A semiparametric linear transformation model for general biased-sampling and right-censored data

The semiparametric linear transformation (SLT) model is a useful alternative to the proportional hazards ([9]) and proportional odds ([4]) models for studying the dependency of survival time on covariates. In this paper, we consider the SLT model for biased-sampling and right-censored data, a feature commonly encountered in clinical trials. Specifically, we develop an unbiased estimating equations approach based on counting process for the simultaneous estimation of unknown coefficients and handling of sampling bias. We establish the consistency and the asymptotic normality of the proposed estimator, and provide a closed form expression for the estimator's covariance matrix that can be consistently estimated by a plug-in method. In a simulation study, we compare the finite sample properties of the proposed estimator with those of existing methods that either assumes that the sampling bias is of the length-bias type, or ignores the sampling bias altogether. The proposed method is further illustrated by two real clinical datasets.