Causal mediation effects in single case experimental designs.

Single case experimental designs (SCEDs) are used to test treatment effects in a wide range of fields and consist of repeated measurements for a single case throughout one or more baseline phases and throughout one or more treatment phases. Recently, mediation analysis has been applied to SCEDs. Mediation analysis decomposes the total treatment-outcome effect into a direct and indirect effect, and therefore aims to unravel the causal processes underlying treatment-outcome effects. The most recent methodological advancement for mediation analysis is the development of causal mediation analysis methodology which clarifies the necessary causal assumptions for mediation analysis. The goal of this article is to derive the causal mediation effects and corresponding standard errors based on piecewise linear regression models for the mediator and outcome and to evaluate the performance of these regression estimators and standard errors. Whereas previous studies estimated the direct and indirect effects as either the change in level or change in trend, we showed that the causal direct and indirect effects incorporate both the change in level and change in trend. Based on our simulation study we showed that for the causal indirect effects, Monte Carlo confidence intervals provided accurate (i.e.,