Using First-Passage Times to Analyze Tumor Growth Delay

Patricia Román-Román, Sergio Román-Román, Juan José Serrano-Pérez and Francisco Torres-Ruiz
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Patricia Román-Román: Departamento de Estadística e Investigación Operativa, Facultad de Ciencias, Universidad de Granada, Avenida Fuente Nueva s/n, 18071 Granada, Spain
Sergio Román-Román: Département de Recherche Translationnelle, Institut Curie, CEDEX 05, 75248 Paris, France
Juan José Serrano-Pérez: Departamento de Estadística e Investigación Operativa, Facultad de Ciencias, Universidad de Granada, Avenida Fuente Nueva s/n, 18071 Granada, Spain
Francisco Torres-Ruiz: Departamento de Estadística e Investigación Operativa, Facultad de Ciencias, Universidad de Granada, Avenida Fuente Nueva s/n, 18071 Granada, Spain

Mathematics, 2021, vol. 9, issue 6, 1-14

Abstract: A central aspect of in vivo experiments with anticancer therapies is the comparison of the effect of different therapies, or doses of the same therapeutic agent, on tumor growth. One of the most popular clinical endpoints is tumor growth delay, which measures the effect of treatment on the time required for tumor volume to reach a specific value. This effect has been analyzed through a variety of statistical methods: conventional descriptive analysis, linear regression, Cox regression, etc. We propose a new approach based on stochastic modeling of tumor growth and the study of first-passage time variables. This approach allows us to prove that the time required for tumor volume to reach a specific value must be determined empirically as the average of the times required for the volume of individual tumors to reach said value instead of the time required for the average volume of the tumors to reach the value of interest. In addition, we define several measures in random environments to compare the time required for the tumor volume to multiply k times its initial volume in control, as well as treated groups, and the usefulness of these measures is illustrated by means of an application to real data.

Keywords: tumor growth; tumor growth delay measurements; first-passage times; diffusion processes (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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