Multiple imputation for systematically missing effect modifiers in individual participant data meta-analysis

Individual participant data (IPD) meta-analysis of randomised trials is a crucial method for detecting and investigating effect modifications in medical research. However, few studies have explored scenarios involving systematically missing data on discrete effect modifiers (EMs) in IPD meta-analyses with a limited number of trials. This simulation study examines the impact of systematic missing values in IPD meta-analysis using a two-stage imputation method. We simulated IPD meta-analyses of randomised trials with multiple studies that had systematically missing data on the EM. A multivariable Weibull survival model was specified to assess beneficial (Hazard Ratio (HR)$=$0.8), null (HR$=$1.0), and harmful (HR$=$1.2) treatment effects for low, medium, and high levels of an EM, respectively. Bias and coverage were evaluated using Monte-Carlo simulations. The absolute bias for common and heterogeneous effect IPD meta-analyses was less than 0.016 and 0.007, respectively, with coverage close to its nominal value across all EM levels. An uncongenial imputation model resulted in larger bias, even when the proportion of studies with systematically missing data on the EM was small. Overall, the proposed two-stage imputation approach provided unbiased estimates with improved precision. The assumptions and limitations of this approach are discussed.