A doubly robust framework for addressing outcome-dependent selection bias in multi-cohort EHR studies

Selection bias can hinder accurate estimation of association parameters in binary disease risk models using non-probability samples like electronic health records (EHRs). The issue is compounded when participants are recruited from multiple clinics/centers with varying selection mechanisms that may depend on the disease/outcome of interest. Traditional inverse-probability-weighted (IPW) methods, based on constructed parametric selection models, often struggle with misspecifications when selection mechanisms vary across cohorts. This paper introduces a new Joint Augmented Inverse Probability Weighted (JAIPW) method, which integrates individual-level data from multiple cohorts collected under potentially outcome-dependent selection mechanisms, with data from an external probability sample. JAIPW offers double robustness by incorporating a flexible auxiliary score model to address potential misspecifications in the selection models. We outline the asymptotic properties of the JAIPW estimator, and our simulations reveal that JAIPW achieves up to 6 times lower relative bias and 5 times lower root mean square error (RMSE) compared to the best performing joint IPW methods under scenarios with misspecified selection models. Applying JAIPW to the Michigan Genomics Initiative (MGI), a multi-clinic EHR-linked biobank, combined with external national probability samples, resulted in cancer-sex association estimates closely aligned with national benchmark estimates. We also analyzed the association between cancer and polygenic risk scores (PRS) in MGI to illustrate a situation where the exposure variable is not measured in the external probability sample.