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Keywords:

  • Angiogenesis and tumor growth;
  • Antiangiogenic drugs;
  • Gompertzian stochastic model;
  • Maximum likelihood estimation;
  • Stochastic differential equations

Summary. The problem of estimating parameters in the drift coefficient when a diffusion process is observed continuously requires some specific assumptions. In this paper, we consider a stochastic version of the Gompertzian model that describes in vivo tumor growth and its sensitivity to treatment with antiangiogenic drugs. An explicit likelihood function is obtained, and we discuss some properties of the maximum likelihood estimator for the intrinsic growth rate of the stochastic Gompertzian model. Furthermore, we show some simulation results on the behavior of the corresponding discrete estimator. Finally, an application is given to illustrate the estimate of the model parameters using real data.