Likelihood adaptively incorporated external aggregate information with uncertainty for survival data

Population-based cancer registry databases are critical resources to bridge the information gap that results from a lack of sufficient statistical power from primary cohort data with small to moderate sample size. Although comprehensive data associated with tumor biomarkers often remain either unavailable or inconsistently measured in these registry databases, aggregate survival information sourced from these repositories has been well documented and publicly accessible. An appealing option is to integrate the aggregate survival information from the registry data with the primary cohort to enhance the evaluation of treatment impacts or prediction of survival outcomes across distinct tumor subtypes. Nevertheless, for rare types of cancer, even the sample sizes of cancer registries remain modest. The variability linked to the aggregated statistics could be non-negligible compared with the sample variation of the primary cohort. In response, we propose an externally informed likelihood approach, which facilitates the linkage between the primary cohort and external aggregate data, with consideration of the variation from aggregate information. We establish the asymptotic properties of the estimators and evaluate the finite sample performance via simulation studies. Through the application of our proposed method, we integrate data from the cohort of inflammatory breast cancer (IBC) patients at the University of Texas MD Anderson Cancer Center with aggregate survival data from the National Cancer Data Base, enabling us to appraise the effect of tri-modality treatment on survival across various tumor subtypes of IBC.