GOODNESS-OF-FIT ANALYSIS FOR THE COX REGRESSION-MODEL BASED ON A CLASS OF PARAMETER ESTIMATORS
GOODNESS-OF-FIT ANALYSIS FOR THE COX REGRESSION-MODEL BASED ON A CLASS OF PARAMETER ESTIMATORS
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DOI：
10.2307/2290404
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发表时间：
1991-09-01
影响因子：
3.7
通讯作者：
LIN, DY
中科院分区：
文献类型：
--
作者：
LIN, DY
本文通过将加权对数秩检验中常用的权函数引入偏似然得分函数中，提出了一类协变量可能依赖于时间的考克斯比例风险模型中回归参数向量的估计函数. 所得估计量的行为很像传统的最大偏似然估计量，因为它们是一致的和渐近正态的。 然而，当考克斯模型不合适时，具有不同权函数的估计量通常收敛到不同的常值向量。 例如，如果协变量效应随时间减少，则使用Kaplan-Meier生存估计量作为权重函数的参数估计量的幅度将随机大于最大偏似然估计量的幅度。 这些事实促使我们通过比较具有不同权函数的参数估计来发展考克斯回归模型的拟合优度方法。 在假设的模型下，最大偏似然估计和加权参数估计之间的归一化差弱收敛到均值为零的多元正态，并提出了一个一致的估计的协方差矩阵。 在误定考克斯模型下，研究了加权参数估计和相关拟合优度检验的渐近性质. 特别是，它表明，拟合优度检验与单调的权重函数是一致的，对单调偏离比例风险假设。 可以基于同时使用多个权重函数来开发具有广泛灵敏度的通用测试程序。 使用真实的数据的三个例子。
In this article we propose a class of estimation functions for the vector of regression parameters in the Cox proportional hazards model with possibly time-dependent covariates by incorporating the weight functions commonly used in weighted log-rank tests into the partial likelihood score function. The resulting estimators behave much like the conventional maximum partial likelihood estimator in that they are consistent and asymptotically normal. When the Cox model is inappropriate, however, the estimators with different weight functions generally converge to nonidentical constant vectors. For example, the magnitude of the parameter estimator using the Kaplan-Meier survival estimator as the weight function will be stochastically larger than that of the maximum partial likelihood estimator if covariate effects diminish over time. Such facts motivate us to develop goodness-of-fit methods for the Cox regression model by comparing parameter estimators with different weight functions. Under the assumed model, the normalized difference between the maximum partial likelihood estimator and a weighted parameter estimator is shown to converge weakly to a multivariate normal with mean zero and with a covariance matrix for which a consistent estimator is proposed. The asymptotic properties of the weighted parameter estimators and those of the related goodness-of-fit tests under misspecified Cox models are also investigated. In particular, it is demonstrated that a goodness-of-fit test with a monotone weight function is consistent against monotone departures from the proportional hazards assumption. Versatile testing procedures with broad sensitivities can be developed based on simultaneous use of several weight functions. Three examples using real data are presented.