Using multilevel modeling in synthesizing single-subject research data with trend---a Monte Carlo study

A baseline trend in single-subject research designs is a threat in accurately estimating the effect of a treatment. In such circumstances, conventional approaches would yield overestimated effect sizes. This dissertation study utilizes a four-parameter regression model and estimates the performance of multilevel modeling for detecting accurate effect sizes in the context of meta-analysis of single-subject data with trend. With the model, the treatment efficacy in this regression model can be expressed in terms of level change and slope change across the baseline and treatment phases.;The main purpose of this dissertation study is to investigate the impact of varying factors on the accuracy of parameter estimates using the proposed multilevel regression model in the context of meta-analysis of two-phase single-subject research designs with baseline trend. Using the Monte Carlo technique, Type I errors and powers were evaluated across a variety of factors, including magnitudes of treatment effects, numbers of data points in baseline and treatment phases, numbers of studies in one meta-analysis, levels of autocorrelations, levels of heterogeneity of variance, and levels of intraclass correlations.;For a researcher who wishes to conduct a meta-analytic study of single-subject designs, the findings from this dissertation study offer the following suggestions for using the multilevel regression model in synthesizing single-subject designs. First, the multilevel regression model is especially useful when the outcome variable contains trend in the baseline phase. In general, the estimates of the fixed-effect parameters were found unbiased, which supports the feasibility of the multilevel regression model in meta-analyzing single-subject designs. Second, when there is no previous information regarding the true effect sizes in a meta-analysis of single-subject designs with a baseline trend, a sample size of 50 in studies is recommended when the multilevel regression model is applied. If a large level change and/or slope change is expected, a number of studies as small as 10 is enough. Further research is needed to investigate the underlying mechanism of the interaction effect between heterogeneity of variance and autocorrelation.