Within-Subject Mediation Analysis in AB/BA Crossover Designs

Abstract

Crossover trials are widely used to assess the effect of a reversible exposure on an outcome of interest. To gain further insight into the underlying mechanisms of this effect, researchers may be interested in exploring whether or not it runs through a specific intermediate variable: the mediator. Mediation analysis in crossover designs has received scant attention so far and is mostly confined to the traditional Baron and Kenny approach. We aim to tackle mediation analysis within the counterfactual framework and elucidate the assumptions under which the direct and indirect effects can be identified in AB/BA crossover studies. Notably, we show that both effects are identifiable in certain statistical models, even in the presence of unmeasured time-independent (or upper-level) confounding of the mediator-outcome relation. Employing the mediation formula, we derive expressions for the direct and indirect effects in within-subject designs for continuous outcomes that lend themselves to linear modelling, under a large variety of settings. We discuss an estimation approach based on regressing differences in outcomes on differences in mediators and show how to allow for period effects as well as different types of moderation. The performance of this approach is compared to other existing methods through simulations and is illustrated with data from a neurobehavioural study. Lastly, we demonstrate how a sensitivity analysis can be performed that is able to assess the robustness of both the direct and indirect effect against violation of the "no unmeasured lowerlevel mediator-outcome confounding" assumption.

More Precise Estimation of Lower-Level Interaction Effects in Multilevel Models

“…As was already mentioned in the introduction, two different strategies for centering lower-level interactions have been suggested. The first approach, advocated by Josephy et al (2015), first multiplies X i j with Z i j , after which the cluster mean average of this product term is subtracted. As such, the "P1C2" estimation model amounts to:…”

“…In contrast to cluster-mean centering an interaction between an upper-and a lower-level variable, or between two upper-level variables, C1P2 and P1C2 produce different predictors when cluster-mean centering a lower-level interaction. Some scholars favored P1C2 (Josephy, Vansteelandt, Vanderhasselt, & Loeys, 2015), while others advised against it and promoted C1P2 instead (Preacher et al, 2016). In this article, we investigate how these two approaches deal with unmeasured upper-level confounding and whether they can unbiasedly estimate the moderated within-subject effect.…”

“…While Josephy et al (2015) considered the traditional multilevel modeling (MLM) framework (also referred to as mixed modeling), Preacher et al (2016) relied on Structural Equation Modeling (SEM). In contrast to the traditional MLM-framework, in which the within-and between-cluster decomposition of a predictor relies on the observed cluster means, latent cluster means are generally used in SEM.…”

Comparison of model- and design-based approaches to detect the treatment effect and covariate by treatment interactions in three-level models for multisite cluster-randomized trials

“…One way to include an interaction term in a multilevel model is to multiply the treatment indicator by the relevant variable and, if necessary, decompose it into different levels by centering the product. This approach was considered by Josephy, Vansteelandt, Vanderhasselt, and Loeys (2015), but its use was criticized by Preacher, Zhang, and Zyphur (2016) because the results are uninterpretable. In this study, we investigated the treatment main effect and Covariate × Treatment interaction due to an L1 moderator (1 × (2→1) design) by decomposing the L1 predictor into between-and within-factor components and then multiplying the components by the treatment indicator.…”

Crossover Designs in Nutrition and Dietetics Research

“…In contrast, a crossover design has all participants receive all levels of the independent variable at some point in the study, but participants do not receive all levels at the same time. [5][6][7][8][9][10][11][12][13] In the most basic illustration of a crossover design, participants are randomized to one of two groups. One group receives the dietary manipulation while the other group receives the control comparison.…”