Efficient Estimation For The Cox Proportional Hazards Cure Model
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While analysing time-to-event data, it is possible that a certain fraction of subjects will never experience the event of interest and they are said to be cured. When this feature of survival models is taken into account, the models are commonly referred to as cure models. In the presence of covariates, the conditional survival function of the population can be modelled by using cure model which depends on the probability of being uncured (incidence) and the conditional survival function of the uncured subjects (latency), and a combination of logistic regression and Cox PH regression is used to model the incidence and latency respectively. In this paper, we take the profile likelihood approach to estimate the cumulative hazard and the regression parameters. We show the asymptotic normality of the profile likelihood estimator via asymptotic expansion of the profile likelihood and obtain the explicit form of the variance estimator. Moreover, the estimators of the regression parameters from the Cox PH cure model are shown to be semiparametric efficient. The numerical result of our proposed method is shown by using the melanoma data from SMCURE R-package (Cai et al., 2012) and we compare the results with the output obtained from SMCURE package.
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