Simultaneous selection and incorporation of consistent external aggregate information.

Interest has grown in synthesizing participant level data of a study with relevant external aggregate information. Several efficient and flexible procedures have been developed under the assumption that the internal study and the external sources concern the same population. This homogeneity condition, albeit commonly being imposed, is hard to check due to limitedly available external information in aggregate data forms. Bias may be introduced when the assumption is violated. In this article, we propose a penalized likelihood approach that avoids undesirable bias by simultaneously selecting and synthesizing consistent external aggregate information. The proposed approach provides a general framework which incorporate consistent external information from heterogeneous study populations as long as the conditional distribution of the dependent variable under investigation is same and differences in the independent variable distributions are properly accounted for via a semi-parametric density ratio model. The proposed approach also properly accounts for the sampling errors in the external information. A two-step estimator and an optimization algorithm are proposed for computation. We establish the selection and estimation consistency and the asymptotic normality of the two-step estimator. The proposed approach is illustrated with an analysis of gestational weight gain management studies.