Mathematical Modeling of Tumor Growth in Preclinical Mouse Models with Applications in Biomarker Discovery and Drug Mechanism Studies

Oncology drug efficacy is evaluated in mouse models by continuously monitoring tumor volumes, which can be mathematically described by growth kinetic models. Although past studies have investigated various growth models, their reliance on small datasets raises concerns about whether their findings are truly representative of tumor growth in diverse mouse models under different vehicle or drug treatments. In this study, we systematically evaluated six parametric models (exponential, exponential quadratic, monomolecular, logistic, Gompertz, and von Bertalanffy) and the semiparametric generalized additive model (GAM) on fitting tumor volume data from more than 30,000 mice in 930 experiments conducted in patient-derived xenografts, cell line-derived xenografts, and syngeneic models. We found that the exponential quadratic model is the best parametric model and can adequately model 87% studies, higher than other models including von Bertalanffy (82%) and Gompertz (80%) models; the latter is often considered the standard growth model. At the mouse group level, 7.5% of growth data could not be fit by any parametric model and were fitted by GAM. We show that endpoint gain integrated in time, a GAM-derived efficacy metric, is equivalent to exponential growth rate, a metric we previously proposed and conveniently calculated by simple algebra. Using five studies on paclitaxel, anti-PD1 antibody, cetuximab, irinotecan, and sorafenib, we showed that exponential and exponential quadratic models achieve similar performance in uncovering drug mechanism and biomarkers. We also compared exponential growth rate-based association analysis and exponential modeling approach in biomarker discovery and found that they complement each other. Modeling methods herein are implemented in an open-source R package freely available at https://github.com/hjzhou988/TuGroMix.Significance: We present a general strategy for mathematically modeling tumor growth in mouse models using data from 30,000 mice and show that modeling and nonmodeling approaches are complementary in biomarker discovery and drug mechanism studies.