Estimating the Bias in Meta Analysis Estimates for Continuous Data With Non-Random Missing Study Variance

Abstract

This paper examines, analytically, the biases introduced in the meta analysis estimates when the study-level variances are missing with non-random missing mechanism (MNAR). Two common approaches in handling this problem is considered, namely, the missing variances are imputed, and the studies with missing study variances are omitted from the analysis. The results suggest the variance will be underestimated if the magnitude of the study-variances that are missing are mostly larger implying false impression of precision. On the other hand, if the missing variances are mostly smaller, the variance of the effect size will be overestimated. Keywords: meta analysis; variance estimates; not missing at random; imputation 2010 Mathematics Subject Classification 62P10; 62P12; 62P15; 62P25