Quantitative oncology
Tumor Growth Rate
Turning Tumor Trajectories into Treatment Insight.
We develop tumor growth rate as a dynamic measure of treatment response—transforming serial measurements into clinically useful evidence.
Conceptual kinetic profileserial measures → response
ggrowth constant
dregression constant
01 / 05
The central idea
A scan is a snapshot. A trajectory tells a story.
Conventional response categories compress a patient's course into a few thresholds. Kinetic modeling instead uses the full longitudinal pattern—separating treatment-sensitive regression from treatment-resistant growth that can occur at the same time.
Model theory
Two processes. One observed trajectory.
The model treats change during therapy as the net result of treatment-sensitive regression and treatment-resistant growth occurring concurrently at constant exponential rates.
A tumor can become smaller even while a resistant component is growing, because regression initially dominates. As the sensitive component diminishes, resistant growth may become visible as a plateau and then regrowth. Serial measurements reveal this trajectory more fully than a single response category.
Tumor quantity may be radiographic burden or a serum marker such as PSA or CA 19-9. Measurements are normalized to baseline and modeled over time. The estimated g-rate describes exponential growth; the d-rate describes exponential regression or decay.
Lower gslower resistant growth
Higher dfaster initial regression
ln(2) / gtumor doubling time
General regression–growth model
f(t) = φe−dt + (1−φ)egt
- f(t)
- normalized tumor quantity at time t
- φ
- fraction exhibiting treatment-related decay
- d
- exponential regression constant
- g
- exponential growth constant
Broad applicability
One framework across tumors and therapies.
The model uses serial tumor quantity and time—not a specific histology or drug mechanism—so it is tumor-type and therapy agnostic by design.
Published tumor-growth kinetics research spans more than 10 cancer types, including prostate, renal cell, colorectal, pancreatic, neuroendocrine, breast, and non-small cell lung cancers. The framework has been applied across chemotherapy, hormonal and androgen-receptor–directed therapy, targeted agents, immunotherapy, anti-angiogenic therapy, PARP inhibition, antibody–drug conjugates, and somatostatin analogs.
The framework is broadly applicable; performance and clinical utility still require validation within each disease and treatment setting. See selected studies.Methodology
From measurements to a biologic rate.
A reproducible framework for estimating the direction and velocity of tumor change during therapy.
Figure 1 · Simulated regression–growth model
The observed trajectory is the sum of two concurrent processes.
Sum of growth and regressionTreatment-sensitive regression (d)Treatment-resistant growth (g)
Serial measurements
Assemble repeated tumor burden, PSA, or other quantitative markers with their observed time points.
Concurrent kinetics
Model simultaneous treatment-sensitive regression and treatment-resistant growth.
Estimate g and d
Calculate patient-level growth and decay constants, with doubling time as an interpretable derivative.
Connect outcomes
Test kinetic estimates against progression, survival, and clinically meaningful treatment benefit.
TUMGr evaluates growth-only, decay-only, combined growth–decay, and φ-weighted combined models. Among fits with significant parameters, the model minimizing Akaike Information Criterion (AIC) is selected.
Open-source software
Download tumgr
The tumgr R package estimates patient-level tumor growth (g), regression (d), and φ from serial tumor measurements. It returns individual and summary results and can plot observed and predicted tumor quantity over time.
R console
# Install from CRAN
install.packages("tumgr")
# Load and estimate rates
library(tumgr)
results <- gdrate(data, 0.10, TRUE)Current CRAN release · v0.0.4 · MIT License
Tumor kinetics bibliography
From foundational theory to FDA-scale validation.
An FDA analysis of the association of tumor growth rate, overall survival, and progression-free survival in metastatic NSCLC
Malinou JN, Fan J, Cheng J, Gong Y, Shen Y-L, Larkins E
FDA analysisCancer interception during treatment: using growth kinetics to create a continuous variable for assessing disease response
Zhou M, Wilkerson J, Bates SE, Fojo AT, et al.
Concept & validationCorrelation between tumor growth rate and survival in patients with metastatic breast cancer treated with trastuzumab deruxtecan
He P, Gambhire D, Zhou H, Fojo AT, Rixe O, et al.
