Treatment-mediator interaction when estimating causal effects
Abstract: In a variety of disciplines, causal mediation analysis is routinely conducted by researchers to examine the roles of variables which lie in the causal paths between the treatment and outcome variables. These effects are commonly estimated using a parametric model approach, where one fits regression models for the mediator and outcome variables. The estimated coefficients from the regression models are then used to estimate the direct and indirect effects. When taking this approach, two potential sources of bias are unobserved confounding and model misspecification. In this thesis, the focus lies on unobserved mediator-outcome confounding and model misspecifiation where an existing treatment-mediator interaction is excluded from the outcome model. We compare and evaluate the magnitude of the bias resulting from these sources in different scenarios through simulations. The results show that, in the worst cases, both sources of bias can result in severely biased effect estimators. It is hard to find an overarching conclusion to which source results in a larger bias in general, as it is highly dependent on the scenario at hand. In addition to the above mentioned bias evaluation, we introduce a statistical test with the goal of aiding researchers contemplating whether or not to include an interaction term in the outcome model. The test is based upon the fact that different definitions of the direct and indirect effects result in different effect estimates when an interaction is present. In an attempt to improve the significance level accuracy of the test for smaller samples, we compute p-values based on inverted bootstrap confidence intervals. Simulations show that using these bootstrap methods does improve the accuracy of a chosen significance level in many situations compared to relying on asymptotic normality of the test statistic. Despite this, our proposed test performs worse than more standard test methods, such as a t-test for the regression coefficient, in most examined scenarios.
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