Efficient estimation for the proportional hazards model with left‐truncated and interval‐censored data

Abstract

SummaryInterval‐censored data often arise in prospective studies involving periodical follow‐up for monitoring the failure event occurrence. In addition to censoring, left truncation also occurs if only participants who have not experienced the failure event are enrolled in the study, which clearly induces the selection bias and makes the analysis more complicated. This work provides an efficient maximum likelihood estimation approach that appropriately adjusts the biased sampling for the proportional hazards model with left‐truncated and interval‐censored data. A flexible and stable expectation–maximisation algorithm via a two‐stage data augmentation is developed to maximise the intractable likelihood function. The asymptotic properties of the proposed estimators are established with the empirical process theory. The numerical results obtained from extensive simulations suggest that the proposed method performs satisfactorily and has some prominent advantages over the competing methods. An application to a colon cancer dataset also demonstrates the usefulness of the proposed method.