Advertisement

A Latent Time Distribution Model for the Analysis of Tumor Recurrence Data: Application to the Role of Age in Breast Cancer

  • Yann De Rycke
  • Bernard AsselainEmail author
Chapter
  • 39 Downloads

Abstract

Many popular statistical methods for survival data analysis do not allow the possibility of cure or at least of considerable lengthening of survival for breast cancer patients. Increasingly prolonged follow-up provides new data about the post-treatment outcome, revealing situations with the possibility of high cure rates for early stage breast cancer patients. Then the exclusive use of “classical” statistical models of survival analysis can lead to conclusions not completely reflecting clinical reality. It therefore appears preferable to perform additional analyses based on survival models with cured fraction to study long-term survival data, especially in oncology. This approach allows statistical methods to be adapted to the biological process of tumor growth and dissemination. After presenting the Cox model with time-dependent covariates and the Yakovlev parametric model, we study the prognostic role of age in young women (≤50 years) in Institut Curie breast cancer data. Age is a prognostic factor within all three models, but the interpretation is not the same. With the Cox model the younger women have a bad prognosis (HR = 1.86) comparing to the older one. But the HR does not verify the proportional hazard hypothesis. So the Cox model with time-dependent covariates gives a better interpretation: the age-effect decreases significantly with time. With the Yakovlev model we find that the decreasing age-effect can be viewed through the proportion of cured patients. More, there is an effect of age on survival (palliative effect) and also on the cure rates (curative effect). So the cure rate models demonstrate their utility in analyzing long-term survival data.

Keywords

Cure rate Time-dependent covariate Survival analysis 

Notes

Acknowledgements

This work is dedicated to Andreï Yakovlev, our friend, who inspired us this way of thinking, and constructing statistical models in relation with the biological knowledge.

We thank Alexia Savignoni for her careful reading and suggestions. The authors also thank the referees and the editor for their constructive comments that allowed us to improve the quality of this paper.

References

  1. 1.
    Appelbaum, F. R., Dahlberg, S., Thomas, E. D., Buckner, C., Cheever, M. A., Clift, R. A., et al. (1984). Bone marrow transplantation or chemotherapy after remission induction for adults with acute nonlymphoblastic leukemia. Annals of Internal Medicine, 101, 581.CrossRefGoogle Scholar
  2. 2.
    Asselain, B., Rycke, Y. D., Savignon, A., & Mould, R. F. (2003). Parametric modelling to predict survival time to first recurrence for breast cancer. Physics in Medicine and Biology, 48, L31.CrossRefGoogle Scholar
  3. 3.
    Broet, P., Rycke, Y., Tubert-Bitter, P., Lellouch, J., Asselain, B., & Moreau, T. (2001). A semiparametric approach for the two-sample comparison of survival times with long-term survivors. Biometrics, 57, 844–852.MathSciNetCrossRefGoogle Scholar
  4. 4.
    Cox, D. R. (1972). Regression models and life tables (with discussion). Journal of the Royal Statistical Society, Series B: Statistical Methodology, 34, 187–220.zbMATHGoogle Scholar
  5. 5.
    Frankel, P., & Longmate, J. (2002). Parametric models for accelerated and long-term survival: A comment on proportional hazards. Statistics in Medicine, 21, 3279–3289.CrossRefGoogle Scholar
  6. 6.
    Hanin, L. G., Miller, A., Zorin, A., & Yakovlev, A. Y. (2006). The University of Rochester model of breast cancer detection and survival. Journal of the National Cancer Institute Monographs, 2006, 66–78.CrossRefGoogle Scholar
  7. 7.
    Ibrahim, J. G., Chen, M. H., & Sinha, D. (2001). Bayesian semiparametric models for survival data with a cure fraction. Biometrics, 57, 383–388.MathSciNetCrossRefGoogle Scholar
  8. 8.
    Nardi, A., & Schemper, M. (2003). Comparing Cox and parametric models in clinical studies. Statistics in Medicine, 22, 3597–3610.CrossRefGoogle Scholar
  9. 9.
    Paoletti, X., & Asselain, B. (2010). Survival analysis in clinical trials: Old tools or new techniques. Surgical Oncology, 19, 55–58.CrossRefGoogle Scholar
  10. 10.
    Tsodikov, A. D., Asselain, B., Fourque, A., Hoang, T., & Yakovlev, A. Y. (1995). Discrete strategies of cancer post-treatment surveillance. Estimation and optimization problems. Biometrics, 51, 437–447.CrossRefGoogle Scholar
  11. 11.
    Wolmark, N., Yothers, G., O’Connell, M., Sharif, S., Atkins, J., Seay, T., et al. (2009). A phase III trial comparing mFOLFOX6 to mFOLFOX6 plus bevacizumab in stage II or III carcinoma of the colon: Results of NSABP Protocol C-08. Journal of Clinical Oncology, 27, 6s.Google Scholar
  12. 12.
    Yakovlev, A. Y., Asselain, B., Bardou, V., Fourquet, A., Hoang, T., Rochefediere, A., et al. (1993). A simple stochastic model of tumor recurrence and its application to data on premenopausal breast cancer. Biometrie et analyse de donnees spatio-temporelles, 12, 66–82.Google Scholar

Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.Service de BiostatistiqueInstitut CurieParisFrance

Personalised recommendations