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Estimating a non-homogeneous Gompertz process with jumps as model of tumor dynamics

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  • Giorno, Virginia
  • Román-Román, Patricia
  • Spina, Serena
  • Torres-Ruiz, Francisco

Abstract

A non-homogeneous stochastic model based on a Gompertz-type diffusion process with jumps is proposed to describe the evolution of a solid tumor subject to an intermittent therapeutic program. Each therapeutic application, represented by a jump in the process, instantly reduces the tumor size to a fixed value and, simultaneously, increases the growth rate of the model to represent the toxicity of the therapy. This effect is described by introducing a time-dependent function in the drift of the process. The resulting model is a combination of several non-homogeneous diffusion processes characterized by different drifts, whose transition probability density function and main characteristics are studied. The study of the model is performed by distinguishing whether the therapeutic instances are fixed in advance or guided by a strategy based on the mean of the first-passage-time through a control threshold. Simulation studies are carried out for different choices of the parameters and time-dependent functions involved.

Suggested Citation

  • Giorno, Virginia & Román-Román, Patricia & Spina, Serena & Torres-Ruiz, Francisco, 2017. "Estimating a non-homogeneous Gompertz process with jumps as model of tumor dynamics," Computational Statistics & Data Analysis, Elsevier, vol. 107(C), pages 18-31.
    • Handle: RePEc:eee:csdana:v:107:y:2017:i:c:p:18-31
    DOI: 10.1016/j.csda.2016.10.005
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    References listed on IDEAS

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    1. L. Ferrante & S. Bompadre & L. Possati & L. Leone, 2000. "Parameter Estimation in a Gompertzian Stochastic Model for Tumor Growth," Biometrics, The International Biometric Society, vol. 56(4), pages 1076-1081, December.
    2. Albano, Giuseppina & Giorno, Virginia & Román-Román, Patricia & Torres-Ruiz, Francisco, 2012. "Inference on a stochastic two-compartment model in tumor growth," Computational Statistics & Data Analysis, Elsevier, vol. 56(6), pages 1723-1736.
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    Cited by:

    1. Albano, G. & Giorno, V., 2020. "Inferring time non-homogeneous Ornstein Uhlenbeck type stochastic process," Computational Statistics & Data Analysis, Elsevier, vol. 150(C).

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