An empirical evaluation of approximate and exact regression-based causal mediation approaches for a binary outcome and a continuous or a binary mediator for case-control study designs

Abstract

Background: In the causal mediation analysis framework, several parametric regression-based approaches have been introduced in past years for decomposing the total effect of an exposure on a binary outcome into a direct effect and an indirect effect through a target mediator. In this context, a well-known strategy involves specifying a logistic model for the outcome and invoking the rare outcome assumption (ROA) to simplify estimation. Recently, exact estimators for natural direct and indirect effects have been introduced to circumvent the challenges prompted by the ROA. As for the approximate approaches relying on the ROA, these exact approaches cannot be used as is on case-control data where the sampling mechanism depends on the outcome.

Methods: Considering a continuous or a binary mediator, we empirically compare the approximate and exact approaches using simulated data under various case-control scenarios. An illustration of these approaches on case-control data is provided, where the natural mediation effects of long-term use of oral contraceptives on ovarian cancer, with lifetime number of ovulatory cycles as the mediator, are estimated.

Results: In the simulations, we found few differences between the performances of the approximate and exact approaches when the outcome was rare, both marginally and conditionally on variables. However, the performance of the approximate approaches degraded as the prevalence of the outcome increased in at least one stratum of variables. Differences in behavior were also observed among the approximate approaches. In the data analysis, all studied approaches were in agreement with respect to the natural direct and indirect effects estimates.

Conclusions: In the case where a violation of the ROA applies or is expected, approximate mediation approaches should be avoided or used with caution, and exact estimators favored.

Keywords: Binary outcomes; Case-control study; Counterfactuals; Mediation analysis; Natural effects; Oral contraceptives; Ovarian cancer; Rare outcome assumption.