基于比例风险模型中协变量调整方法的研究
Research on Covariate Adjustment Method Based on Proportional Hazards Model
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摘要: 在实际数据中, 尤其是医学数据,其协变量受到某些因素的污染或干扰, 而真实的协变量无法观测.本文所讨论的是在比例风险模型中如何对受干扰的协变量进行调整的问题.目前所存在的协变量调整方法不能直接用于生存数据, 为了解决这个问题, 我们运用核函数来构造干扰因子的分布函数,对受干扰的协变量进行平滑得到真实协变量的估计值,再代入到模型中得到参数的回归估计值,并完成了估计值满足相合性和渐近正态性证明.又提出运用极小极大算法(minorization-maximization algorithm,MM得到参数估计值, 第一个M是通过指数函数和负对数函数的凸性来构造一个黑塞矩阵为对角矩阵的替代函数; 第二个M是对替代函数求最大值. 最后通过数值模拟和真实数据研究来说明我们所提出方法的可行性.Abstract: In actual data, especially medical data, the covariates are contaminated or interfered by certain factors, while the real covariates cannot be observed. This paper discusses how to adjust the disturbed covariates in the proportional risk model. Covariate existed in the adjustment methods cannot be directly used for survival data, in order to solve this problem, we use kernel functions to construct the interference factors of the distribution function, the interference of covariate smoothly get the estimate of the real covariate, again to get the parameters in the model of regression estimate, and completed the estimate satisfying consistency and asymptotic normality. We also proposed the use of Minorization-Maximization (MM) algorithm to obtain parameter estimates. The first M is to construct a surrogate function by the convexity of the exponential function and the negative logarithm function, which the Hessian matrix is a diagonal matrix; The second M is to obtain the estimators by maximizing the surrogate function. Finally, we demonstrate the feasibility of our proposed method through numerical simulation and real data research.