A More Efficient Causal Mediator Model Without the No-Unmeasured-Confounder Assumption

Mediator models have been developed primarily under the assumption of no-unmeasured-confounding. In many situations, this assumption is violated and may lead to the identification of mediator variables that actually are statistical artifacts. The rank preserving model (RPM) is an alternative approach to estimate controlled direct and mediator effects. It is based on the structural mean models framework and a no-effect-modifier assumption. The RPM assumes that unobserved confounders do not interact with treatment or mediators. This assumption is often more plausible to hold than the no-unmeasured-confounder assumption. So far, models using the no-effect-modifier assumption have been rarely used, which might be due to its low power and inefficiency in many scenarios. Here, a semi-parametric nonlinear extension, the nRPM, is proposed that overcomes this inefficiency using thin plate regression splines that both increase the predictive power of the model and decrease the misspecification present in many situations. In a simulation study, it is shown that the nRPM provides estimates that are robust against the violation of the no-effect-modifier assumption and that are substantively more efficient than those of the RPM. The model is illustrated using a data set on CD4 cell counts in a context of the human immunodeficiency virus (HIV).