Efficient inferences for linear transformation models with doubly censored data

Doubly-censored data, which consist of exact and case-1 interval-censored observations, often arise in medical studies, such as HIV/AIDS clinical trials. This article considers nonparametric maximum likelihood estimation (NPMLE) of semiparametric transformation models that encompass the proportional hazards and proportional odds models when data are subject to double censoring. The maximum likelihood estimator is obtained by directly maximizing a nonparametric likelihood concerning a regression parameter and a nuisance function parameter, which facilitates efficient and reliable computation. Statistical inferences can be conveniently made from the inverse of the observed information matrix. The estimator is shown to be consistent and asymptotically normal. The limiting variances for the estimators can be consistently estimated. Simulation studies demonstrate that the NPMLE works well even under a heavy censoring scheme and substantially outperforms methods based on estimating functions in terms of efficiency. The method is illustrated through an application to a data set from an AIDS clinical trial.