| In medical research,Cox model is a classical model for survival data which builds the relationship between survival time and covariates,it extends survival analysis from empirical research to prognosis.Because of the flexibility of Cox model,it is widely used in other fields such as biology,economics,management and so on.However,in practice,researchers can't collect observations of all covariates which are related to the hazard function.One reason is that some covariates are difficult to observe straightforward and researchers can only collect observations with measurement error.The other reason is that there exist some potential factors which are unobservable.In addition,with the improvement of information,there is more and more concerned about the relevance among multiple events in clinical research.However,the classical Cox model can only estimate the hazard function of a single event and can't handle the correlation of hazards of multiple events.This paper constructs two extended Cox model in order to solve the above problems.First,in terms of one terminal event,the paper combines measurement error,potential factors and Cox model,and estimates parameters with the method which is based on profile likelihood and EM algorithm.This method not only reduces the dimension of parameters,but also ensures the stability of the estimation.The numerical simulation proves that this method performs better than other algorithms on bias and MSE.Besides,this method is applied to analyze the data of the AIDS Clinical Trials Group.Second,this paper extends the first model to the semi-competing risks data which contains at least two events,builds semi-competing risks Cox model,and proposes an estimation method based on maximum likelihood and EM algorithm.The numerical simulation shows that,compared with the existing methods,such as MCMC algorithm based on Bayesian estimation and Netwon-Raphson method based on marginal likelihood,the method this paper proposes performs better. |
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