Risk projection for time-to-event outcome from population-based case–control studies leveraging summary statistics from the target population

Risk stratification based on prediction models has become increasingly important in preventing and managing chronic diseases. However, due to cost- and time-limitations, not every population can have resources for collecting enough detailed individual-level information on a large number of people to develop risk prediction models. A more practical approach is to use prediction models developed from existing studies and calibrate them with relevant summary-level information of the target population. Many existing studies were conducted under the population-based case–control design. Gail et al. (J Natl Cancer Inst 81:1879–1886, 1989) proposed to combine the odds ratio estimates obtained from case–control data and the disease incidence rates from the target population to obtain the baseline hazard function, and thereby the pure risk for developing diseases. However, the approach requires the risk factor distribution of cases from the case–control studies be same as the target population, which, if violated, may yield biased risk estimation. In this article, we propose two novel weighted estimating equation approaches to calibrate the baseline risk by leveraging the summary information of (some) risk factors in addition to disease-free probabilities from the targeted population. We establish the consistency and asymptotic normality of the proposed estimators. Extensive simulation studies and an application to colorectal cancer studies demonstrate the proposed estimators perform well for bias reduction in finite samples.