With the development of biomedical science, researchers have increasing access to an abundance of studies focusing on similar research questions. There is a growing interest in the integration of summary information from those studies to enhance the efficiency of estimation in their own internal studies. In this work, we present a comprehensive framework on integration of summary information from external studies when the data are modeled by semiparametric models. Our novel framework offers straightforward estimators that update conventional estimations with auxiliary information. It addresses computational challenges by capitalizing on the intricate mathematical structure inherent to the problem. We demonstrate the conditions when the proposed estimators are theoretically more efficient than initial estimate based solely on internal data. Several special cases such as proportional hazards model in survival analysis are provided with numerical examples.

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