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 Chen, K., Jin, Z. and Ying, Z. 2002. Semiparametric analysis of transformation models with censored data. Biometrika, 89: 659–668. Crossref], Web of Science ®] Google Scholar]], we propose an estimator (denoted by ?β) 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 ?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 Cai, T. and Cheng, S. 2004. Semiparametric regression analysis for doubly censored data. Biometrika, 91: 277–290. Crossref], Web of Science ®] Google Scholar]] for the case when L and U are always observed.