A unified approach for synthesizing population-level covariate effect information in semiparametric estimation with survival data

There has been a growing interest in developing methodologies to combine information from public domains to improve efficiency in the analysis of relatively small-scale studies that collect more detailed patient-level information. The auxiliary information is usually given in the form of summary statistics or regression coefficients. Thus, the question arises as to how to incorporate the summary information in the model estimation procedure. In this article, we consider statistical analysis of right-censored survival data when additional information about the covariate effects evaluated in a reduced Cox model is available. Recognizing that such external information can be summarized using population moments, we present a unified framework by employing the generalized method of moments to combine information from different sources for the analysis of survival data. The proposed estimator can be shown to be consistent and asymptotically normal; moreover, it is more efficient than the maximum partial likelihood estimator. We also consider incorporating uncertainty of the external information in the inference procedure. Simulation studies show that, by incorporating the additional summary information, the proposed estimators enjoy a substantial gain in efficiency over the conventional approach. A data analysis of a pancreatic cancer cohort study is presented to illustrate the methods and theory.