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Abstract:
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With the increasing availability of data in the public domains, there has been a growing interest in exploiting information from external sources to improve the analysis of smaller-scale studies. An emerging challenge in the era of big data is that the subject-level data are high-dimensional, but the external information is at an aggregate level and of a lower dimension. Moreover, heterogeneity and uncertainty in the auxiliary information are often not accounted for. In this paper, we propose a unified framework to summarize various forms of aggregated information via estimating equations and develop a penalized empirical likelihood approach to incorporate such information in logistic regression. When the homogeneity assumption is violated, we extend the method to account for population heterogeneity among different sources of information. When the uncertainty in the external information is not negligible, we propose a variance estimator adjusting for the uncertainty. The proposed estimators are asymptotically more efficient than the conventional penalized maximum likelihood estimator and enjoy the oracle property even with a diverging number of predictors. Simulation studies show
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