Semiparametric analysis of transformation models with doubly censored data

Double censoring arises when T represents an outcome variable that can only be accurately measured within a certain range, [L, U], where L and U are the left-and right-censoring variables, respectively. In this note, using Martingale arguments of Chen et al. [3], we propose an estimator (denoted by (beta) over tilde) for estimating regression coefficients of transformation model when L is always observed. Under Cox proportional hazards model, the proposed estimator is equivalent to the partial likelihood estimator for left-truncated and right-censored data if the left-censoring variables L were regarded as left-truncated variables. In this case, the estimator (beta) over tilde can be obtained by the standard software. A simulation study is conducted to investigate the performance of (beta) over tilde. For the purpose of comparison, the simulation study also includes the estimator proposed by Cai and Cheng [2] for the case when L and U are always observed.