Using First-Passage Times to Analyze Tumor Growth Delay Román Román, Patricia Román Román, Sergio Serrano Pérez, Juan José Torres Ruiz, Francisco De Asís Tumor growth Tumor growth delay measurements First-passage times Diffusion processes 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 2021-03-18T11:44:13Z 2021-03-18T11:44:13Z 2021-03-17 info:eu-repo/semantics/article Román-Román, P.; Román-Román, S.; Serrano-Pérez, J.J.; Torres-Ruiz, F. Using First-Passage Times to Analyze Tumor Growth Delay. Mathematics 2021, 9, 642. [https://doi.org/10.3390/math9060642] http://hdl.handle.net/10481/67323 10.3390/math9060642 eng http://creativecommons.org/licenses/by/3.0/es/ info:eu-repo/semantics/openAccess Atribución 3.0 España Mdpi