Semiparametric analysis of transformation models with doubly censored data

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