二元区间删失数据的统计推断

This project will discuss statistical inference for bivariate interval censored failure time data. Bivariate interval-censored failure time data arise in a number of fields including biology, medical science, social science. In this project, we will focus on bivariate interval censored data, which arise if a survival study involves two related failure events and only interval censored data are available on both events. Firstly, we will provide a class of semiparametric transformation models and general correlation structure modeling for bivariate interval-censored data, a sieve maximum likelihood approach will be developed. The model provides a great flexibility, in particular including the commonly used proportional hazards model as a special case. In the approach, Bernstein polynomials will be employed. This approach can be easily implemented. Secondly, we will discuss regression analysis of bivariate current status or case I interval-censored failure time data under the marginal proportional hazards model. An unknown copula model will be used to describe correlation structure modeling. By using Bernstein polynomials.and an unspecified copula model, we develop a sieve maximum likelihood estimation approach. In particular, it allows one to estimate the underlying copula model. This approach applies to much more general situations and effectively avoids the undesirable consequences when correlation structure is specified wrongly. Finally, we will consider the case where one or more explanatory variables in the statistical model with bivariate interval censored data are subject to measurement error. We will extend the SIMEX approach to the model in order to estimate the effect of measurement error on the bias of the estimators and to reduce this bias. Furthermore, for both bivariate interval censored failure time data and bivariate case I interval-censored failure time data , a goodness-of-fit test will be constructed for the nonparametric components in the models based on the sieve likelihood ratio and the adaptive LASSO procedure will be used to select significant variables when the number of potential covariates in the models is large.

二元区间删失数据广泛出现于医学、生物学、社会学等领域。 在生存统计分析研究中当两个可能相关的失效时间都被区间删失时，便得到二元区间删失数据。针对二元区间删失数据，首先将提出一类半参数转换模型，此模型将提供统一的相关结构和边际模型框架来建模，很多已有模型可作为其特例, 将通过极大化sieve似然进行估计, 计算简便; 其次将研究二元I型区间删失数据回归分析，相关结构用未知的Copula模型来刻画，利用Bernstein多项式来近似未知的Copula模型和边际非参数分量, 适用于比较广泛的相关结构并可有效避免相关结构错误指定时带来的不良后果; 最后利用SIMEX算法研究存在测量误差情形。进一步在二元区间删失和二元I型区间删失下，还将研究变量选择问题和非参数分量的sieve似然比检验。

区间删失数据广泛出现于医学、生物学、社会学等领域。针对二元区间删失数据，首先研究了一类半参数转换模型，此模型将提供统一的相关结构和边际模型框架来建模，很多已有模型可作为其特例, 将通过极大化sieve似然进行估计; 其次研究了二元I型区间删失数据回归分析，相关结构用未知的Copula模型来刻画，利用Bernstein多项式来近似未知的Copula模型和边际非参数分量, 该方法适用于比较广泛的相关结构并可有效避免相关结构错误指定时带来的不良后果; 最后利用SIMEX算法和sieve 似然研究了协变量存在测量误差情形，带治愈亚组和区间删失三种问题都存在时的统计推断。进一步我们研究了在相依区间删失假设下，半参数转换模型和Probit模型的统计推断问题。