Exponential Quadratic Modeling Emerges as the Best Fit Across 30,000 Mice
Tumor volume curves in preclinical oncology are often treated as if one equation can tame them all. In a new analysis spanning more than 30,000 mice and 930 experiments, that assumption did not hold, but one model came closer than the others: the exponential quadratic form. It fit tumor growth data better than the long-favored Gompertz curve and adequately modeled 87% of studies, compared with 82% for von Bertalanffy and 80% for Gompertz. The scale of the dataset matters here. Much of the earlier modeling literature relied on relatively small collections of mice, a setting where an apparently elegant equation can look stronger than it truly is once it is asked to perform across patient-derived xenografts, cell line-derived xenografts, and syngeneic systems.
The practical consequence is simple and important: preclinical tumor kinetics are not interchangeable across model systems or treatment conditions. Drug exposure, host biology, and tumor origin all leave fingerprints on the growth curve, and any model that hopes to support efficacy readouts has to accommodate that heterogeneity without forcing every dataset into the same mold.
Why One Growth Curve Failed to Rule Them All
The analysis compared six parametric models — exponential, exponential quadratic, monomolecular, logistic, Gompertz, and von Bertalanffy — alongside a semiparametric generalized additive model, or GAM. At the mouse group level, 7.5% of growth data could not be fit by any parametric model and required GAM instead. That small fraction is not a statistical footnote. It marks the boundary where rigid assumptions stop working and flexible smoothing becomes necessary, especially in datasets shaped by treatment response, delayed acceleration, and irregular biological behavior.
The broader message is mechanistic as much as mathematical. A tumor under drug pressure may not grow along a neat trajectory; it may flatten, rebound, or change slope as resistant subclones expand or drug-sensitive cells are suppressed. The exponential quadratic model appears to capture more of that complexity while still remaining tractable enough for routine use. Compared with the standard Gompertz approach, which has long served as the default in preclinical growth modeling, the new results argue for a more careful fit-to-data standard rather than inherited preference.
Endpoint Gain Integrated in Time Tracks a Simpler Growth Rate Metric
One of the more useful findings is methodological rather than purely comparative. Endpoint gain integrated in time, a GAM-derived efficacy metric, was equivalent to the exponential growth rate metric previously proposed by the investigators and calculable by straightforward algebra. In other words, a flexible nonparametric output and a simple parametric summary arrived at the same biological signal. That kind of convergence matters in preclinical pharmacology, where an efficacy metric has to be not only accurate but also practical enough to move across studies, compounds, and tumor models without collapsing under computational complexity.
The equivalence also strengthens confidence in the earlier growth-rate framework. If two different analytic routes produce the same underlying estimate, then the biological signal is less likely to be a model artifact. For drug development groups trying to compare vehicle and treatment arms across experiments, the appeal is obvious: a compact summary can capture the same direction of effect as a more elaborate smoothing method, while remaining easier to calculate and apply at scale.
Drug Mechanism and Biomarker Signals Survive Across Modeling Frameworks
To test whether the choice of growth model changes downstream biological interpretation, the study examined five treatment examples: paclitaxel, anti-PD1 antibody, cetuximab, irinotecan, and sorafenib. Exponential and exponential quadratic models performed similarly in uncovering drug mechanism and biomarkers. This is reassuring, but only within limits. The main point is not that the models are identical; it is that, in these examples, the biological conclusions were stable enough to survive differences in curve shape.
A second comparison looked at biomarker discovery using exponential growth rate-based association analysis and an exponential modeling approach. The two methods complemented each other rather than replacing one another. In practice, that means some signals may emerge more cleanly from a direct growth-rate association, while others surface only after explicit modeling of the tumor trajectory. For translational oncology, this duality is valuable. Biomarkers linked to treatment response can be missed if investigators rely on a single analytic lens, especially when the signal is subtle or dispersed across heterogeneous mouse cohorts.
Heterogeneous Mouse Cohorts Demand Flexible, Open Methods
The data set included patient-derived xenografts, cell line-derived xenografts, and syngeneic models, three experimental systems that differ in how faithfully they represent human cancer biology and immune context. A model that works well in one may underperform in another. The authors therefore built a general strategy for tumor growth modeling that is intended to handle mixed preclinical settings rather than a narrow experimental slice.
The release of an open-source R package, TuGroMix, is a practical extension of that goal. Open tools matter in this setting because preclinical modeling is often only as reproducible as the code behind it. When tumor growth analysis becomes part of biomarker discovery and mechanism work, hidden implementation details can distort comparisons across laboratories. A shared package lowers that risk and makes it easier for other groups to test whether the same model ranking holds in their own cohorts.
What the Dataset Suggests About Preclinical Oncology Readouts
The most useful lesson from this work is not that one formula replaces all others. It is that preclinical tumor growth analysis should be matched to the data rather than to tradition. The exponential quadratic model performed best overall, but a nontrivial share of mouse groups still required GAM, and biomarker work benefited from using modeling and nonmodeling strategies together. In a field where tumor volume is often the central readout for drug efficacy, those distinctions influence how an experiment is interpreted long before a manuscript is written.
There is also a clear translational constraint. These results are grounded in preclinical mouse models, not patients, and the mathematical fit of a tumor curve does not guarantee direct clinical portability. Even so, better modeling in animals can improve which hypotheses move forward, which biomarkers survive replication, and which mechanisms are pursued in later-stage studies. The remaining challenge is not whether tumor growth can be modeled, but how consistently the chosen method preserves biological meaning across model systems, treatments, and experimental noise.