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Cancer interception during treatment: using growth kinetics to create a continuous variable for assessing disease

Mengxi Zhou1,2, Antonion T Fojo1,2, Lawrence H Schwartz3

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|October 22, 2025
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Summary

A simple mathematical model accurately describes tumor growth kinetics in most patients, with growth rate correlating inversely with overall survival. This finding offers a new marker for therapy efficacy across various cancers.

Keywords:
clinical trialcontinuous variableendpointsg rategrowth kineticsoverall survival

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Area of Science:

  • Oncology
  • Mathematical Modeling
  • Biostatistics

Background:

  • Eleven mathematical models of tumor growth were applied to extensive clinical trial data.
  • A biexponential model previously demonstrated efficacy in describing tumor growth kinetics and correlating with survival.
  • This study aimed to extend the analysis to more cancer types and evaluate alternative models for challenging datasets.

Purpose of the Study:

  • To validate and extend the application of a simple mathematical model for tumor growth kinetics.
  • To assess the utility of alternative models when the primary model fails.
  • To evaluate the correlation between tumor growth rate and overall survival across diverse cancer types.

Main Methods:

  • Analysis of data from 17,140 patients, including imaging and serum tumor markers.
  • Application of a biexponential model to determine tumor growth (g) and regression (d) rates.
  • Assessment of seven alternative models for datasets not fitting the biexponential model.
  • Examination of the association between continuous growth rate (g rate) and overall survival.

Main Results:

  • The biexponential model successfully described tumor growth and regression in 86% of patients.
  • An alternative model fit the data for an additional 7% of patients.
  • Tumor growth rate showed an inverse correlation with overall survival, consistent across different histologies.
  • Growth rates could be estimated even during net regression phases with sufficient data points.

Conclusions:

  • A simple mathematical model effectively quantifies tumor growth across various cancers.
  • The estimated tumor growth rate serves as a robust marker for therapy efficacy.
  • This approach allows for the estimation of treatment-resistant cancer cell subpopulations.