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Relaxed Poisson cure rate models.

Josemar Rodrigues1, Gauss M Cordeiro2, Vicente G Cancho1

  • 1Department of Applied Mathematics and Statistics, Instituto de Ciências Matemáticas e de Computação, Universidade de São Paulo, São Carlos-SP, Brazil.

Biometrical Journal. Biometrische Zeitschrift
|December 22, 2015
PubMed
Summary
This summary is machine-generated.

This study introduces a flexible relaxed cure rate model using a fractional Poisson distribution. This new model extends the standard Poisson cure rate model, offering a competitive alternative with superdispersion capabilities.

Keywords:
Bayesian inferenceFractional Poisson distributionGeometric cure rate modelMittag-Leffler relaxation functionPoisson cure rate modelRelaxed Poisson cure rate model

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Area of Science:

  • Biostatistics
  • Mathematical Oncology
  • Pharmacometrics

Background:

  • Standard cure rate models in cancer research often assume a Poisson distribution for cell counts.
  • Existing models may lack flexibility in capturing complex biological processes, such as superdispersion.

Purpose of the Study:

  • To enhance the standard promotion cure rate model by incorporating a fractional Poisson distribution.
  • To develop a more flexible and less restrictive cure rate model for analyzing treatment outcomes.

Main Methods:

  • Utilizing a fractional Poisson distribution for modeling the number of lesions or altered cells.
  • Employing the Mittag-Leffler relaxation function to construct the new cure rate model.
  • Exploring mathematical properties of the relaxed Poisson density.

Main Results:

  • A novel relaxed cure rate model is derived, offering a compromise between promotion and geometric models.
  • The proposed model allows for superdispersion, outperforming standard Poisson models.
  • The model is presented as a competitor to negative-binomial cure rate models.

Conclusions:

  • The relaxed cure rate model provides a more flexible extension of the Poisson cure rate model.
  • This approach accommodates superdispersion and offers a valuable alternative for analyzing treatment efficacy.
  • The study includes simulation results and a Bayesian illustration for practical application.