Natural Effects in the Presence of an Intermediate Confounder: Evaluation of Pragmatic Estimation Strategies With an Emphasis on the Relationship Between Natural and Interventional Effects.

Abstract

Mediation analysis using the so-called natural effects is an essential tool to uncover causal pathways between an exposure and an outcome. However, natural effects are not generally identified in the presence of an intermediate confounder ( $L$ ), a situation that arguably arises frequently in practice. Three pragmatic approaches can be used to estimate natural effects when such a confounder $L$ is present: Natural effects estimators that omit $L$ , natural effects estimators that consider $L$ as a pre-exposure confounder, or interventional effects estimators. Interventional effects are analogous to natural effects, but remain identified when $L$ is present. The goal of this study was two-fold: (1) to assess the extent to which natural and interventional estimands differ under a variety of data-generating mechanisms with intermediate confounding and (2) using simulations, to investigate the corresponding performance of the three aforementioned strategies to estimate natural effects. In the continuous outcome case, using interventional effects estimators was found to be a better analytic strategy for estimating natural effects than using standard natural effects estimators when the interaction term between $L$ and $M$ in the outcome model was null or moderate in comparison to the other parameters. However, the performance of interventional effects declined as the $L$ - $M$ interaction was increased. In the binary outcome case, the three estimation strategies yielded more similar results than in the continuous outcome case. The difference between the three analytic strategies is illustrated using data from the World Value Survey.