Imputation methods for the semiparametric transformation models with doubly-truncated and interval-censored data

Interval sampling is often used in epidemiological studies. With interval sampling, data are collected only from individuals who fail within a certain calendar time interval. Such interval sampling induces doubly truncated (DT) data if the calendar time of the failure event can be observed exactly. In practice, the failure time may not be directly observed and it is only recorded within time intervals, leading to doubly truncated and interval censored (DTIC) data. In this article, we analyze DTIC data using a class of semiparametric transformation models. By iterating between an imputation step and an optimization step for DT data, we propose two imputation methods for obtaining parameter estimates for regression parameters and cumulative hazard function of models. Simulation studies indicate that the proposed estimators perform adequately.