Cancer Interception During Treatment: Using Growth Kinetics to Create a Continuous Variable for Assessing Disease Response

Abstract

Background: We applied 11 mathematical models of tumor growth to clinical trial data available from public and private sources. We have previously described the remarkable capacity for a simple biexponential model of tumor growth to fit thousands of datasets, and to correlate with overall survival. The goal of this study was to extend our analysis to additional tumor types and to evaluate whether alternate growth models could describe the time course of disease burden in the small subset of patients in whom the biexponential model failed. Methods: For this analysis, we obtained data for tumor burden from 17,140 patients with six different tumor types. Imaging data and serum levels of tumor markers were available for 3,346 and 13,794 patients, respectively. Data from patients were first analyzed using the biexponential model to determine rates of tumor growth (g) and regression (d); for those whose data could not be described by this model, fit of their data was assessed using seven alternative models. The model that minimized the Akaike Information Criterion was selected as the best fit. Using the model that best fit an individual patient's data, we estimated the rates of growth (g) and regression (d) of disease burden over time. The rates of tumor growth (g) were examined for association with a traditional endpoint (overall survival). Findings: For each model, the number of patient datasets that fit the model were obtained. As we have previously reported, data from most patients fit a simple model of exponential growth and exponential regression (86%). Data from another 7% of patients fit an alternative model, including 3% fitting to a model of constant or linear regression and exponential growth of tumor on the surface and 3% fitting to model of exponential decay on tumor surface with asymmetric growth. As previously reported, we found that growth rate correlates well with overall survival, remarkably even when data from various histologies are considered together. For patients with multiple timepoints of tumor measurement, the growth rate could often be estimated even during the phase when only net regression of tumor quantity could be discerned. Interpretation: The validation of a simple mathematical model across different cancers and its application to existing clinical data allowed estimation of the rate of growth of a treatment resistant subpopulation of cancer cells. The quantification of available clinical data using the growth rate of tumors in individual patients and its strong correlation with overall survival makes the growth rate an excellent marker of the efficacy of therapy specific to the individual patient.