Statistical Inference Of General Biased Data In Survival Analysis

Survival analysis came from the study of life table in the 19 th century,and now has developed into an important branch of statistics.Through the modeling of the life function,the survival analysis can solve all kinds of problems encountered in the research,and provide some theoretical support and guidance to solve the practical problems.The data types of survival analysis include simple data,missing data,censored data,truncated data,longitudinal data(or panel data),time series data and recurring data.A variety of models have been developed according to the needs of practical research questions,including Cox model,risk rate model,residual life model,transfer model and accelerated failure model and so on.In order to obtain the parameters or nonparametric estimates,a number of estimation methods have been developed: the moment estimation method,the least squares estimation method,the maximum likelihood estimation method,the quasi-likelihood estimation method,the partial likelihood estimation method and the estimation equation method.This paper mainly considers the estimation and application of the semiparametric model of general biased data in survival analysis.The general biased data that we specific study mainly include length biased data,case cohort data,stratified case cohort data and general case cohort data.The study of the above data not only has important theoretical significance,but also has a wide range of application background.Through the study of the relevant literature,in addition to the transfer model,we find the lack of the study about unified method for the general biased data under the rest of the models.In order to further improve the theoretical research,this paper studies the uniform method under the general biased data under the additive risk model and the multiplicative mean residual life model.The second chapter mainly studies the estimation of the additive risk model under the general biased data.The risk function is an important characteristic function of the failure time,indicating the instantaneous mortality of the observed object at a given time.Risk function is a very important concept in reliability theory,survival analysis,medicine,engineering,geophysics,decision theory,queuing theory and survival theory.It is a common and important tool in statistical analysis.According to the need of the research,it is assumed that the population data satisfies the additive risk model.On this basis,the estimation equation is established by finding the 0 mean process for the general biased data.The estimated equation is used to solve the equation to get the estimator of parameter.In order to verify the validity of the proposed method,we give the stochastic simulation experiment under different biased data,respectively,using different form of large law and central limit theorem to prove the large sample properties of the estimator-consistency and asymptotic normality,and different methods of random simulation comparison experiments in some specific cases o;finally,we analysis three practical examples-shrub data(length biased data without censoring),Channing House data(length biased data with censoring),South Wales nickel refinery data(case cohort data).Chapter 3 presents a unified method for general biased data under the proportional mean residual lifetime model.The mean residual life function is another important characteristic function of the failure time,which indicates the mean value of the remaining life of the individual when the individual is still alive at t moment.Because the mean residual life function is clear and intuitive,it is easy to understand and explain,and corresponds to the distribution function of the survival time,which makes the researcher pay special attention to this index in some areas.Therefore,this paper uses proportional mean residual life model to study the general estimation of general biased data.The research program is similar to the second chapter.The proposed method has the following advantages: First,with a wide range of applicability,even if you do not know the specific type of data,the proposed method is still valid;Second,when the data belongs to the length of deviation data,even the truncation variable information unknown,the proposed method can still be used to obtain effective estimators;Third,our method not only can estimate the parameters,but also can estimate nonparametric part.