Synthesis of single-case design mediation effects using two-stage multilevel modeling

Mediation analysis in single-case experimental designs (SCEDs) allows for evaluating mechanisms through which interventions achieve effects for a single individual. Modeling approaches have been described and empirically validated for mediation analysis in the AB phase design (i.e., SCED involving only one participant with one baseline and one intervention condition). However, no study to date has focused on synthesizing indirect effects across participants from a multiple-baseline design (MBD). The current study fills this gap by investigating the performance of the two-stage multilevel modeling approach to synthesize indirect effects using a large-scale Monte Carlo simulation study. An empirical demonstration with interpretation of results is provided. The results are promising for estimation of the indirect effect, as unbiased effects are obtained under all conditions that have more than three participants. If statistical inference is of interest, then the approach can be recommended for at least 20 study participants and a nonzero value for the mediator-outcome relation. Under these conditions, the coverage proportion is close to the nominal level of .95, and the Type I error rate is controlled. To obtain sufficient power to identify a true indirect effect, at least eight participants, a low between-case variance in mediator-outcome relation, and a mediator-outcome relation of 0.39 or higher are needed.