Estimation of Controlled Direct Effects in Longitudinal Mediation Analyses with Latent Variables in Randomized Studies

Abstract In a randomized study with longitudinal data on a mediator and outcome, estimating the direct effect of treatment on the outcome at a particular time requires adjusting for confounding of the association between the outcome and all preceding instances of the mediator. When the confounders are themselves affected by treatment, standard regression adjustment is prone to severe bias. In contrast, G-estimation requires less stringent assumptions than path analysis using SEM to unbiasedly estimate the direct effect even in linear settings. In this article, we propose a G-estimation method to estimate the controlled direct effect of treatment on the outcome, by adapting existing G-estimation methods for time-varying treatments without mediators. The proposed method can accommodate continuous and noncontinuous mediators, and requires no models for the confounders. Unbiased estimation only requires correctly specifying a mean model for either the mediator or the outcome. The method is further extended to settings where the mediator or outcome, or both, are latent, and generalizes existing methods for single measurement occasions of the mediator and outcome to longitudinal data on the mediator and outcome. The methods are utilized to assess the effects of an intervention on physical activity that is possibly mediated by motivation to exercise in a randomized study.