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Inference on an heteroscedastic Gompertz tumor growth model.

G Albano1, V Giorno2, P Román-Román3

  • 1Dipartimento di Studi Politici e Sociali, Università di Salerno, Italy.

Mathematical Biosciences
|July 27, 2020
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Summary

This study introduces a new Gompertz diffusion model to analyze tumor growth dynamics. The model effectively captures the impact of anti-cancer therapies on tumor progression and validates its efficacy with real-world data.

Keywords:
Anti-proliferative and cell death-induced therapiesBootstrap testsInference in diffusion processesModified Gompertz diffusion processTumor growth

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Area of Science:

  • Mathematical Biology
  • Biophysics
  • Cancer Research

Background:

  • Tumor growth dynamics are complex and influenced by various factors.
  • Existing models may not fully capture the effects of anti-cancer therapies.
  • Understanding therapy-induced changes in tumor progression is crucial for effective treatment.

Purpose of the Study:

  • To develop a non-homogeneous Gompertz diffusion model for describing tumor dynamics under therapeutic interventions.
  • To incorporate time-dependent exogenous factors influencing infinitesimal moments and variance.
  • To propose an estimation procedure and hypothesis testing framework for model inference.

Main Methods:

  • Utilizing a non-homogeneous Gompertz diffusion process with time-dependent exogenous factors.
  • Implementing an estimation procedure with control and treated groups.
  • Employing concatenated hypothesis tests to assess the significance of time-dependent functions.
  • Conducting simulations to evaluate procedural efficiency and validate hypothesis testing.

Main Results:

  • The proposed model successfully describes tumor dynamics influenced by anti-proliferative and cell death-inducing therapies.
  • The estimation procedure effectively infers model parameters and time-dependent terms.
  • Hypothesis tests confirm the necessity of including time-dependent functions in specific scenarios.
  • Simulations demonstrate the efficiency of the proposed methods.

Conclusions:

  • The developed Gompertz diffusion model provides a robust framework for analyzing tumor growth under therapy.
  • The estimation and hypothesis testing procedures are effective for model validation and parameter inference.
  • The model and methods are applicable to real-world cancer data, offering insights into therapeutic effects.