【作者】 王楠；

【导师】 袁晓惠；

【作者基本信息】 长春工业大学 ， 统计学， 2025， 硕士

【摘要】 在生存分析研究领域中,寿命数据常常因受到截断和删失而呈现出不完全性特征。此类数据在医学、生物学等领域广泛存在,但此类不完全数据对于模型的参数估计与变量选择提出了严峻挑战。本文围绕半参数加速失效时间模型的稳健推断问题,针对左截断右删失数据与右删失两种数据展开研究,基于秩估计框架研究了高效的算法。全文研究内容分为以下两部分:第一部分:左截断右删失数据下半参数加速失效时间模型的惩罚秩估计。针对左截断右删失数据下传统方法依赖强分布假设且计算效率低的问题,本文提出了一种基于秩估计的参数估计与变量选择算法。首先,将秩估计方程与惩罚函数结合,构建统一的U统计量型目标函数,在半参数加速失效时间模型中实现左截断右删失数据的稀疏估计,避免了对误差分布与截断删失机制进行参数假设。其次,设计了新的坐标下降算法来实现惩罚秩估计的求解,降低模型计算复杂度。同时通过相关极限理论克服了U统计量带来的渐近推导困难,证明了估计量的相合性与Oracle性质。最后通过模拟研究和实证分析验证该方法在有限样本情况下的有效性以及实例数据下的适用性。第二部分:右删失数据下半参数加速失效时间模型的光滑惩罚秩估计。针对右删失数据中传统秩估计方法中存在的非光滑性导致的计算效率低、收敛困难等问题,本研究提出了一种右删失数据下半参数加速失效时间模型的高斯核光滑秩估计。传统方法因目标函数包含示性函数而缺乏光滑性,导致算法效率低。同时,现有惩罚方法依赖删失分布假设且对高删失率数据敏感易出现参数估计偏差。为此,本文首先引入高斯核函数对秩损失进行连续光滑逼近,构造二阶可微目标函数。其次,结合SCAD、LASSO和ALASSO三种惩罚项,提出一种高效变量选择算法实现参数更新。最后通过模拟研究与实证分析表明所提方法为右删失数据下的高维生存分析提供了稳健高效的算法。本文在半参数加速失效时间模型的秩估计框架下开展的研究在数值模拟与临床数据上的表现良好,均体现出了有效性和适用性,为受删失影响的生存数据提供了半参数加速失效时间模型的稳健秩估计。更多还原

【Abstract】 In the field of survival analysis research,event time data often exhibits incomplete characteristics due to truncation and deletion.This type of data is widely present in fields such as medicine and biology.However,such incomplete data poses a serious challenge to the parameter estimation and variable selection of the model.This article focuses on the robust inference problem of the semi parametric accelerated failure time model,and conducts research on two types of data:left truncated right censored data and right censored data.Based on the rank estimation framework,efficient algorithms are studied.The research content of the full text is divided into the following two parts:The first part:Penalty rank estimation of the lower half parameter AFT model with left truncated and right censored data.This paper proposes a rank estimation based parameter estimation and variable selection algorithm to address the problem of traditional methods relying on strong distribution assumptions and low computational efficiency in LTRC data.Firstly,by combining the rank estimation equation with the penalty function,a unified U-statistic type objective function is constructed to achieve sparse estimation of left truncated and right censored data in the semi parametric AFT model,avoiding parameter assumptions on error distribution and truncation censoring mechanism.Secondly,a new coordinate descent algorithm was designed to solve the penalty rank estimation and reduce the computational complexity of the model.At the same time,the asymptotic derivation difficulty caused by the U statistic was overcome through relevant limit theory,and the consistency of the estimator and Oracle properties were proved.Finally,the effectiveness of the method in limited sample situations and its applicability in case data were verified through simulation research and empirical analysis.The second part:Smooth penalty rank estimation of the lower half parameter accelerated failure time model for right censored data.In response to the problems of low computational efficiency and difficult convergence caused by non smoothness in traditional rank estimation methods for right censored data,this study proposes a Gaussian kernel smooth rank estimation method for the lower half parameter accelerated failure time model of right censored data.Traditional methods lack smoothness due to the inclusion of explicit functions in the objective function,resulting in low algorithm efficiency.Meanwhile,existing punishment methods rely on the assumption of censoring distribution and are sensitive to high censoring rate data,which can lead to parameter estimation bias.Therefore,this article first introduces Gaussian kernel function for continuous smooth approximation of rank loss,and constructs a second-order differentiable objective function.Secondly,an efficient variable selection algorithm is proposed to update parameters by combining the three penalty terms of SCAD,LASSO,and ALASSO.Finally,simulation studies and empirical analysis demonstrate that the proposed method provides a robust and efficient algorithm for high-dimensional survival analysis under right censored data.The research conducted in this article under the rank estimation framework of the semi parametric accelerated failure time model has shown good performance in system simulation and clinical data,demonstrating effectiveness and applicability,providing robust parameter rank estimation for survival data affected by censoring.更多还原