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


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.


Cure rate Time-dependent covariate Survival analysis 



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.


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© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.Service de BiostatistiqueInstitut CurieParisFrance

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