Tutorial: The practical application of longitudinal structural equation mediation models in clinical trials

Abstract

The study of mediation of treatment effects, or how treatments work, is important to understanding and improving psychological and behavioral treatments, but applications often focus on mediators and outcomes measured at a single time point. Such cross-sectional analyses do not respect the implied temporal ordering that mediation suggests. Clinical trials of treatments often provide repeated measures of outcomes and, increasingly, of mediators as well. Repeated measurements allow the application of various types of longitudinal structural equation mediation models. These provide flexibility in modeling, including the ability to incorporate some types of measurement error and unmeasured confounding that can strengthen the robustness of findings. The usual approach is to identify the most theoretically plausible model and apply that model. In the absence of clear theory, we put forward the option of fitting a few theoretically plausible models, providing a type of sensitivity analysis for the mediation hypothesis. In this tutorial, we outline how to fit several longitudinal mediation models, including simplex, latent growth and latent change models. This will allow readers to learn about one type of model that is of interest, or about several alternative models, so that they can take this sensitivity approach. We use the Pacing, Graded Activity, and Cognitive Behavioral Therapy: A Randomized Evaluation (PACE) trial of rehabilitative treatments for chronic fatigue syndrome (ISRCTN 54285094) as a motivating example and describe how to fit and interpret various longitudinal mediation models using simulated data similar to those in the PACE trial. The simulated data set and Mplus code and output are provided. (PsycINFO Database Record

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Figures

Figure 1

Four group dual process simplex model with lagged b paths and contemporaneous residual covariance paths. Numbers in round brackets are standard errors, numbers in square brackets are 95% confidence intervals. The lower table shows indirect and direct effect estimates for the third post-randomization time point. Significant effects shown in bold font, R1 R2 and R3 = dummy variables for randomized treatment group, M0, M1, M2, M3 = mediator measurements taken at baseline, 1st follow-up time point, 2nd follow-up time point and 3rd follow-up time point post-randomization, Y0, Y1, Y2, Y3 = outcome measurements taken at the same time points, FM0, FM1, FM2, FM3 = true latent mediator scores at the given time points, FY0, FY1, FY2, FY3 = true latent outcome scores at the given time points,b0 = “bpath” from baseline measure, bL = lagged b path, m1, m2, m3 = paths between M0 and M1, M1 and M2, M2 and M3, respectively, with y1, y2, y3 the same for the outcome variable, (r#) in the table indicates that the number of the treatment group of interest (R1, R2 or R3) should be substituted. aIn the Mplus output, this value shows up as 0.000 due to the number of decimal points displayed. It was obtained by creating another parameter multiplied by 100, which is not in the Mplus code included with the tutorial.

Figure 2

Four group dual process simplex model with contemporaneous bpaths and contemporaneous residual covariance paths. Numbers in round brackets are standard errors, numbers in square brackets are 95% confidence intervals. The lower table shows indirect and direct effect estimates for the third post-randomization time point. Significant effects shown in bold font, R1 R2 and R3 = dummy variables for randomized treatment group, M0, M1, M2, M3 = mediator measurements taken at baseline, 1st follow-up time point, 2nd follow-up time point and 3rd follow-up time point post-randomization, Y0, Y1, Y2, Y3 = outcome measurements taken at the same time points, FM0, FM1, FM2, FM3 = true latent mediator scores at the given time points, FY0, FY1, FY2, FY3 = true latent outcome scores at the given time points,b0 = “bpath” from baseline measure, bC = contemporaneous b path, m1, m2, m3 = paths between M0 and M1, M1 and M2, M2 and M3, respectively, with y1, y2, y3 the same for the outcome variable, (r#) in the table indicates that the number of the treatment group of interest (R1, R2 or R3) should be substituted.

Figure 3

Four group dual process latent growth model, square root of time point slope loadings, final loading estimated, with contemporaneous residual covariance paths. Numbers in round brackets are standard errors, numbers in square brackets are 95% confidence intervals. The lower table shows indirect and direct effect estimates for the third post-randomization time point. Significant effects shown in bold font, R1 R2 and R3 = dummy variables for randomized treatment group, M0, M1, M2, M3 = mediator measurements taken at baseline, 1st follow-up time point, 2nd follow-up time point and 3rd follow-up time point post-randomization, Y0, Y1, Y2, Y3 = outcome measurements taken at the same time points, IM = intercept for the mediator, SM = slope for the mediator, IY = intercept for the outcome, SY = slope for the outcome, covariances are allowed between IM and SY and IY and SM in the model but are not shown in the figure,(r#) in the table indicates that the number of the treatment group of interest (R1, R2 or R3) should be substituted.

Figure 4

Four group dual process modified latent change score model with contemporaneous mediation and residual covariance paths. Numbers in round brackets are standard errors, numbers in square brackets are 95% confidence intervals. The lower table shows indirect and direct effect estimates for the third post-randomization time point. Significant effects shown in bold font, estm = estimates for all mediator measure factor loadings except at the same time point, which is set = 1 to provide the latent variable scale, esty = estimates for outcome measure as described for the mediator, R1 R2 and R3 = dummy variables for randomized treatment group, M0, M1, M2, M3 = mediator measurements taken at baseline, 1st follow-up time point, 2nd follow-up time point and 3rd follow-up time point post-randomization, Y0, Y1, Y2, Y3 = outcome measurements taken at the same time points, FM0 = true latent mediator score at baseline, FM1, FM2, FM3 = modified true latent mediator change between each time point and the previous time point, FY0 = true latent outcome score at baseline FY1, FY2, FY3 = modified true latent outcome change between each time point and the previous time point,(r#) in the table indicates that the number of the treatment group of interest (R1, R2 or R3) should be substituted.