Statistical Causal Inferences and Their Applications in Public Health Research

Part of the series ICSA Book Series in Statistics pp 263-293


A Comparison of Potential Outcome Approaches for Assessing Causal Mediation

  • Donna L. CoffmanAffiliated withThe Methodology Center, Pennsylvania State University Email author 
  • , David P. MacKinnonAffiliated withDepartment of Psychology, Arizona State University
  • , Yeying ZhuAffiliated withDepartment of Statistics and Actuarial Science, University of Waterloo
  • , Debashis GhoshAffiliated withDepartment of Biostatistics and Informatics, University of Colorado

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Mediation occurs as part of a hypothesized causal chain of events: An intervention or treatment, T, has an effect on the mediator, M, which then affects an outcome variable, Y. Within the potential outcomes framework for causal inference, three different definitions of the mediation effects have been proposed: principal strata effects (e.g., Rubin, Scand. J. Stat. 31:161–170, 2004; Jo, Psychol. Methods 13:314–336, 2008), natural effects (e.g., Pearl, Proceedings of the Seventeenth Conference on Uncertainty in Artificial Intelligence, 2001; Imai et al., Psychol. Methods 15:309–334, 2010), and controlled effects (e.g., Robins and Greenland, Epidemiology 3:143–155, 1992; VanderWeele, Epidemiology 20:18–26, 2009). We illustrate that each of these definitions answers a different scientific question. We examine five different estimators of the various definitions and discuss identifying assumptions about unmeasured confounding, the existence of direct effects (i.e., the effect of T on Y that is not due to M), iatrogenic effects of T on M, the existence of post-treatment confounders, and the existence of interactions. We assess the robustness of each of the estimators to violations of the assumptions using a simulation study that systematically challenges different aspects of these assumptions. We found that when no assumptions were violated, as may be expected, each approach was unbiased for its respective population value and 95 % confidence interval (CI) coverage was maintained. However, when assumptions are violated, the effects may be severely biased and 95 % CI coverage is not maintained. We suggest that researchers choose the appropriate definition based on the scientific question to be addressed and the identifying assumptions that are plausible given their data.