The Robust Inference for the Cox Proportional Hazards Model
作者:
D.Y. Lin,
L.J. Wei,
期刊:
Journal of the American Statistical Association
(Taylor Available online 1989)
卷期:
Volume 84,
issue 408
页码: 1074-1078
ISSN:0162-1459
年代: 1989
DOI:10.1080/01621459.1989.10478874
出版商: Taylor & Francis Group
关键词: Asymptotic theory;Model misspecification;Partial likelihood;Regression;Robustness;Survival data
数据来源: Taylor
摘要:
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 vectorn1/2(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.
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