Journal
JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
Volume 111, Issue 513, Pages 107-117Publisher
AMER STATISTICAL ASSOC
DOI: 10.1080/01621459.2015.1123157
Keywords
Case-control study; Empirical likelihood; Generalized regression estimator; Misspecified model; Profile-likelihood
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Funding
- U.S. National Cancer Institute
- Ministry of Science and Technology of Taiwan [NSC101-2118-M-001-002-MY3]
- National Cancer Institute [U01-CA057030]
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Information from various public and private data sources of extremely large sample sizes are now increasingly available for research purposes. 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. Asymptotic theory and variance estimators are developed for each case. We use simulation studies and a real data application to assess the performance of the proposed methods in contrast to the generalized regression calibration methodology that is popular in the sample survey literature. Supplementary materials for this article are available online.
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