@misc{10481/67323,
year = {2021},
month = {3},
url = {http://hdl.handle.net/10481/67323},
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},
publisher = {Mdpi},
keywords = {Tumor growth},
keywords = {Tumor growth delay measurements},
keywords = {First-passage times},
keywords = {Diffusion processes},
title = {Using First-Passage Times to Analyze Tumor Growth Delay},
doi = {10.3390/math9060642},
author = {Román Román, Patricia and Román Román, Sergio and Serrano Pérez, Juan José and Torres Ruiz, Francisco De Asís},
}