Nonparametric efficient estimation of the longitudinal front-door functional

Abstract: 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 are measured repeatedly over time. However, to the best of our knowledge, applications of the longitudinal front-door criterion remain unexplored. This may reflect both limited awareness of the method and the absence of suitable estimation techniques. In this report, we propose nonparametric efficient estimators of the longitudinal front-door functional. The estimators are multiply robust and allow for the use of data-adaptive (machine learning) methods for nuisance estimation while providing valid inference. The theoretical properties of the estimators are showcased in a simulation study.