Inference on an heteroscedastic Gompertz tumor growth model

Albano, Giuseppina; Giorno, Virginia; Román-Román, Patricia; Roman‐Roman, Sergio; Serrano-Pérez, Juan José; Torres-Ruiz, Francisco

doi:10.1016/j.mbs.2020.108428

Cited by 8 publications

(3 citation statements)

References 31 publications

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“…On the other hand, the fact that the Gompertz curve is an excellent model for the description of tumor growth has motivated the introduction of several diffusion processes associated with it (see, for example, Lo [19] and Ferrante [20]). On the basis of these processes, various modifications have subsequently been made with the goal of describing the evolution of tumor growth in the presence of therapeutic treatments (Albano et al [21][22][23]).…”

Section: Introductionmentioning

confidence: 99%

Hyperbolastic Models from a Stochastic Differential Equation Point of View

2021

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A joint and unified vision of stochastic diffusion models associated with the family of hyperbolastic curves is presented. The motivation behind this approach stems from the fact that all hyperbolastic curves verify a linear differential equation of the Malthusian type. By virtue of this, and by adding a multiplicative noise to said ordinary differential equation, a diffusion process may be associated with each curve whose mean function is said curve. The inference in the resulting processes is presented jointly, as well as the strategies developed to obtain the initial solutions necessary for the numerical resolution of the system of equations resulting from the application of the maximum likelihood method. The common perspective presented is especially useful for the implementation of the necessary procedures for fitting the models to real data. Some examples based on simulated data support the suitability of the development described in the present paper.

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Section: Introductionmentioning

confidence: 99%

Hyperbolastic Models from a Stochastic Differential Equation Point of View

2021

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“…Moreover, various efforts are direct to computational approaches (Di Nardo et al [18], Taillefumier and Magnasco [19], D'Onofrio and Pirozzi [20]) that also involve methods of statistical inferences (Albano et al [21], Albano and Giorno [22], Ramos-Ábalos et al [23]). Specifically, in Di Nardo et al [18] and Taillefumier and Magnasco [19] methods to construct first-passage-time probability density functions for Gauss-Markov processes through timedependent boundaries are proposed.…”

Section: Introductionmentioning

confidence: 99%

“…In D'Onofrio and Pirozzi [20], the problem of escape times from a region confined by two time-dependent boundaries is considered for a class of Gauss-Markov processes. Moreover, numerical procedures to infer the models based on time-inhomogeneous diffusion processes are proposed in Albano et al [21], Albano and Giorno [22], and Ramos-Ábalos et al [23].…”

Section: Introductionmentioning

confidence: 99%

On the Simulation of a Special Class of Time-Inhomogeneous Diffusion Processes

Giorno

Nobile

2021

Mathematics

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General methods to simulate probability density functions and first passage time densities are provided for time-inhomogeneous stochastic diffusion processes obtained via a composition of two Gauss–Markov processes conditioned on the same initial state. Many diffusion processes with time-dependent infinitesimal drift and infinitesimal variance are included in the considered class. For these processes, the transition probability density function is explicitly determined. Moreover, simulation procedures are applied to the diffusion processes obtained starting from Wiener and Ornstein–Uhlenbeck processes. Specific examples in which the infinitesimal moments include periodic functions are discussed.

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