  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.

Methodology