Synthesizing effects for multiple outcomes per study using robust variance estimation versus the three-level model

Abstract

Primary studies increasingly report information that can be used to provide multiple effect sizes. Of interest in this study, primary studies might compare a treatment and a control group on multiple related outcomes that result in multiple dependent effect sizes to be synthesized. There are a number of ways to handle the resulting within-study “multiple-outcome” dependency. The present study focuses on use of the multilevel meta-analysis model (Van den Noortgate, López-López, Marín-Martínez, & Sánchez-Meca, 2013) and robust variance estimation (Hedges, Tipton, & Johnson, 2010) for handling this dependency, as well as for estimating outcome-specific mean effect sizes. We assessed these two approaches under various conditions that differed from each other in within-study sample size; the number of effect sizes per outcome; the number of outcomes per study; the number of studies per meta-analysis; the ratio of variances at Levels 1, 2, and 3; and the true correlation between pairs of effect sizes at the between-study level. Limitations and directions for future research are discussed.