Optimal Practices for Mediation Analysis in AB Single Case Experimental Designs (Poster 9)

• In Event: Methodological Innovations and Complexities in the Analysis and Meta-Analysis of Single-Subject Experimental Design Data

Abstract

Mediation analysis in Single Case Experimental Designs (SCEDs) allows for evaluating mechanisms through which interventions achieve desired effects for a single individual. Both frequentist and Bayesian approaches have been described for mediation analysis using piecewise regression in the AB design, however, no study to date has compared the statistical properties of the indirect effects using the proposed approaches under realistic conditions in SCEDs.
Despite recent methodological developments in mediation analysis for SCEDs, there are still no clear guidelines for designing SCEDs in a way that maximizes the power to detect indirect effects. The current study fills the gap in the literature by comparing frequentist and Bayesian methods and (1) evaluating the minimum required sample size to detect paths that constitute the indirect effects in the AB design, (2) comparing the power to detect indirect effects through proximal versus distal mediators, and (3) determining the optimal allocation of observations between the baseline and treatment phases.
Conditions in the simulation study were designed based on reviews of SCED studies, re-analyses of raw SCED data retrieved from published studies, and previous simulation studies. The total number of measurement occasions was set to 10, 20, 40, 60 or 100. Second, the true values for the immediate treatment effect for both the mediator variable and the outcome variable were set to 0 or 2. Next, the true values for the changes in slope between the baseline and the treatment phases for both the mediator and the outcome variable were set to either 0 or 0.2. The strength of the relation between the outcome variable and the mediator was manipulated to equal either 0 (no effect) or 0.59 (large effect) following commonly used values in simulation studies evaluating methods for mediation analysis with group. All three simulation studies were conducted in R. Data were analyzed using three methods (1) ordinary least squares (OLS) regression for point estimates and indirect effects through changes in level and trend and distribution of the product confidence limits obtained using RMediation for interval estimates of indirect effects; (2) Bayesian estimation with normal priors for all regression coefficients centered at 0 with precision hyperparameters equal to 0.001 estimated using JAGS and the R package rjags; (3) Bayesian estimation with normal priors for all regression coefficients centered at the OLS estimates for each coefficient obtained using the lm() function in R and precision hyperparameters of .001. In both Bayesian methods the residual precisions were assigned gamma priors with both hyperparameters equal to 0.5.
Findings from three simulation studies suggest that for commonly encountered effect sizes in SCEDs research, the highest power to detect the indirect effect occurs with a proximal mediator and with at least 60 time points in the design that are evenly allocated to the A and B phases of the design. Findings from this study have important implications for the design and statistical analysis in numerous fields that routinely employ SCEDs, ranging from psychology to education and nursing.

Authors

• Mariola Moeyaert, University at Albany - SUNY

• Milica Miocevic, McGill University

• Fayette Klaassen, Harvard University

• Gemma Geuke, Utrecht University