© 1994 by Biometrika Trust
Articles |
Proportional hazards tests and diagnostics based on weighted residuals
1 Division of Biostatistics, School of Public Health, University of Minnesota Minneapolis, Minnesota 55455, U.S.A.
2 Department of Health Science Research Mayo Clinic, Rochester, Minnesota 55905, U.S.A.
Received for publication 1 March 1993.
Revision received 1 January 1994.
| Abstract |
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Nonproportional hazards can often be expressed by extending the Cox model to include time varying coefficients; e.g., for a single covariate, the hazard function for subject i is modelled as exp {β(t)Zi(t)}. A common example is a treatment effect that decreases with time. We show that the function βi(t) can be directly visualized by smoothing an appropriate residual plot. Also, many tests of proportional hazards, including those of Cox (1972), Gill & Schumacher (1987), Harrell (1986), Lin (1991), Moreau, O'Quigley & Mesbah (1985), Nagelkerke, Oosting & Hart (1984), O'Quigley & Pessione (1989), Schoenfeld (1980) and Wei (1984) are related to time-weighted score tests of the proportional hazards hypothesis, and can be visualized as a weighted least-squares line fitted to the residual plot.
Key Words: Cox model Loess Schoenfeld residuals Weighted regression
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E. Hoster, M. Dreyling, W. Klapper, C. Gisselbrecht, A. van Hoof, H. C. Kluin-Nelemans, M. Pfreundschuh, M. Reiser, B. Metzner, H. Einsele, et al. A new prognostic index (MIPI) for patients with advanced-stage mantle cell lymphoma Blood, January 15, 2008; 111(2): 558 - 565. [Abstract] [Full Text] [PDF] |
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K. Miller, M. Wang, J. Gralow, M. Dickler, M. Cobleigh, E. A. Perez, T. Shenkier, D. Cella, and N. E. Davidson Paclitaxel plus Bevacizumab versus Paclitaxel Alone for Metastatic Breast Cancer N. Engl. J. Med., December 27, 2007; 357(26): 2666 - 2676. [Abstract] [Full Text] [PDF] |
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T. G. Liou, F. R. Adler, D. R. Cox, and B. C. Cahill Lung Transplantation and Survival in Children with Cystic Fibrosis N. Engl. J. Med., November 22, 2007; 357(21): 2143 - 2152. [Abstract] [Full Text] [PDF] |
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E. O. Hanrahan, A. M. Gonzalez-Angulo, S. H. Giordano, R. Rouzier, K. R. Broglio, G. N. Hortobagyi, and V. Valero Overall Survival and Cause-Specific Mortality of Patients With Stage T1a,bN0M0 Breast Carcinoma J. Clin. Oncol., November 1, 2007; 25(31): 4952 - 4960. [Abstract] [Full Text] [PDF] |
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K.-L. Chien, H.-C. Hsu, T.-C. Su, M.-F. Chen, Y.-T. Lee, and F. B. Hu Apolipoprotein B and non-high density lipoprotein cholesterol and the risk of coronary heart disease in Chinese J. Lipid Res., November 1, 2007; 48(11): 2499 - 2505. [Abstract] [Full Text] [PDF] |
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P. Mathew, P. F. Thall, C. D. Bucana, W. K. Oh, M. J. Morris, D. M. Jones, M. M. Johnson, S. Wen, L. C. Pagliaro, N. M. Tannir, et al. Platelet-Derived Growth Factor Receptor Inhibition and Chemotherapy for Castration-Resistant Prostate Cancer with Bone Metastases Clin. Cancer Res., October 1, 2007; 13(19): 5816 - 5824. [Abstract] [Full Text] [PDF] |
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M. C. Pinder, Z. Duan, J. S. Goodwin, G. N. Hortobagyi, and S. H. Giordano Congestive Heart Failure in Older Women Treated With Adjuvant Anthracycline Chemotherapy for Breast Cancer J. Clin. Oncol., September 1, 2007; 25(25): 3808 - 3815. [Abstract] [Full Text] [PDF] |
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A. Lipton, R. J. Cook, P. Major, M. R. Smith, and R. E. Coleman Zoledronic Acid and Survival in Breast Cancer Patients with Bone Metastases and Elevated Markers of Osteoclast Activity Oncologist, September 1, 2007; 12(9): 1035 - 1043. [Abstract] [Full Text] [PDF] |
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L. Sjostrom, K. Narbro, C. D. Sjostrom, K. Karason, B. Larsson, H. Wedel, T. Lystig, M. Sullivan, C. Bouchard, B. Carlsson, et al. Effects of Bariatric Surgery on Mortality in Swedish Obese Subjects N. Engl. J. Med., August 23, 2007; 357(8): 741 - 752. [Abstract] [Full Text] [PDF] |
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