Estimating Risk with Time-to-Event Data: An Application to the Women's Health Initiative

Accurate and individualized risk prediction is critical for population control of chronic diseases such as cancer and cardiovascular disease. Large cohort studies provide valuable resources for building risk prediction models, as the risk factors are collected at the baseline and subjects are followed over time until disease occurrence or termination of the study. However, for rare diseases the baseline risk may not be estimated reliably based on cohort data only, due to sparse events. In this paper, we propose to make use of external information to improve efficiency for estimating time-dependent absolute risk. We derive the relationship between external disease incidence rates and the baseline risk, and incorporate the external disease incidence information into estimation of absolute risks, while allowing for potential difference of disease incidence rates between cohort and external sources. The asymptotic properties, namely, uniform consistency and weak convergence, of the proposed estimators are established. Simulation results show that the proposed estimator for absolute risk is more efficient than that based on the Breslow estimator, which does not utilize external disease incidence rates. A large cohort study, the Women's Health Initiative Observational Study, is used to illustrate the proposed method.