Multilevel Meta-Analysis of Individual Participant Data of Single-Case Experimental Designs: One-Stage versus Two-Stage Methods

Abstract

To conduct a multilevel meta-analysis of multiple single-case experimental design (SCED) studies, the individual participant data (IPD) can be analyzed in one or two stages. In the one-stage approach, a multilevel model is estimated based on the raw data. In the two-stage approach, an effect size is calculated for each participant and these effect sizes and their sampling variances are subsequently combined to estimate a meta-analytic multilevel model. The multilevel model in the two-stage approach has fewer parameters to estimate, in exchange for the reduction of information of the raw data to effect sizes. In this paper we explore how the one-stage and two-stage IPD approaches can be applied in the context of meta-analysis of single-case designs. Both approaches are compared for several single-case designs of increasing complexity. Through a simulation study we show that the two-stage approach obtains better convergence rates for more complex models, but that model estimation does not necessarily converge at a faster speed. The point estimates of the fixed effects are unbiased for both approaches across all models, as such confirming results from methodological research on IPD meta-analysis of group-comparison designs. In light of these results, we discuss the implementation of both methods in R.

Keywords: Single-case experimental design; effect size; individual participant data; meta-analysis; multilevel modeling.