Estimation and Variable Selection for Interval-censored Failure Time Data with Random Change Point and Application to Breast Cancer Study

Motivated by a breast cancer study, we consider regression analysis of interval-censored failure time data in the presence of a random change point. Although a great deal of literature on interval-censored data has been established, it does not seem to exist an established method that can allow for the existence of random change points. Such data can occur in, for example, clinical trials where the risk of a disease may dramatically change when some biological indexes of the human body exceed certain thresholds. To fill the gap, we will first consider regression analysis of such data under a class of linear transformation models and provide a sieve maximum likelihood estimation procedure. Then a penalized method is proposed for simultaneous estimation and variable selection, and the asymptotic properties of the proposed method are established. An extensive simulation study is conducted and indicates that the proposed methods work well in practical situations. The approaches are applied to the real data from the breast cancer study mentioned above.

本研究受一项乳腺癌临床研究启发，针对存在随机变点（random change point）的区间截尾失效时间数据（interval-censored failure time data）开展回归分析。尽管现有大量关于区间截尾数据的研究成果，但目前尚未有成熟方法可适配随机变点的存在场景。此类数据常见于临床试验场景，例如当人体某项生物学指标超过特定阈值时，疾病发病风险会发生显著变化。为填补这一研究空白，本文首先基于一类线性变换模型（linear transformation models）开展此类数据的回归分析，并提出筛法极大似然估计流程（sieve maximum likelihood estimation procedure）；随后提出一种惩罚化方法（penalized method）以实现参数估计与变量选择（variable selection）的同步进行，并证明所提方法的渐近性质（asymptotic properties）。本文开展了大规模模拟实验，结果表明所提方法在实际场景中表现优良；最后将所提方法应用于前文提及的乳腺癌研究真实数据集。

搜集汇总

背景与挑战

背景概述

该数据集围绕乳腺癌研究，提出了针对区间删失失效时间数据在随机变化点存在情况下的回归分析和变量选择方法。研究通过线性变换模型和筛最大似然估计，解决了现有方法在随机变化点处理上的不足，并通过模拟研究和实际数据应用验证了方法的有效性。