Goodness-of-fit Test For Partly Interval-censored Data With A Cured Fraction

In survival analysis,we need to build appropriate models to fit the distribution of survival data for analysis.These models include parametric ones and non-parametric ones.When a parametric model is properly specified,it is more precise,concise and robust.For the purpose of utilizing these nice properties without making false deductions,statisticians come out with goodness-of-fit tests.Nowadays,all areas develop rapidly,producing a large variety of survival data.The data could be sorted into censored data and uncensored data according to the existence of censoring;or be sorted into cured data and uncured data according to the existence of cured subject.Classical goodness-of-fit tests mainly concern uncensored or right-censored uncured data.As a result,researchers face the problem of lacking rigorous theoretical support when fitting parametric models to data of other types.In order to address this problem,we propose a new goodness-of-fit test based on the mixed cure model for partly interval-censored data.Firstly,a non-parametric estimator is applied to estimate the cure parameter of the model,and then a partial likelihood method is used to estimate the distribution parameters of the model.After that,the Cramér-von Mises test is used to quantify how well the parametric model fits the data.The Monte Carlo simulation shows that compared with the old methods,the proposed method can provide more accurate and efficient deduction for the data under given conditions,and act as reliable verification and guarantee for applying the parametric model instead of the non-parametric one.The paper is organized as below.In Chapter 1,we introduce the background knowledge of interval-censored data,the mixture cure model,and the goodness-of-fit test.In Chapter 2,we describe the non-parametric/parametric mixture cure model as well as the goodness-of-fit test in detail and build the hypothesis test procedure.Chapter 3 shows the identically independently distributed representation of intermediate variables and the asymptotic properties of the test statistic.The computation adopts the empirical bootstrap method for simplicity.In Chapter 4,the finite sample performances are examined through four representative distribution functions.In Chapter 5,we employ this method to analyze the smoking cessation data and the AIDS Clinical Trial Group(ACTG)study data to check its practical value.