Semi-supervised Estimation of Event Rate with Doubly-censored Survival Data

Electronic Health Record (EHR) has emerged as a valuable source of data for translational research. To leverage EHR data for risk prediction and subsequently clinical decision support, clinical endpoints are often time to onset of a clinical condition of interest. Precise information on clinical event times is often not directly available and requires labor-intensive manual chart review to ascertain. In addition, events may occur outside of the hospital system, resulting in both left and right censoring often termed double censoring. On the other hand, proxies such as time to the first diagnostic code are readily available yet with varying degrees of accuracy. Using error-prone event times derived from these proxies can lead to biased risk estimates while only relying on manually annotated event times, which are typically only available for a small subset of patients, can lead to high variability. This signifies the need for semi-supervised estimation methods that can efficiently combine information from both the small subset of labeled observations and a large size of surrogate proxies. While semi-supervised estimation methods have been recently developed for binary and right-censored data, no methods currently exist in the presence of double censoring. This paper fills the gap by developing a robust and efficient Semi-supervised Estimation of Event rate with Doubly-censored Survival data (SEEDS) by leveraging a small set of gold standard labels and a large set of surrogate features. Under regularity conditions, we demonstrate that the proposed SEEDS estimator is consistent and asymptotically normal. Simulation results illustrate that SEEDS performs well in finite samples and can be substantially more efficient compared to the supervised counterpart. We apply the SEEDS to estimate the age-specific survival rate of type 2 diabetes using EHR data from Mass General Brigham.