Abstract Information: Purpose A critical limitation to conventional and most contemporary natural mediation frameworks involving multiple mediators is that the validity of their inferences requires the correct a priori specification of the causal structure among mediators because of cross-world counterfactual assumption. Recent work has developed an alternative framework based on ‘interventional effects’ that relaxes this assumption. The purpose of this study was to extend the interventional mediation framework to multilevel settings. Within this context, we developed principles of design, estimation, sampling variability, and inferential tests. The results provide tools to design and analyze multilevel mediation studies using the much more flexible interventional mediation framework. Background Multilevel mediation analyses play an essential role in helping researchers develop, probe, and refine theories of action underlying interventions and documenting how interventions impact outcomes. There is a growing body of literature that delineates the (nearly impossible) assumptions needed in conventional and most contemporary (e.g., natural indirect effects) frameworks to correctly identify mediation effects (VanderWeele, 2010). Studies involving multiple mediators must meet a strenuous set of assumptions to produce valid inferences (Vansteelandt & Daniel, 2017). In many instances, however, little is known about the definitive casual structure among multiple mediators and it is difficult to exhaustively identify and control for potential confounding variables, which are essential for mediation effects. In this way, a significant gap in this literature is the development of methods and designs that can relax or weaken assumptions around the causal structure of multiple mediators or methods that are robust to misspecified causal structures. The natural mediation effect highly relies on the cross-world counterfactual assumption, which necessitates the absence of exposure-induced mediator-outcome confounders that are unobservable. This assumption, however, does not hold in the case of interventional mediation effects (Vansteelandt & Daniel, 2017). Therefore, conventional mediation analyses of natural mediation effects with multiple mediators necessitate the sequential ignorability assumption (e.g., Kelcey et al., 2020). In contrast, through the incorporation of information regarding the exposure level of each mediator and the avoidance of the cross-world counterfactual assumption, interventional effect analysis allows the effects of non-treatment-exposure mediators on a single treatment-exposure mediator, as reflected in their interactions. As such, the interventional mediation effect is the combined result of the natural mediation effect and interactions between the specific treatment-exposure mediator and other non-treatment-exposure mediators. As a result, an interventional indirect effect captures the collective indirect effect along all causal pathways leading from a treatment through a specific mediator to an outcome (Loh et al., 2020 ). Therefore, in the analysis of mediation effects with multiple mediators, the interventional mediation effect offers more flexibility than the natural mediation effect, which strictly presupposes a causal mediation structure. We extend this method to multilevel settings by developing principles of estimation, sampling variability, and design. By applying the framework to an illustrated example, we demonstrate the feasibility and usefulness of this approach in situations where prior research or theory are unclear for the causal mediation structures.
Relevance Statement: Appendix A. References Kelcey, B., Dong, N., Spybrook, J., & Shen, Z. (2017). Experimental power for indirect effects in group-randomized studies with group-level mediators. Multivariate Behavioral Research, 52(6), 699-719. https://doi.org/10.1080/00273171.2017.1356212 Kelcey, B., Spybrook, J., & Dong, N. (2019). Sample size planning for cluster-randomized interventions probing multilevel mediation. Prevention Science, 20(3), 407-418. https://doi.org/10.1007/s11121-018-0921-6 Kelcey, B., Spybrook, J., Dong, N., & Bai, F. (2020). Cross-level mediation in school-randomized studies of teacher development: Experimental design and power. Journal of Research on Educational Effectiveness, 13(3), 459-487. https://doi.org/10.1080/19345747.2020.1726540 Ozkal, N. (2019). Relationships between self-efficacy beliefs, engagement and academic performance in math lessons. Cypriot Journal of Educational Sciences, 14(2), 190-200. https://doi.org/10.18844/cjes.v14i2.3766 VanderWeele, T. J. (2010). Direct and indirect effects for neighborhood-based clustered and longitudinal data. Sociological Methods & Research, 38(4), 515-544. https://doi.org/10.1177/0049124110366236 VanderWeele, T. J., Vansteelandt, S., & Robins, J. M. (2014). Effect decomposition in the presence of an exposure-induced mediator-outcome confounder. Epidemiology (Cambridge, Mass.), 25(2), 300-306. https://doi.org/10.1097/EDE.0000000000000034 Vansteelandt, S., & Daniel, R. M. (2017). Interventional effects for mediation analysis with multiple mediators. Epidemiology (Cambridge, Mass.), 28(2), 258-265. https://doi.org/10.1097/EDE.0000000000000596
Appendix B. Tables and Figures Table 1. The comparison of the power calculated by our formulas and reject rate by simulation based on the Monte Carlo test. Design Type Sample Size Parameters Power n_1 n_2 〖ICC〗_(M1|) 〖ICC〗_(M2|) 〖ICC〗_(Y|) τ_(1,2|) σ_(1,2|) a_1 a_2 B_1 B_2 D c^' b_1 b_2 d ∆_1 ∆_2 Reject Rate M_1 Formula Power M_1 Reject Rate M_2 Formula Power M_2 2-1-1-1 10 50 0.50 0.50 0.50 0.25 0.20 0.50 0.30 0.50 0.10 0.10 0.15 0.05 0.30 0.05 0.15 0.25 0.384 0.397 0.033 0.028 2-1-1-1 20 100 0.20 0.20 0.20 0.10 0.30 0.80 0.50 0.30 0.30 0.30 0.25 0.10 0.05 0.10 0.25 0.35 0.457 0.459 0.405 0.388 2-1-1-1 50 200 0.05 0.05 0.05 0.02 0.50 0.30 0.80 0.10 0.50 0.10 0.35 0.30 0.10 0.02 0.35 0.15 0.268 0.236 0.985 0.993
