Semiparametric likelihood estimation in survival models with informative censoring

Semiparametric proportional hazard regression models are the cornerstone in modern survival analysis. Most estimation methodologies developed in the literature, such as the famous partial likelihood based estimation, are built on the ground that the censoring is noninformative. However, in many applications, the censoring is indeed informative. In this paper, we study the survival regression models with an informative censoring that is easy to detect and apply. A very important problem in practice is how to estimate the survival models more efficiently with the information from the informative censoring. We propose a semiparametric maximum likelihood approach that is easily implementable to estimate both the nonparametric baseline hazard and the parametric coefficients in the survival models with informative censoring. Different from the methods in the literature, we do not apply least informative approach to the baseline, which does not work well in our simulation. We solve the difficulty in semiparametric estimation by suggesting an indirect application of local kernel smoothing to the baseline. Asymptotic theory of the proposed estimators is established under informative and noninformative likelihoods, respectively. We suggest a cross-validation method to detect the informative censoring in application. The performances of the estimators in finite samples are investigated by Monte Carlo simulation. Both asymptotic theory and simulation show that the suggested semiparametric approach provides more efficient estimators of the parameters for informative censoring, and estimates the baseline function accurately. The proposed method is applied to analyse the data about the infants hospitalised for pneumonia, which leads to interesting findings.