Semiparametric Density Ratio Model for Survival Data with a Cure Fraction

The paper proposes a class of semiparametric transformation models for survival data with a cure fraction. Particularly, we assume a semiparametric density ratio model for the unknown proper conditional distribution function. The density ratio model is closely related to the generalized linear models and is desirable for modeling skewed survival data. We develop nonparametric likelihood-based estimation and inference procedures. Compared to some existing cure rate models, the estimation of the unknown proper baseline cumulative distribution function is more natural without imposing additional constraints. We establish the consistency and asymptotic normality of the proposed nonparametric maximum likelihood estimators. Extensive simulation studies demonstrate that the proposed methods perform well under practical settings. The proposed methods are also shown to be robust under certain model mis-specifications. We illustrate the proposed methods using two real applications.