Longitudinal Mediation Analysis Using Natural Effect Models

Mediation analysis is concerned with the decomposition of the total effect of an exposure on an outcome into the indirect effect, through a given mediator, and the remaining direct effect. This is ideally done using longitudinal measurements of the mediator, which capture the mediator process more finely. However, longitudinal measurements pose challenges for mediation analysis, because the mediators and outcomes measured at a given time point can act as confounders for the association between mediators and outcomes at a later time point; these confounders are themselves affected by the prior exposure and outcome. Such posttreatment confounding cannot be dealt with using standard methods (e.g., generalized estimating equations). Analysis is further complicated by the need for so-called cross-world counterfactuals to decompose the total effect. This work addresses these challenges. In particular, we introduce so-called natural effect models, which parameterize the direct and indirect effect of a baseline exposure with respect to a longitudinal mediator and outcome. These can be viewed as a generalization of marginal structural mean models to enable effect decomposition. We introduce inverse probability weighting techniques for fitting these models, adjusting for (measured) time-varying confounding of the mediator-outcome association. Application of this methodology uses data from the Millennium Cohort Study, a longitudinal study of children born in the United Kingdom between September 2000 and January 2002.

Generalized Structural Mean Models for Evaluating Depression as a Post-treatment Effect Modifier of a Jobs Training Intervention

In randomized controlled trials, the evaluation of an overall treatment effect is often followed by effect modification or subgroup analyses, where the possibility of a different magnitude or direction of effect for varying values of a covariate is explored. While studies of effect modification are typically restricted to pretreatment covariates, longitudinal experimental designs permit the examination of treatment effect modification by intermediate outcomes, where intermediates are measured after treatment but before the final outcome. We present a novel application of generalized structural mean models (GSMMs) for simultaneously assessing effect modification by post-treatment covariates and accounting for noncompliance to assigned treatment status. The proposed approach may also be used to identify post-treatment effect modifiers in the absence of noncompliance. The methods are evaluated using a simulation study that demonstrates that our approach retains consistent estimation of effect modification by intermediate variables that are affected by treatment and also predict outcomes. We illustrate the method using a randomized trial designed to promote re-employment through teaching skills to enhance self-esteem and inoculate job seekers against setbacks in the job search process. Our analysis provides some evidence that the intervention was much less successful among subjects that displayed higher levels of depression at intermediate post-treatment waves of the study. We also compare the assumptions of our approach and principal stratification as alternatives to account for differences in effects by intermediate variables.