Cox regression model with doubly truncated and interval-censored data

Interval sampling is an efficient sampling scheme used in epidemiological studies. Doubly truncated (DT) data arise under this sampling scheme when the failure time can be observed exactly. In practice, the failure time may not be observed and might be recorded only within time intervals, leading to doubly truncated and interval censored (DTIC) data. This article considers regression analysis of DTIC data under the Cox proportional hazards (PH) model and develops the conditional maximum likelihood estimators (cMLEs) for the regression parameters and baseline cumulative hazard function of models. The cMLEs are shown to be consistent and asymptotically normal. Simulation results indicate that the cMLEs perform well for samples of moderate size.