A mixture model combining logistic regression with proportional hazards regression

Maximum likelihood estimation in the proportional hazards cure model

“…Survival models with a cure rate have received much attention in recent years (Farewell, 1982(Farewell, , 1986Kuk and Chen, 1992;Sy and Taylor, 2000;Peng and Dear, 2000, among others). These models are useful when a proportion of study subjects never experience the event of interest.…”

“…Kuk and Chen (1992) proposed the so-called proportional hazards cure model in which the proportional hazards regression (Cox 1972) models the survival times of susceptible subjects while the logistic regression models the cure fraction.…”

“…As noted by Kuk and Chen (1992), if the cure fraction 1 − π(γ X) is not equal to zero, the hazard function of T is no longer proportional and the simple form of the partial likelihood function, like that for the usual Cox proportional hazards model, can not be obtained here. To solve this difficulty, they proposed to consider the following complete but unobserved likelihood function:…”

Analysis of a semiparametric mixture model for competing risks

“…Indeed, the authors found that, while the two factors they considered in the analysis of the prostate cancer data have significant effects in the generalized logistic model, neither of them seemed to be significant in the conditional hazards. Note that the model (1) and (2) is related to semiparametric mixture models for survival data with cure fraction (see, among others, Kuk and Chen 1992;Taylor 1995;Sy and Taylor 2000;Peng 2003, who investigated the computational issues raised by the estimation in this class of models. See also Fang et al (2005) and Lu (2008) who studied the large-sample properties of maximum likelihood estimators in the proportional hazards cure model).…”

A general transformation class of semiparametric cure rate frailty models

“…The mixture cure model (1) has been extensively studied in the literature, which includes the work of Gray and Tsiatis (1989), Kuk and Chen (1992), Taylor (1995), Sy and Taylor (2000), Peng and Dear (2000), and Betensky and Schoenfeld (2001), among others. A comprehensive discussion of the mixture cure model is given by Maller and Zhou (1996).…”