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Regression Models and Non‐Proportional Hazards in the Analysis of Breast Cancer Survival

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  • Sheila M. Gore
  • Stuart J. Pocock
  • Gillian R. Kerr

Abstract

The Western General breast cancer series of 3922 patients sets research methodology for survival data in practical perspective and illustrates that the waning of covariate effects through time is an important phenomenon in medical applications. Non‐monotone convergent hazard functions are associated with most clinical covariates in breast cancer; an unusual hazard pattern according to menopausal state is also reported. These features contraindicate the use of standard regression models for survival such as Weibull and proportional hazards. Inferences about covariate effects are compared under these and a log‐logistic model which implies proportionality of the cumulative odds on death. Regression models are shown to be useful in exploratory analysis. In particular, a step‐function proportional hazards model elucidates the time‐dependent influence of initial covariates and leads to a more appropriate final model, but one whose virtues are balanced by computational difficulty.

Suggested Citation

  • Sheila M. Gore & Stuart J. Pocock & Gillian R. Kerr, 1984. "Regression Models and Non‐Proportional Hazards in the Analysis of Breast Cancer Survival," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 33(2), pages 176-195, June.
    • Handle: RePEc:bla:jorssc:v:33:y:1984:i:2:p:176-195
    DOI: 10.2307/2347444
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    Cited by:

    1. Congdon, Peter, 2008. "A bivariate frailty model for events with a permanent survivor fraction and non-monotonic hazards; with an application to age at first maternity," Computational Statistics & Data Analysis, Elsevier, vol. 52(9), pages 4346-4356, May.
    2. Devarajan, Karthik & Ebrahimi, Nader, 2011. "A semi-parametric generalization of the Cox proportional hazards regression model: Inference and applications," Computational Statistics & Data Analysis, Elsevier, vol. 55(1), pages 667-676, January.
    3. D. Stogiannis & C. Caroni & C. E. Anagnostopoulos & I. K. Toumpoulis, 2011. "Comparing first hitting time and proportional hazards regression models," Journal of Applied Statistics, Taylor & Francis Journals, vol. 38(7), pages 1483-1492, June.
    4. Chengyuan Lu & Jelle Goeman & Hein Putter, 2023. "Maximum likelihood estimation in the additive hazards model," Biometrics, The International Biometric Society, vol. 79(3), pages 1646-1656, September.
    5. Ofosu, Yaw., 1993. "Socio-economic change and evolution of cultural models of reproduction in Ghana: implications for population policy," ILO Working Papers 992920673402676, International Labour Organization.
    6. Ian W. McKeague & Mourad Tighiouart, 2000. "Bayesian Estimators for Conditional Hazard Functions," Biometrics, The International Biometric Society, vol. 56(4), pages 1007-1015, December.
    7. Gupta, Ramesh C. & Gupta, Pushpa L., 2000. "On the crossings of reliability measures," Statistics & Probability Letters, Elsevier, vol. 46(3), pages 301-305, February.
    8. Qin, Fei, 2015. "Global talent, local careers: Circular migration of top Indian engineers and professionals," Research Policy, Elsevier, vol. 44(2), pages 405-420.
    9. repec:ilo:ilowps:292067 is not listed on IDEAS

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