in a simulation study, and we apply the estimators to a trial of peanut allergy in infants.

翻译：前门准则是干预特异性平均结果的一种识别策略，适用于标准后门准则因存在未测量的暴露-结果混杂因子而失效，但存在一个完全中介暴露对结果的影响且不受未测量混杂影响的中间变量的情况。前门准则已被扩展到纵向设置，其中暴露和中介变量随时间变化。然而，除了简单的插件估计量外，尚未提出合适的估计技术。在这项工作中，我们推导了纵向前门泛函的非参数高效估计量。这些估计量能够处理高维中介变量，具有多重稳健性，并允许使用数据自适应方法来估计干扰函数，同时仍能提供有效的推断。估计量的理论性质通过模拟研究进行了说明，我们还将这些估计量应用于一项婴儿花生过敏试验。