Handling missing disease information due to death in diseases that need two visits to diagnose

In studies that assess disease status periodically, time of disease onset is interval censored between visits. Participants who die between two visits may have unknown disease status after their last visit. In this work, we consider an additional scenario where diagnosis requires two consecutive positive tests, such that disease status can also be unknown at the last visit preceding death. We show that this impacts the choice of censoring time for those who die without an observed disease diagnosis. We investigate two classes of models that quantify the effect of risk factors on disease outcome: a Cox proportional hazards model with death as a competing risk and an illness death model that treats disease as a possible intermediate state. We also consider four censoring strategies: participants without observed disease are censored at death (Cox model only), the last visit, the last visit with a negative test, or the second last visit. We evaluate the performance of model and censoring strategy combinations on simulated data with a binary risk factor and illustrate with a real data application. We find that the illness death model with censoring at the second last visit shows the best performance in all simulation settings. Other combinations show bias that varies in magnitude and direction depending on the differential mortality between diseased and disease-free subjects, the gap between visits, and the choice of the censoring time.