Semiparametric transformation models and the missing information principle

Semiparametric transformation models play an important role in predicting survival. The linear transformation model is one class of such models which includes the proportional hazards and proportional odds models. We consider estimation of the regression coefficients in the linear transformation model, when the data are right censored and the censoring may depend on the covariate. We propose a simple estimator based on the well-known missing information principle and derive its asymptotic properties for the general case in which the censoring can depend on the covariate, but assuming that the covariate takes values in a finite set. We show how this estimator leads to another estimator recently proposed in the literature. Results of a numerical study show the correctness of the proposed inference procedures.