Breast cancerAssessing olaparib efficacy in U.S. Veterans with metastatic prostate cancer utilizing a time-indifferent g-rate method
Leuva H, Bates SE, Fojo AT, et al.
Prostate cancerAssessment of PSA responses and changes in the rate of tumor growth with immune checkpoint inhibitors in U.S. Veterans
Leuva H, Bose A, Bates SE, et al.
Prostate cancerAnalysis of data from the PALOMA-3 trial confirms the efficacy of palbociclib and offers alternatives for novel assessment of clinical trials
Yeh C, Zhou M, Bapodra N, Fojo AT, Bates SE, et al.
Breast cancerTumor Growth Rate Informs Treatment Efficacy in Metastatic Pancreatic Adenocarcinoma
Yeh C, Zhou M, Bates SE, Fojo AT, et al.
Pancreatic cancerNovel Tumor Growth Rate Analysis in the Randomized CLARINET Study Establishes the Efficacy of Lanreotide Depot/Autogel
Dromain C, Loaiza-Bonilla A, Mirakhur B, Fojo AT, et al.
Neuroendocrine tumorsEnhanced Detection of Treatment Effects on Metastatic Colorectal Cancer with Volumetric CT Measurements for Tumor Burden Growth Rate Evaluation
Maitland ML, Wilkerson J, Zhou M, Fojo AT, et al.
Colorectal cancerA novel approach to assess real-world efficacy of cancer therapy in metastatic prostate cancer
Leuva H, Wilkerson J, Bates SE, Fojo AT, et al.
Real-world methodsEstimation of tumour regression and growth rates during treatment in patients with advanced prostate cancer
Wilkerson J, Abdallah K, Fojo AT, et al.
Prostate cancerContinuing a cancer treatment despite tumor growth may be valuable: sunitinib in renal cell carcinoma as example
Burotto M, Wilkerson J, Stein WD, Bates SE, Fojo AT, et al.
Renal cell carcinomaAnalyzing the pivotal trial that compared sunitinib and IFN-α in renal cell carcinoma using a method that assesses tumor regression and growth
Stein WD, Wilkerson J, Bates SE, Fojo AT, et al.
Renal cell carcinomaTumor regression and growth rates determined in five intramural NCI prostate cancer trials: the growth rate constant as an indicator of therapeutic efficacy
Stein WD, Gulley JL, Schlom J, Bates SE, Fojo AT, et al.
Prostate cancerOther paradigms: growth rate constants and tumor burden determined using computed tomography data correlate strongly with overall survival
Stein WD, Yang J, Bates SE, Fojo AT
Foundational methodsProgression-free survival is simply a measure of a drug’s effect on tumor growth while administered
Wilkerson J, Fojo AT
Endpoint theoryTumor growth rates derived from clinical-trial data correlate strongly with patient survival
Stein WD, Yang J, Bates SE, Fojo AT
Foundational methodsBevacizumab reduces the growth rate constants of renal carcinomas
Stein WD, Yang J, Bates SE, Fojo AT
Renal cell carcinomaOngoing work
Research portfolio
Four connected lines of inquiry move the method from measurement to decision-making.
01Clinical validation
Prospective validation in clinical trials
Testing whether early kinetic changes provide an actionable signal of treatment benefit before conventional progression endpoints mature.
02Methods development
Dynamic survival models
Comparing growth rate at three, six, and later months to determine when kinetic estimates become stable and prognostically useful.
03Real-world evidence
Therapy comparison at scale
Applying time-indifferent growth-rate methods to longitudinal clinical data, including irregularly spaced measurements.
04Translational research
Biology × kinetics
Linking tumor-growth phenotypes with genomic and circulating biomarkers to understand resistance and treatment sensitivity.
Next-generation tools
Built to translate.
Planned tools will make tumor kinetics more accessible to researchers, clinicians, and trainees.
In development01
Interactive growth-rate calculator
Enter serial measurements and dates to explore patient-level growth estimates and doubling time.
Planned02
Educational resource hub
Methods primers, worked examples, implementation notes, and teaching materials for quantitative oncology.
Contact us
Let’s study tumor kinetics together.
For research collaborations, data partnerships, or implementation questions, contact the Tumor Growth Rate Research Program.