Statistical Inference Of Accelerated Hazard Rate Model In Complex Informative Censored Data

Complex censored data widely appear in fields such as biology,clinical medicine,and demography.Censoring of data generally refers to the event or failure time of interest that cannot be accurately observed.Two common types of censoring data are Interval-censored data and double censored data.Interval-censored data(Sun 2006)refer to the failure time that cannot be accurately observed,and people only know that it occurs in a specific interval.For example,blood pressure,blood sugar,and other indicators can only be measured at a fixed time point in the hospital,and cannot be continuously observed.Therefore,doctors can only determine during which time period the patient has developed the disease through changes in these physiological indicators.Double censored data refer to the existence of an effective observation interval,and the failure time of interest can only be accurately observed within the interval.If the failure time falls outside the interval,it will only be recorded as left censoring and right censoring.For example,in biological experiments using matrix chips to measure RNA indicators(Li et al.(2008)),reliable data can only be obtained within its precision reading range,while data that fall outside of precision reading cannot be considered reliable,as they provide deleted information below and above the precision limit.There has been considerable work on independently deleting the aforementioned data.For example,Liu and Qin(2018)proposed a maximum likelihood method under the Probit model.Li et al.(2021)considered the regression problem of type Ⅰ interval-censored data with misclassified covariates in an additive model.Li et al.(2018)provided a Sieve method under a semi parametric transformation model.Li et al.(2019)studied a non parametric maximum likelihood estimation method based on the EM algorithm.In this paper,we are more concerned with the issue of dependent censoring,which means that the failure time is related to the observation process.For example,if a patient participates in a medical project that requires long-term observation of physical indicators,the number of times they go to the hospital for measurement may be related to the degree of deterioration of their condition.The second chapter of the paper mainly discusses the regression problem of K-type interval-censored data with information under the accelerated risk model,that is,the failure time of interest comes from the accelerated risk model and is related to its observation process.To analyze this clinically common data,we provided a method based on bow strength and demonstrated the consistency and asymptotic normality of the estimators.We also provide the corresponding data simulation results and analyze a clinical diagnosis dataset of AIDS in the part of actual data analysis.In the third chapter of the paper,we focused on regression problem of information with double censored data in a generalized accelerated risk model.we considered a special censoring scenario where the failure event is independent of the observation process.For the case of independent censoring,we provide a method based on Sieve maximum likelihood estimation to infer the model.In this case,the estimation of variance can be obtained by solving the inverse of the Hessian matrix.We demonstrated the consistency and asymptotic normality of parameter estimators under information and independent censoring,and applied them to the AIDS Clinical Trials Group Protocol。The fourth chapter of the paper also discusses the regression problem of information with double censored data in a generalized accelerated risk model.Different from the third chapter,we consider an informative double censored mechanism.We constructed a joint model for the double censored data of information and the corresponding observation process,and used an EM algorithm based method to infer it.Finally,we use the profile method to calculate the estimated variance.We demonstrated the consistency and asymptotic normality of parameter estimators under information and independent censoring,and applied them to the AIDS Clinical Trials Group Protocol,respectively 320(ACTG 320)data analysis.The fifth chapter of the paper mainly considers a joint analysis problem based on interval-censored data,panel count data,and dependent observation processes.The failure time comes from a generalized accelerated risk model,and the relationship among failure time,panel count data,and observation process is characterized by two fragile terms.For this problem,we provide an estimation method based on the EM algorithm and demonstrate the consistency and asymptotic normality of the estimators.