Boosting the precision of mediation analyses of randomised experiments through covariate adjustment.

Analyses of randomised experiments frequently include attempts to decompose the intention-to-treat effect into a direct and indirect effect, mediated by given intermediaries, with the aim to shed light onto the treatment mechanism. Methods from causal mediation analysis have facilitated this by allowing for arbitrary models for the outcome and the mediator. They thereby generalise the traditional approach to direct and indirect effects, which is essentially limited to linear models. The default maximum likelihood methods make use of a model for the conditional distribution of the mediator, given treatment and baseline covariates, but are prone to bias when that model is misspecified. In randomised experiments, specification of such model can be easily avoided, but at the expense of a sometimes major efficiency loss when those baseline covariates are predictive of the mediator. In this article, we develop a compromise approach: it makes use of a model for the mediator to optimally extract information from the baseline covariate data but is insulated from the impact of misspecification of that model; it achieves this by exploiting the known randomisation probabilities. Simulation studies and the analysis of a randomised study show major efficiency gains and confirm our theoretical findings that the default methods from causal mediation analysis are sometimes, although not always, reasonably robust to model misspecification.