Constrained Maximum Likelihood Estimation for Model Calibration Using Summary-Level Information From External Big Data Sources

Statistical methods are needed for using information from such big data sources while analyzing data from individual studies that may collect more detailed information required for addressing specific hypotheses of interest. In this article, we consider the problem of building regression models based on individual-level data from an “internal” study while using summary-level information, such as information on parameters for reduced models, from an “external” big data source.

We identify a set of very general constraints that link internal and external models. These constraints are used to develop a framework for semiparametric maximum likelihood inference that allows the distribution of covariates to be estimated using either the internal sample or an external reference sample. We develop extensions for handling complex stratified sampling designs, such as case-control sampling, for the internal study.