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Using First-Passage Times to Analyze Tumor Growth Delay

Author

Listed:
  • Patricia Román-Román

    (Departamento de Estadística e Investigación Operativa, Facultad de Ciencias, Universidad de Granada, Avenida Fuente Nueva s/n, 18071 Granada, Spain
    Instituto de Matemáticas, Universidad de Granada, Calle Ventanilla 11, 18001 Granada, Spain
    These authors contributed equally to this work.)

  • Sergio Román-Román

    (Département de Recherche Translationnelle, Institut Curie, CEDEX 05, 75248 Paris, France
    These authors contributed equally to this work.)

  • Juan José Serrano-Pérez

    (Departamento de Estadística e Investigación Operativa, Facultad de Ciencias, Universidad de Granada, Avenida Fuente Nueva s/n, 18071 Granada, Spain
    These authors contributed equally to this work.)

  • Francisco Torres-Ruiz

    (Departamento de Estadística e Investigación Operativa, Facultad de Ciencias, Universidad de Granada, Avenida Fuente Nueva s/n, 18071 Granada, Spain
    Instituto de Matemáticas, Universidad de Granada, Calle Ventanilla 11, 18001 Granada, Spain
    These authors contributed equally to this work.)

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.

Suggested Citation

  • Patricia Román-Román & Sergio Román-Román & Juan José Serrano-Pérez & Francisco Torres-Ruiz, 2021. "Using First-Passage Times to Analyze Tumor Growth Delay," Mathematics, MDPI, vol. 9(6), pages 1-14, March.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:6:p:642-:d:519069
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    References listed on IDEAS

    as
    1. Patricia Román-Román & Juan José Serrano-Pérez & Francisco Torres-Ruiz, 2018. "Some Notes about Inference for the Lognormal Diffusion Process with Exogenous Factors," Mathematics, MDPI, vol. 6(5), pages 1-13, May.
    2. Román, P. & Serrano, J.J. & Torres, F., 2008. "First-passage-time location function: Application to determine first-passage-time densities in diffusion processes," Computational Statistics & Data Analysis, Elsevier, vol. 52(8), pages 4132-4146, April.
    Full references (including those not matched with items on IDEAS)

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