Comparison of Traditional Regression and Interventional Analogues in a Three-Wave Autoregressive Mediation Model

Introduction: Randomized interventions involving a treatment and control group are used to study intervention effects on hypothesized mediators and subsequent effects of hypothesized mediators on drug-use outcomes over two or more measurement waves. When three waves of data are collected on mediator and outcome variables, autoregressive mediation models can be used to study the effects of how interventions achieve and maintain their health promoting effects over time (MacKinnon, 2008). Recently, the potential outcomes framework was applied to an autoregressive mediation model from MacKinnon (2008) with time-varying intervention (VanderWeele & Tchetgen, 2014). VanderWeele and Tchetgen (2014) defined the natural direct and indirect effects for this autoregressive model with time-varying intervention and defined interventional analogues which are used to estimate mediated effects when a key causal assumption is violated. Interventional analogues of longitudinal mediated effects can be estimated without making the assumption that the error term of the outcome under one level of the intervention (e.g., treatment group) is independent of the error term of the mediator under the other value of the intervention (e.g., control group), which is known as the cross-world independence assumption. This study aims to define the potential outcomes for this three-wave mediation model with randomized intervention and compare the traditional regression approach to estimating mediated effects in a three-wave mediation model with a randomized intervention (i.e., not time-varying) and VanderWeele and Tchetgen’s (2014) interventional analogues when the cross-world independence assumption is violated.

Method: A Monte Carlo simulation study was used to investigate the statistical performance and confidence interval coverage of the traditional regression approach and interventional analogues for estimating longitudinal mediated effects across three waves with a randomized intervention. The Monte Carlo study consisted of a sample size often found in prevention research: 200; parameter sizes of the mediated effect corresponding to zero, small, medium, and large effect sizes; and cross-world correlation corresponding to zero, small, and large effect sizes.

Results: Preliminary results suggest a tradeoff between implementation and performance of the traditional regression approach and interventional analogues when the cross-world assumption is violated.

Conclusions: Although the interventional analogues may perform better when a key causal assumption is violated, the implementation of the method and interpretation of results is not as straightforward as traditional regression approaches for estimating longitudinal mediated effects.