title: Estimating and determining the effect of a therapy on tumor dynamics by means of a modified Gompertz diffusion process.
abstract: A modified Gompertz diffusion process is considered to model tumor dynamics. The infinitesimal mean of this process includes non-homogeneous terms describing the effect of therapy treatments able to modify the natural growth rate of the process. Specifically, therapies with an effect on cell growth and/or cell death are assumed to modify the birth and death parameters of the process. This paper proposes a methodology to estimate the time-dependent functions representing the effect of a therapy when one of the functions is known or can be previously estimated. This is the case of therapies that are jointly applied, when experimental data are available from either an untreated control group or from groups treated with single and combined therapies. Moreover, this procedure allows us to establish the nature (or, at least, the prevalent effect) of a single therapy in vivo. To accomplish this, we suggest a criterion based on the Kullback-Leibler divergence (or relative entropy). Some simulation studies are performed and an application to real data is presented.
authors.affiliation: Dip. di Scienze Economiche e Statistiche, Università di Salerno, Italy. Electronic address: pialbano@unisa.it.
authors.forename: Giuseppina
authors.initials: G
authors.lastname: Albano
authors.affiliation: Dip. di Studi e Ricerche Aziendali (Management and Information Technology), Università di Salerno, Italy.
authors.forename: Virginia
authors.initials: V
authors.lastname: Giorno
authors.affiliation: Dpto. de Estadística e Investigación Operativa, Universidad de Granada, Spain.
authors.forename: Patricia
authors.initials: P
authors.lastname: Román-Román
authors.affiliation: Dép. de Recherche Translationnelle, Institut Curie, France.
authors.forename: Sergio
authors.initials: S
authors.lastname: Román-Román
authors.affiliation: Dpto. de Estadística e Investigación Operativa, Universidad de Granada, Spain.
authors.forename: Francisco
authors.initials: F
authors.lastname: Torres-Ruiz
mesh_terms: D000465:Algorithms; D000818:Animals; D000970:Antineoplastic Agents / Q000737:chemistry; D017209:Apoptosis; D016923:Cell Death; D049109:Cell Proliferation / Q000187:drug effects; D003198:Computer Simulation; D006801:Humans; D008545:Melanoma / Q000473:pathology* / Q000628:therapy; D051379:Mice; D008954:Models, Biological; D009368:Neoplasm Transplantation; D009369:Neoplasms / Q000473:pathology*; D015203:Reproducibility of Results; D014604:Uveal Neoplasms / Q000473:pathology* / Q000628:therapy
chemical_list: D000970:Antineoplastic Agents
keywords: Kullback–Leibler divergence; Prevalent effect; Resistor average distance; Therapy effect estimation; Tumor growth