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Cited by 2,695Statistical Methods and InferenceProbability and Statistical ResearchStatistical Distribution Estimation and Applications

The DOI matches its Crossref record; 4 of the 4 references it cites were found in a registry or an index.

The Robust Inference for the Cox Proportional Hazards Model

Lin, D. Y., Wei, L. J.·1989·Journal of the American Statistical Association
DOI 10.1080/01621459.1989.10478874
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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.

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Crossref · 10.1080/01621459.1989.10478874

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4 of 4 references verified0 citation errors · 0 not checkable

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Citations

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Research works printed but not linked: 17

  1. 10.1214/aos/1176346054 · DOI
  2. 10.1093/biomet/62.2.269 · DOI
  3. 10.1093/biomet/71.3.431 · DOI
  4. Huber, P. J. “The Behavior of Maximum Likelihood Estimates Under Nonstandard Conditions,”. Proceedings of the Fifth Berkeley Symposium in Mathematical Statistics and Probability. pp.221–233. Berkeley: University of California Press.
  5. Kent J. T., 1982, Biometrika, 69, 19
  6. 10.1093/biomet/75.1.156 · DOI
  7. 10.2307/2531154 · DOI
  8. Lin D. Y., 1989, “Goodness-of-Fit Tests and Robust Statistical Inference for the Cox Proportional Hazards Model,”
  9. Morgan T. M., 1986, Biometrics, 42, 993, 10.2307/2530716 · DOI
  10. Nés T., 1982, Scandinavian Journal of Statistics, 9, 107
  11. O'Neill T. J., 1986, Statistics & Probability Letters, 4, 219, 10.1016/0167-7152(86)90091-X · DOI
  12. Press W. H., 1986, Numerical Recipes: The Art of Scientific Computing
  13. 10.2307/1403146 · DOI
  14. 10.1093/biomet/71.2.291 · DOI
  15. 10.1093/biomet/73.2.363 · DOI
  16. 10.1214/aos/1176345335 · DOI
  17. 10.2307/1912526 · DOI

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Metadata

Authors
Lin, D. Y., & Wei, L. J.
Affiliations
  • Harvard University (US)
  • University of Wisconsin–Madison (US)
ORCID
Venue
Journal of the American Statistical Association
Publisher
Informa UK Limited
Published
1989-12
Volume
84
Issue
408
Pages
1074-1078
ISSN
  • 0162-1459 (ISSN-L)
  • 1537-274X
DOI
10.1080/01621459.1989.10478874
OpenAlex
W2012658469
Cited by
2,695
References
4
Citations by year
2026: 126 · 2025: 108 · 2024: 89 · 2023: 88 · 2022: 117 · 2021: 118 · 2020: 126 · 2019: 124 · 2018: 112 · 2017: 118 · 2016: 94 · 2015: 117 · 2014: 122 · 2013: 130 · 2012: 118
FWCI
8.75
Type
journal article
Language
en
Open access
closed
Locations
Journal of the American Statistical Association (publishedVersion)
Topics
  • Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Inference
  • Physical Sciences › Mathematics › Statistics and Probability › Probability and Statistical Research
  • Physical Sciences › Mathematics › Statistics and Probability › Statistical Distribution Estimation and Applications
Keywords
Cox proportional hazards model, robust inference, model misspecification, asymptotic normality, sandwich estimator, interval estimation, small sample inference, confidence interval coverage

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