Random Effects Meta-Analysis When the Studies Use Regression Models With Different Covariate Sets

Thomas M. Menino Convention & Exhibition Center 

In regression meta-analysis, we often encounter situations where multiple studies use linear regression models, and only a subset of covariates is observed in each study, with different studies using different subsets. In such situations, important confounders are omitted in the studies, and this makes the regression coefficients unidentifiable. Prior methods propose ways to estimate the regression coefficients despite the omission of confounders, but they overlook inherent heterogeneity across studies. We propose a random effects meta-analytic model, accounting for study heterogeneity by viewing the study-specific regression coefficients as iid draws from a normal distribution. The model requires that for each study, we have estimates of the joint distribution of the covariates for that study. These are available from an external source of unlabelled data. We develop consistent and asymptotically normal estimates of the mean and variance of the normal distribution, and obtain closed-form expressions for estimates of the study-specific regression coefficients. We develop an iterative algorithm for estimation and illustrate its performance through simulations and real data analysis.

Causal effect

Data integration

Meta-analysis

Observational studies

Random effects 

Biometrics Section