The Robust Inference for the Cox Proportional Hazards Model
研究了在Cox比例风险模型可能设定错误时，最大偏似然估计量的渐近性质，提出了类似三明治方差估计的稳健协方差矩阵估计量，并验证了其在小样本下稳健得分检验的良好表现。
Abstract We derive the asymptotic distribution of the maximum partial likelihood estimator β for the vector of regression coefficients β under a possibly misspecified Cox proportional hazards model. As in the parametric setting, this estimator β converges to a well-defined constant vector β*. In addition, the random vector n 1/2(β – β*) is asymptotically normal with mean 0 and with a covariance matrix that can be consistently estimated. The newly proposed robust covariance matrix estimator is similar to the so-called “sandwich” variance estimators that have been extensively studied for parametric cases. For many misspecified Cox models, the asymptotic limit β* or part of it can be interpreted meaningfully. In those circumstances, valid statistical inferences about the corresponding covariate effects can be drawn based on the aforementioned asymptotic theory of β and the related results for the score statistics. Extensive studies demonstrate that the proposed robust tests and interval estimation procedures are appropriate for practical use. In particular, the robust score tests perform quite well even for small samples. In contrast, the conventional model-based inference procedures often lead to tests with supranominal size and confidence intervals with rather poor coverage probability.