Maximum Weighted Partial Likelihood Estimators for the Cox Model
Cox 模型的最大加权偏似然估计AI 解读 ↓
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Cox 模型的最大加权偏似然估计
- 研究问题
- 如何降低异常观测及长期存活个体对 Cox 回归估计的潜在影响，同时保留较好的模型内渐近效率？
- 方法与思路
- 作者对偏似然加权，以计数过程和鞅研究渐近性质；还考察按风险集人数加权及提前截断事件的估计方式。
- 材料陈述的贡献
- 摘要称，部分加权估计具有有界影响曲线和较好渐近相对效率；其中 Wilcoxon 型估计的有界影响需协变量空间紧致。
- 阅读关注点
- 应核对权重如何进入估计方程、有界影响所需条件、效率比较的基准，以及人工删失时间改变后的估计目标。
- 阅读边界
- 仅据 OpenAlex 索引摘要，稿件版本未注明；有界影响带有条件，小规模模拟不能支持所有删失机制及异常模式下的优势。
原文摘要
New estimators for Cox regression that maximize a weighted version of the partial likelihood are considered. Their asymptotic properties on the model are sketched. Estimators with bounded influence curves are identified and shown to have good asymptotic relative efficiency. The results of a small simulation study are included. The estimators are applied to a well-known data set. The possible influence of an outlying observation on the Cox estimator can be of any magnitude. Individuals who survive longest have a high potential of being influential. In analogy with weighted linear rank tests, we introduce estimators of the regression coefficients that maximize a weighted partial likelihood. For instance, by using weights proportional to the number at risk, one obtains a Wilcoxon-type estimator. This estimator has bounded influence (provided the covariate space is compact), and in a wide variety of situations its asymptotic relative efficiency is at least as good as that of the Wilcoxon test. Asymptotic properties of the estimators follow in a straightforward manner using counting processes and martingales. Another approach that has proven useful in simulations is to estimate the parameters using only those events that occur before a certain time. For example, one might calculate the Cox estimator artificially censoring individuals after 3, 4, 5, 6, and 7 years. A comparison of the five different estimators can be illuminating.