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A new long-term survival model with dispersion induced by discrete frailty

  • Vicente G. Cancho
  • Márcia A. C. MaceraEmail author
  • Adriano K. Suzuki
  • Francisco Louzada
  • Katherine E. C. Zavaleta
Article
  • 32 Downloads

Abstract

Frailty models are generally used to model heterogeneity between the individuals. The distribution of the frailty variable is often assumed to be continuous. However, there are situations where a discretely-distributed frailty may be appropriate. In this paper, we propose extending the proportional hazards frailty models to allow a discrete distribution for the frailty variable. Having zero frailty can be interpreted as being immune or cured (long-term survivors). Thus, we develop a new survival model induced by discrete frailty with zero-inflated power series distribution, which can account for overdispersion. A numerical study is carried out under the scenario that the baseline distribution follows an exponential distribution, however this assumption can be easily relaxed and some other distributions can be considered. Moreover, this proposal allows for a more realistic description of the non-risk individuals, since individuals cured due to intrinsic factors (immune) are modeled by a deterministic fraction of zero-risk while those cured due to an intervention are modeled by a random fraction. Inference is developed by the maximum likelihood method for the estimation of the model parameters. A simulation study is performed in order to evaluate the performance of the proposed inferential method. Finally, the proposed model is applied to a data set on malignant cutaneous melanoma to illustrate the methodology.

Keywords

Discrete frailty Zero-inflated power series distribution Cure rate models Overdispersion Maximum likelihood estimation 

Notes

Acknowledgements

This work was partially funded by the Brazilian institutions FAPESP, CAPES and CNPq.

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of StatisticsUniversidade de São PauloSão CarlosBrazil
  2. 2.Department of StatisticsUniversidade Federal de São CarlosSão CarlosBrazil

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