Abstract
Studying the incidence of rare events is both scientifically important and statistically challenging. When few events are observed, standard survival analysis estimators behave erratically, particularly if covariate adjustment is necessary. In these settings, it is possible to improve upon existing estimators by considering estimation in a bounded statistical model. This bounded model incorporates existing scientific knowledge about the incidence of an event in the population. Estimators that are guaranteed to agree with existing scientific knowledge on event incidence may exhibit superior behavior relative to estimators that ignore this knowledge. Focusing on the setting of competing risks, we propose estimators of cumulative incidence that are guaranteed to respect a bounded model and show that when few events are observed, the proposed estimators offer improvements over existing estimators in bias and variance. We illustrate the proposed estimators using data from a recent preventive HIV vaccine efficacy trial. Copyright © 2017 John Wiley & Sons, Ltd.