Confounder detection in linear mediation models: Performance of kernel-based tests of independence

It is well-known that the identification of direct and indirect effects in mediation analysis requires strong unconfoundedness assumptions. Even when the predictor is under experimental control, unconfoundedness assumptions must be imposed on the mediator-outcome relation in order to guarantee valid indirect-effect identification. Researchers are therefore advised to test for unconfoundedness when estimating mediation effects. Significance tests to evaluate unconfoundedness usually rely on an instrumental variable (IV)-that is, a variable that is nonindependent of the explanatory variable and, at the same time, independent of all exogenous factors that affect the outcome when the explanatory variable is held constant. Because IVs may be hard to come by, the present study shows that confounders of the mediator-outcome relation can be detected without making use of IVs when variables are nonnormal. We show that kernel-based tests of independence are able to detect confounding under nonnormality. Results from a simulation study are presented that suggest that these tests perform well in terms of Type I error protection and statistical power, independent of the distribution or measurement level of the confounder. A real-world data example from the Job Search Intervention Study (JOBS II) illustrates how the presented approach can be used to minimize the risk of obtaining biased indirect-effect estimates. The data requirements and role of unconfoundedness tests as diagnostic tools are discussed. A Monte Carlo-based power analysis tool for sample size planning is also provided.