Confounding in statistical mediation analysis: What it is and how to address it

Abstract

Psychology researchers are often interested in mechanisms underlying how randomized interventions affect outcomes such as substance use and mental health. Mediation analysis is a common statistical method for investigating psychological mechanisms that has benefited from exciting new methodological improvements over the last 2 decades. One of the most important new developments is methodology for estimating causal mediated effects using the potential outcomes framework for causal inference. Potential outcomes-based methods developed in epidemiology and statistics have important implications for understanding psychological mechanisms. We aim to provide a concise introduction to and illustration of these new methods and emphasize the importance of confounder adjustment. First, we review the traditional regression approach for estimating mediated effects. Second, we describe the potential outcomes framework. Third, we define what a confounder is and how the presence of a confounder can provide misleading evidence regarding mechanisms of interventions. Fourth, we describe experimental designs that can help rule out confounder bias. Fifth, we describe new statistical approaches to adjust for measured confounders of the mediator-outcome relation and sensitivity analyses to probe effects of unmeasured confounders on the mediated effect. All approaches are illustrated with application to a real counseling intervention dataset. Counseling psychologists interested in understanding the causal mechanisms of their interventions can benefit from incorporating the most up-to-date techniques into their mediation analyses. (PsycINFO Database Record

(c) 2017 APA, all rights reserved).

Figures

Figure 1. Single Mediator Model

Note. Upper panel illustrates the general single mediator model and abbreviations (X, Y, M, and a, b, and c’). Lower panel illustrates the specific single mediator model that is used as our running example.

Figure 2. Single Mediator Model with Confounder of M – Y relation

Note. This figure demonstrates the potential confounding effect of physical mobility on number of agency contacts (M) and number of days stably housed (Y). If this confounder is present and not adjusted for, the observed mediated effect will be biased and will not accurately represent the mechanism for which X has its effect on Y.

Figure 3. L.O.V.E. Plot for Homelessness Data

Note. This L.O.V.E. plot was computed using data from the running example, in which M is the number of housing contacts and Y is the number of days stably housed per month. Coordinates that lie on the curved line indicate combinations of correlations between an unmeasured confounder and M and an unmeasured confounder and Y that are sufficient to eliminate the observed mediated effect. For example, the plot indicates that if ru-m = 0.5 and ru-y = 0.8, then the observed mediated effect would equal zero—it is completely explained by the unmeasured confounder.