Improved risk prediction via cross-domain calibration in a retrospective case-control study.

Given a well calibrated standard model involving standard predictors, we propose a constrained maximum likelihood approach to incorporate the biomarker sampled from a different population without having to correctly model them to improve the prediction. The constraints ensure that the averaged risk with the biomarker included is as close as that from the standard model. Our method allows different distributions of the standard risk predictors between the target population and the source population of the study data, and relies on the study data to inform the relationship between biomarker and standard predictors. We develop large sample theory of our method for parameters and measures for predictive accuracy, and perform simulation studies to assess the finite sample performance of our method. We apply our method to analyze a case-control study of breast cancer to develop a model that includes both standard breast cancer risk predictors and the biomarker mammographic density.