Investigating the Influence of Unmeasured Confounding in the Single Mediator Model with Nonrandomized Exposure

Introduction: In prevention science, identifying mechanisms of change, or mediators, can aid in developing more effective and less expensive interventions. For the single mediator model, exposure to X causes the mediator M, which then causes the outcome Y. When estimating the single mediator model, researchers rely on the following assumptions, which are collectively referred to as sequential ignorability.

1. There is no unmeasured confounder of the effect of X on M. We define the unmeasured confounder U_XM as an extraneous variable that causes both X and M.
2. There is no unmeasured confounder U_XY of the effect of X on Y.
3. There is no unmeasured confounder U_MY of the effect of M on Y.
4. X does not cause any measured or unmeasured confounder of the effect of M on Y.

When X denotes treatment assignment in a randomized experiment, (1) and (2) are satisfied in expectation via randomization. Because participants typically cannot be randomly assigned to different levels of M, most existing research focuses on the influence of unmeasured confounding on the effect of M on Y (e.g., Cox et al., 2014; MacKinnon & Pirlott, 2015; Fritz et al., 2016). However, randomly assigning participants to different levels of X may also be infeasible or unethical, such as when investigating the effects of smoking, obesity, or nationwide policy changes over time. If neither X nor M is randomly assigned, the effects of X on M, X on Y, and M on Y may be affected by unmeasured confounding. We propose methods for assessing the robustness of the mediated effect to unmeasured confounding when neither X nor M is randomly assigned.

Methods: First we describe how to assess the effect of an unmeasured confounder separately for the effects of X on M, X on Y, and M on Y. Then we describe how to assess the joint effect of three unmeasured confounders, U_XM, U_XY, and U_MY. Because U_XM, U_XY, and U_MY may be correlated or may even be the same variable, additional considerations are necessary. We apply these methods to data where the effects of X on M, X on Y, and/or M on Y are affected by unmeasured confounding.

Results: We demonstrate the calculations and describe plots showing the sensitivity of the results to unmeasured confounding. We outline recommendations for assessing the plausibility of an unmeasured confounder or set of unmeasured confounders that would nullify the mediated effect (e.g., based on the range of observed correlations between X, M, and Y and other measured variables).

Conclusions: Because sequential ignorability is unlikely to hold, evaluating unmeasured confounding is critical when neither X nor M is randomly assigned. Understanding the robustness of the mediated effect to confounding has important implications for the interpretability and utility of the results.