Cure Mixture Models in Breast Cancer Survival Studies

  • Nahida H. Gordon
Chapter

Abstract

A considerable proportion of breast cancer patients will die of unrelated causes, thus complicating the analysis of the effect of prognostic factors or treatment. I assume the survival function of breast cancer patients to be a mixture of two survival functions representing those who will die from other causes (i.e., cured) and those from breast cancer. The hazard function for breast cancer death incorporates covariates representing breast cancer risk factors. Using the proposed cure mixture model, I consider the questions whether newly diagnosed node positive breast cancer is a late manifestation of node negative breast cancer or whether it is an inherently more aggressive disease. Using census and clinical trial data, I estimate the proportion of patients dying of other causes and of breast cancer for each of the node negative and node positive groups. An estimated 55.9% and 26.0% of node negative and positive patients, respectively, will die from other causes. Of those patients who will die from breast cancer, node positive patients were prone to have a significantly higher breast cancer death rate indicating that their disease is not simply a late manifestation of node negative disease.

Keywords

Breast Cancer Breast Cancer Patient Mixture Model Node Positive Patient Node Negative Patient 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
This is a preview of subscription content, log in to check access

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Berkson, J. and Gage, R. P. (1952), “Survival Curve for Cancer Patients Following Treatment,” Journal American Statistical Association, 47, 501–515.CrossRefGoogle Scholar
  2. Boag, J. W. (1949), “Maximum Likelihood Estimates of the Proportion of Patients Cured by Cancer Therapy,” J. R. Statist. Soc. (B), 11, 15–53.MATHGoogle Scholar
  3. Brinkley, D. and Haybittle, J. L. (1984), “Long-term Survival of Women with Breast Cancer, ” The Lancet, i, 1118.Google Scholar
  4. Chen, W. C., Hill, B. M., Greenhouse, J. B., and Fayos, J. V. (1985), “Bayesian Analysis of Survival Curves for Cancer Patients Following Treatment,” Bayesian Statistics, 2, 299–328.MathSciNetGoogle Scholar
  5. Early Breast Cancer Trialists’ Collaborative Group (1992), “Systemic Treatment of Early Breast Cancer by Hormonal, Cytotoxic, or Immune Therapy: 133 Randomized Trials Involving 31,000 Recurrences and 24,000 Deaths Among 75,000 Women,” The Lancet 339, 1–15, 71–85.Google Scholar
  6. Farewell, V. T. (1982), “The Use of Mixture Models for the Analysis of Survival Data with Long-term Survivors,” Biometrics, 38, 1041–1046.CrossRefGoogle Scholar
  7. Fisher B., Redmond C., Fisher E. R., et al. (1980), “The Contribution of Recent NSABP Clinical Trials of Primary Breast Cancer Therapy to an Understanding of Tumor Biology - an Overview of Findings,” Cancer, 46, 1009–1025CrossRefGoogle Scholar
  8. Goldman, A. (1984), “Survivorship Analysis When Cure is a Possibility: A Monte Carlo Study,” Statistics in Medicine, 3, 155–156.CrossRefGoogle Scholar
  9. Gordon, N. H. (1990a), “Application of the Theory of Finite Mixtures for the Estimation of ‘Cure’ Rates of Treated Cancer Patients,” Statistics in Medicine, 9, 397–407.CrossRefGoogle Scholar
  10. Gordon, N. H. (1990b), “Maximum Likelihood Estimation for Mixtures of Two Gompertz Distributions when Censoring Occurs,” Commun. Statist.-Simula., 19 (2), 733–747.MATHCrossRefGoogle Scholar
  11. Gordon, N. H., Crowe, J. P., Brumberg, D. J, Berger, N. A. (1992), “Socioeconomic Factors and Race in Breast Cancer Recurrence and Survival,” American Journal of Epidemiology, 135, 609–618.Google Scholar
  12. Greenwood, M. (1926), “A report on the Natural Duration of Cancer, ” Reports on Public Health and Medical Subjects, 33, 1–26.Google Scholar
  13. Haybittle, J. L. (1983), “Is Breast Cancer Ever Cured?,” Reviews on Endocrine-Related Cancer, 14, 13–18.Google Scholar
  14. Hubay, C. A., Gordon, N. H., et al. (1985), “Eight-year Follow-up of Adjuvant Therapy for Stage II Breast Cancer,” World Journal of Surgery, 9, 738–749.CrossRefGoogle Scholar
  15. Kuk, A. Y. and Chen, C. H. (1992), “A Mixture Model combining Logistic Regression with Proportional Hazards Regression,” Biometrika, 79, 531–541.MATHCrossRefGoogle Scholar
  16. Pearson, O. H., Hubay C. A., Gordon, N. H., et al. (1989), “Endocrine Versus Endocrine Plus 5-drug Chemotherapy in Postmenopausal Women with Stage II, Estrogen Receptor Positive Disease,” Cancer, 64, 1819–1823.CrossRefGoogle Scholar
  17. U. S. Department of Health and Human Services, Public Health Service, National Center for Health Statistics. Vital Statistics of the United States 1980, Volume II-Mortality, art A.Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 1996

Authors and Affiliations

  • Nahida H. Gordon
    • 1
  1. 1.Department of Epidemiology and BiostatisticsCase Western Reserve UniversityClevelandUSA

Personalised recommendations