Statistical modelling and confounder selection for causal mediation analyses

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The proposed research program concerns the development of statistical methods for causal mediation. Mediation analyses are an increasingly popular class of techniques used for estimating exposure (treatment) effects under the assumption that there is a mediating variable on the causal pathway between exposure and outcome. Such an analysis aims to decompose the total exposure effect in an indirect effect through the mediator and in a direct effect which avoids the mediation path. The program is divided in three themes that address relevant modelling issues in causal mediation: (1) developing an exact regression-based mediation approach for a binary outcome; (2) adapting two existing Bayesian regression models for purposes of causal mediation; (3) investigating confounder selection for valid estimation of mediation effects. Regarding (1), we have recently observed that the "rare outcome assumption" made in the conventional regression approach for a binary outcome can lead to wrong inferences in practice. We will propose an exact estimator for the natural direct and indirect effects whose theoretical validity does not rely on the rareness (or commonness) of the outcome. This will be accomplished for both binary and continuous mediators, where a logit-normal representation will be used for the nested counterfactual outcome probabilities in the latter case. For theme (2), we are planning to expand on Bayesian mediation methodology by building on two regression models with attractive features. First, we propose a latent multivariate Student-t model as a basis for an exact mediation approach for a binary outcome and possibly multiple binary mediators. Secondly, we aim to elaborate a flexible mediation strategy based on Bayesian additive regression trees (BART) models. The Mediation Formula will be used to express the natural mediation effects from both model specifications. There is currently a lack of information regarding how to select covariates for adjustment in causal mediation models when substantive knowledge is alone not sufficient for this task. In theme (3), we will target two well known confounder selection algorithms introduced for non-mediated contexts and investigate how they can be modified for mediation contexts in order to yield unbiased and efficient estimators of direct and indirect effects. All three themes will require theoretical developments and validation through simulation studies. Open-access software will be created and comprehensive examples will be made available to increase uptake by substantive researchers. To conclude, this program is about original and innovative statistical developments on several important aspects of causal mediation analyses. It is expected to increase the reliability of results obtained from this type of analyses in many fields of applied research (e.g., social science, epidemiology).