Confound It: Assessing the Impact of Confounders on Mediation

The accuracy of the mediated effect estimate depends on assuming that there is no confounding of the path linking either the predictor to the mediator or the mediator to the outcome. Random assignment removes confounding between the predictor and the mediator but it does not eliminate the risk of confounding between the mediator and the outcome as noted by many researchers (Holland, 1988; Mackinnon, 2008). Sensitivity analysis has been suggested as way to assess how confounding might estimates of the mediated effect (Imai, Keele, and Yamamoto, 2010; Cox, Kisbu-Sakarya, Miočević, and MacKinnon, 2014).  A variety of methods have been proposed to conduct this sensitivity analysis including elaborate resampling methods.  The purpose of this poster is to describe how to use standard structural equation programs to conduct analysis to assess sensitivity of the observed mediation results to unmeasured confounders.  We describe sensitivity analysis for confounders using the Mplus structural equation modeling program for the single mediator model. For maximum likelihood, a residual covariance between M and Y can be fixed to some value other than zero and used to explore the possible range of confounding. Plots of how the mediated effect changes as a function of the size of the residual covariance are presented. 

This poster combines results from a simulation study along with data from the PHLAME intervention intended to increase firefighter’s knowledge regarding the benefits of fruits and vegetables and their subsequent eating of fruits and vegetables (Yuan and MacKinnon, 2009).

Consistent with other uses of sensitivity analysis, the addition of the confounding estimate typically, but not always, reduces the estimated mediated effect. For example, when the a and b paths reflect a medium effect size and the N = 100 and there is no confounding, estimating a residual correlation of .1 reduces the mediated effect from .26 to .19, while a value of -.1 increases the mediated effect to 0.33. However, under the same situation where there is a small confounding of the b path, not accounting for the confounding causes the mediated effect to increase from .26 to .33. When the residual correlation of .1 is correctly specified the estimated mediated effect equals the true mediated effect, while using a residual correlation of -.1 causes the estimated mediated effect to increase from .26 to .39. Overall, these sensitivity analyses typically produce reduced estimates of the mediated effect.

In the case of the PHLAME data, when there is no assumed residual correlation the mediated effect is .049. Assuming there is a residual correlation of -.1 increases the mediated effect to .095, while assuming a residual correlation of .1 decreases the mediated effect to .018.