区间删失下时变系数Cox 模型的贝叶斯方法研究

Interval censoring is an important research topic in medicine, economy, and engineering, etc. Cox model, i.e., the proportional hazards model, is commonly used to analyze the relationship between risk factors and survival time. Though not always valid, the coefficient of covariate in the Cox model is usually assumed to be constant. This project will conduct several studies about Cox models with one or multiple outcomes and time-varying coefficients. Firstly, the univariate Cox model will be studied. The likelihood function of interval-censored data can be expressed as a product of likelihood of right-censored subjects by applying latent variable technique. With the Markov process prior, the posterior distribution can be computed by an improved reversible jump Markov chain Monte Carlo method based on the piecewise constant assumption for both baseline hazard function and time-varying coefficients. The Bayesian convergence properties will be discussed. Secondly, the models with multiple outcomes and time-varying coefficients, including the bivariate model which has two correlated interval-censored outcomes, as well as the joint model of interval censoring and discrete variable, will be studied by extending the aforementioned Bayesian method for the univariate model. Finally, the properties of the aforementioned methods will be investigated by several simulation studies. The models will also be applied to the Alzheimer disease data from US ADNI database to see the contribution of this project. In this project, a Bayesian approach to the Cox models with time-varying coefficients and interval-censored data will be developed, which can be used in future medical studies.

区间删失是医学、经济学、工程学等研究领域中的重要问题，学者们常常使用Cox模型对区间删失数据和风险因素进行回归分析。但是，Cox模型中的固定系数假设在实际应用中往往并不成立，且现有研究通常只针对一个区间删失变量。因此，本项目拟基于时变系数，对一个和两个终点变量的Cox模型，运用贝叶斯方法进行研究。首先，对于一个区间删失变量的Cox模型，在时变系数为分段常数的假设基础上，选择马尔可夫过程先验，运用改进后的可逆跳转马尔可夫链蒙特卡洛算法计算后验，并讨论贝叶斯收敛性质。其次，基于上述时变系数的贝叶斯估计方法，研究两个相关区间删失变量的二元模型，以及区间删失和离散数据的联合模型。最后，通过模拟计算评估上述方法的稳定性和准确性，并应用美国ADNI数据库中的阿尔茨海默数据进行实证分析。本项目将建立区间删失下时变系数Cox模型的贝叶斯估计方法，为相关的医学研究提供统计方法以及应用工具。

区间删失是医学、经济学、工程学等研究领域中的重要问题，学者们常常使用Cox模型对区间删失数据和风险因素进行回归分析。但是，Cox模型中的固定系数假设在实际应用中往往并不成立。因此，本项目针对区间删失Cox模型中时变系数的估计和推断进行了研究。针对区间删失数据，我们建立了一个具有时变系数的比例风险模型。在估算中，为了减轻计算负担，时变系数将会基于B样条基中进行估计，使其易于实现。我们严格地证明了该估计是一致的，收敛于最小最大最优速率，并且还提供了一致的方差估计。通过模拟研究证明了所提出模型的有效性，并应用在CLHLS数据中进行老年人的认知受损研究，以识别地理因素的时变影响位置（南部vs北部）。