Debray TP, Jolani S, Koffijberg H, van Buuren S, Moons KG
Individual participant data meta-analyses (IPD-MA) are increasingly used for developing and validating multivariable (diagnostic or prognostic) risk prediction models. Unfortunately, some predictors or even outcomes may not have been measured in each study and are thus systematically missing in some individual studies of the IPD-MA. As a consequence, it is no longer possible to evaluate between-study heterogeneity and to estimate study-specific predictor effects, or to include all individual studies, which severely hampers the development and validation of prediction models. Here, we describe a novel approach for imputing systematically missing data and adopt a generalized linear mixed model to allow for between-study heterogeneity. This approach can be viewed as an extension of Resche-Rigon's method (Stat Med 2013), relaxing their assumptions regarding variance components and allowing imputation of linear and nonlinear predictors. We illustrate our approach using a case study with IPD-MA of 13 studies to develop and validate a diagnostic prediction model for the presence of deep venous thrombosis. We compare the results after applying four methods for dealing with systematically missing predictors in one or more individual studies: complete case analysis where studies with systematically missing predictors are removed, traditional multiple imputation ignoring heterogeneity across studies, stratified multiple imputation accounting for heterogeneity in predictor prevalence, and multilevel multiple imputation (MLMI) fully accounting for between-study heterogeneity. We conclude that MLMI may substantially improve the estimation of between-study heterogeneity parameters and allow for imputation of systematically missing predictors in IPD-MA aimed at the development and validation of prediction models.