| Interval-censored data is a kind of important but also complex data in survival analysis.The event of interest sometimes cannot be continuously observed due to various constraints,but it can be observed discontinuously.So,the occurrence of events can’t be accurate but only be conjectured in a certain interval,such data is interval-censored data,which occur in many fields,including biology,medicine,demography,economics and sociology,etc.For example,the time of tumor formation in a cancer patient or the time of failure of a product can not be accurately measured,but only be determined between two adjacent tests.In general,right censored data,left censored data and current status data can all be regarded as special cases of interval-censored data.The model assumptions and inference methods based on right censored data in traditional survival analysis can not be applied to interval-censored data due to the unique data structure and complex censoring mechanism.Therefore,it is much more difficult to analyze interval-censored data than right censored data.In recent years,the inference method of interval-censored data has attracted wide attention of statisticians,and many models and methods have been proposed.However,the existing research is still not perfect,there are some problems,such as the model hypothesis is extremly strict and the estimation method is not robust enough,etc.In this paper,on the basis of predecessors’research,aimed at a broad model-semiparametric transformation model,from the development of model and the improvement of method,we study the parameter estimation and model selection problem,further improve the range interval-censored data statistical inference theory frame,and provide a practical method for related applications support.The research contents of this paper mainly include three aspects,namely,regres-sion analysis of interval-censored data under semiparametric linear transformation model,robust regression of clustered interval-censored data under semiparametric linear transformation model with random effects,and sparse estimation of dependent status data under semiparametric linear transformation model.First of all,linear transformation model is a class of important semiparamet-ric model for survival analysis,which includes some common models such as Cox proportional hazard model,proportional odds model and Probit model,etc,all of which are widely used.For the regression analysis of interval-censored data under this model,most of the existing methods involve the estimation of conditional sur-vival distribution,so it is only applicable to the case where the covariable is discrete.In this paper,we introduce the propensity score method to construct a new class of unbiased estimation equations,and on this basis,we estimate the regression co-efficient.This new method has no assumption on the types of covariates,and it is applicable for both discrete covariates and continuous covariates.In addition,we proved the consistency and asymptotic normality of the estimators,and numerical simulation and two actual data examples illustrate the rationality of the proposed model and method.Next,we extend the linear transformation model and discuss the robust re-gression problem of clustered interval-censored data under a class of more general semiparametric transformation model with random effects.In this model,the trans-formation of response time is an unknown monotone function,and the distribution of errors is also unknown as well as the random effects.These loose assumptions make this model more widely applicable,and many existing models can be regarded as special cases of this model.Under this model,we propose a robust estimation method based on maximum rank correlation,the Nelder-Mead simplex algorith-m also be used to estimate the parameters,then we demonstrate the consistency and asymptotic normality of the estimator.The simulation results verify that the proposed model and method are reasonable.In addition,we applied the proposed model and method to the empirical analysis of Nigerian Demographic and Health Survey data and lymphatic filariasis data,and obtained some significant results.Finally,we discussed the sparse estimation of dependent status data under the linear transformation model and propose a Copula model to describe the correlation between event occurrence time and censored time.In the process of estimation,we adopt a two-step estimation method.First,we estimate the distribution of the cen-soring time and use the Sieve method based on Bernstein polynomials to estimate baseline risk function of the event occurrence time.Finally,the BAR penalty func-tion is used to construct the penalized sieve maximum likelihood function to realize variable selection and parameter estimation simultaneously.Moreover,we prove the Oracle property of regression coefficient estimation and verify the rationality of the proposed variable selection method through numerical simulation.Finally,we ap-ply the proposed method to the data analysis of Alzheimer’s disease research,and obtain some reasonable results. |
