Statistical Inference Of The Proportional Hazards Cure Model For Survival Data

With the improvement of medical treatment and the survival quality of individuals,the populations in epidemiology,oncology,and other fields generally possess a cure fraction.The feature of cure indicates that a subgroup of subjects will not experience the events of interest during a long follow-up,where the events include disease infection,recurrence,or death.In survival analysis,when the population contains a cure fraction,the data sampled from the population are named as survival data with a cure fraction.Cox proportional hazards model is one of the regression models widely used in analyses of survival data.One of the basic assumptions in this model is that the population will inevitably experience the failure event as time goes on.Many medical data with a cure fraction contradict the hypothesis of the model.Thus the Cox model and its statistical inference can not deal with these data.The proportional hazards cure model extends the Cox model,which can solve the problem of violating the model assumption,while retaining the feature of proportional hazards among different subjects in the Cox model.In this dissertation,a proportional hazards cure model is adopted to analyze survival data with a cure fraction.Likelihood estimation methods and their statistical properties are proposed,and statistical inference is applied to analyses of real data.The research content consists of three parts discussed gradually.The first part conducts the statistical analysis for case I interval-censored data with a cure fraction.The proportional hazards cure model is adopted as the research model.The sieve space based on the Bernstein polynomials is constructed to approximate the parameter space,and the order constraint on the coefficients is imposed to guarantee the monotone non-decreasing shape of the estimator of the nonparametric component.Then the sieve maximum likelihood estimation of the proportional hazards cure model is proposed.An expectation-maximization(EM)algorithm utilizing two layers of Poisson latent variables is developed to calculate the estimates.Based on the research of the first part,the second part further analyzes censored and missing data in cohort studies.The pseudo-maximum likelihood estimation with the sieve method is proposed for survival data in case-cohort and nested case-control studies.On the other hand,an EM algorithm is constructed to avoid the loss of efficiency,which provides the calculation of the efficient estimates.In cohort studies,the data of some members are regarded as auxiliary information,while the real data outside the studies provide much auxiliary information as well.The third part focuses on the enhanced inference based on auxiliary information.The survival probabilities of cancer patients provided by large cancer databases are regarded as auxiliary information.We utilize the empirical likelihood method in which the survival probabilities are summarized as the unbiased estimation equations.The constrained maximum likelihood for right-censored data is proposed by combining the unbiased estimation equations and the observed likelihood,which improves the efficiency of the estimators.In this dissertation,the asymptotic properties of the above likelihood estimators are established.Simulation studies and real data analyses demonstrate that the proposed methods have good properties.