Statistical Inference Of Cure Model Of FréChet Distribution

In the survival analysis,because the observation research can not be carried out indefinitely,at the end of the observation research,all the subjects do not necessarily have the events we are interested in(i.e.terminal events).Even if the observation time is sufficient,there may be some cases in the survival data that some individuals will never have the end event(events we are interested in).For example,when studying the factors that affect the unemployed to find new jobs,some of them will remain unemployed for some special reasons,and they will never "find new jobs".These individuals are called "long-term survivors.".The term "long-term survivor" refers to the observation object who will never have an end point event(or expected study outcome)even if the observation study continues indefinitely.In the field of medical research,there is a widespread phenomenon of "longterm survivors".From the perspective of biomedicine,these people can also be called "healers".The cure model is a study of the survival model of individuals with "cured"(long-term survivors).In medical research,"long-term survivors" data are widespread.W.Weibull found that extremum distribution can be widely used to fit all kinds of life data.At present,the distribution used to fit the failure time(i.e.the occurrence time of the event of interest)data in the survival data simulation is mainly exponential distribution,Weibull distribution,lognormal distribution,gamma distribution and so on.Fréchet distribution is the extremum type ? distribution,also known as the inverse Weibull distribution(IW),which is widely used in the field of survival analysis.In this paper,we mainly study the statistical inference of Fréchet distribution in the nonmixed cure model,that is,when we use the same distribution(Fréchet distribution)to fit the survival time of "cured" and "non-cured" individuals,how to use the maximum likelihood method to estimate the parameters under the model,and verify the estimation method by numerical simulation,and use autogenous bone marrow transplantation The data of relapse of post white blood patients were analyzed by the case of Fréchet distribution non mixed cure model.At present,in the analysis of "long-term survivors" data,the commonly used proportional risk cure model requires that the survival data must meet the proportional risk assumption.The accelerated failure time hybrid cure model can solve this problem and provide support for the analysis of "long-term survivors" data.At the same time,this paper mainly studies the accelerating effect of covariates on the individual survival time when using Fréchet distribution to fit the survival time of non "cured" individuals under the hybrid cure model,that is,the statistical inference problem in the aft hybrid cure model based on Fréchet distribution,analyzes how to use the maximum likelihood method to estimate the parameters under the model,and uses the number to estimate the parameters Finally,we use the real data of P2 P network loan platform to analyze the aft hybrid cure model based on Fréchet distribution.