Three endpoints of in vivo tumour radiobiology and their statistical estimation
Open accessAbstract
PURPOSE: To review the existing endpoints of tumour growth delay assays in experimental radiobiology with an emphasis on their efficient estimation for statistically significant identification of the treatment effect. To mathematically define doubling time (DT), tumour-growth delay (TGD) and cancer-cell surviving fraction (SF) in vivo using exponential growth and regrowth models with tumour volume measurements obtained from animal experiments. MATERIALS AND METHODS: A statistical model-based approach is used to define and efficiently estimate the three endpoints of tumour therapy in experimental cancer research. RESULTS: The log scale is advocated for plotting the tumour volume data and the respective analysis. Therefore, the geometric mean should be used to display the mean tumour volume data, and the group comparison should be a t-test for the log volume to comply with the Gaussian-distribution assumption. The relationship between cancer-cell SF, TGD and rate of growth is rigorously established. The widespread formula for cell kill is corrected; it has been rigorously shown that TGD is the difference between DTs. The software for the tumour growth delay analysis based on the mixed modeling approach with a complete set of instructions and example can be found on the author's webpage. CONCLUSIONS: The existing practice for TGD data analysis from animal experiments suffers from imprecision and large standard errors that yield low power and statistically insignificant treatment effect. This practice should be replaced with a model-based statistical analysis on the log scale.
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Integrity signals
Registry
Cites
Statistics
Claims the paper makes
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
The combination of palbociclib and cetuximab was proposed as a potential strategy to overcome cetuximab resistance by targeting cyclin D1 deregulation.
“The combination of the CDK4/6 inhibitor palbociclib and the EGFR inhibitor cetuximab was proposed as a potential strategy to overcome cetuximab resistance by targeting cyclin D1 deregulation (28).”
From Statistical Assessment of Drug Synergy from <i>In Vivo</i> Combination Studies Using Mouse Tumor Models (2023) · cites this paper as [28]
The Introduction and Discussion describe statistical estimation of tumour-treatment endpoints, while the photodynamic radiotherapy example concerns a mouse prostate-tumour model. Searches for palbociclib, cetuximab resistance, and cyclin D1 found no passage addressing the proposed combination or its rationale in our copy. (LLM, conf=0.78)
Experimental — accuracy not yet measured
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
Cites
Laird, A. K. (1964) · British Journal of Cancer · doi:10.1038/bjc.1964.55 · Cited by 880 · see citing works
Lord, B. I. (1978) · British Journal of Cancer · doi:10.1038/bjc.1978.97 · Cited by 669 · see citing works
Демиденко, Е. Ю. (2004) · Wiley series in probability and statistics · doi:10.1002/0471728438 · Cited by 491 · see citing works
Experimental antitumor activity of taxotere (RP 56976, NSC 628503), a taxol analogue.
Bissery, M.-C., Guénard, D., Guéritte, F., & Lavelle, F. (1991) · PubMed · Cited by 481 · see citing works
Predicting the course of Gompertzian growth
Norton, L., Simon, R. M., Brereton, H. D., & Bogdén, A. E. (1976) · Nature · doi:10.1038/264542a0 · Cited by 308 · see citing works
Differential Equations and Mathematical Biology
Jones, D. S., Plank, M. J., & Sleeman, B. D. (2009) · Chapman & Hall/CRC eBooks · doi:10.1201/9781420083583 · Cited by 237 · see citing works
Growth and Diffusion Phenomena
Banks, R. B. (1994) · Texts in applied mathematics · doi:10.1007/978-3-662-03052-3 · Cited by 234 · see citing works
Human Tumor Xenograft Models in NCI Drug Development
Plowman, J., Dykes, D. J., Hollingshead, M. G., Simpson‐Herren, L., & Alley, M. C. (1997) · Humana Press eBooks · doi:10.1007/978-1-4615-8152-9_6 · Cited by 221 · see citing works
The gross response of an experimental tumour to single doses of x-rays.
Thomlinson, R. H., & Craddock, E. A. (1967) · British Journal of Cancer · doi:10.1038/bjc.1967.10 · Cited by 170 · see citing works
Rodent tumor models in experimental cancer therapy
van der Kogel, A. J. (1988) · Radiotherapy and Oncology · doi:10.1016/0167-8140(88)90271-x · Cited by 167 · see citing works
Differential Equations and Mathematical Biology
Jones, D. S., & Sleeman, B. D. (2003) · Chapman & Hall/CRC eBooks · doi:10.4324/9780203009314 · Cited by 92 · see citing works
Rodent tumor models in experimental cancer therapy
Kallman, R. F. (1987) · Cited by 90 · see citing works
Statistical analysis of in vivo tumor growth experiments.
Heitjan, D. F., Manni, A., & Santen, R. J. (1993) · PubMed · Cited by 82 · see citing works
Pretreatment photosensitizer dosimetry reduces variation in tumor response
Zhou, X. R., Pogue, B. W., Chen, B., Demidenko, E., Joshi, R. P., Hoopes, J. P., & Hasan, T. G. (2006) · International Journal of Radiation Oncology*Biology*Physics · doi:10.1016/j.ijrobp.2005.11.019 · Cited by 82 · see citing works
Self-citationOzono, S. (2004) · Japanese Journal of Clinical Oncology · doi:10.1093/jjco/hyh011 · Cited by 75 · see citing works
Quantitation and Gompertzian analysis of tumor growth
Rygaard, K., & Spang‐Thomsen, M. (1997) · Breast Cancer Research and Treatment · doi:10.1023/a:1005906900231 · Cited by 70 · see citing works
Radiobiological Basis for Cancer Therapy by Total or Half-Body Irradiation
Sakamoto, K. (2004) · Nonlinearity in Biology Toxicology Medicine · doi:10.1080/15401420490900254 · Cited by 58 · see citing works
Human Tumor Xenograft Models in NCI Drug Development
Alley, M. C., Hollingshead, M. G., Dykes, D. J., & Waud, W. R. (2004) · Humana Press eBooks · doi:10.1007/978-1-59259-739-0_7 · Cited by 48 · see citing works
Analysis of growth delay data: potential pitfalls.
Begg, A. C. (1980) · Europe PMC (PubMed Central) · Cited by 48 · see citing works
(1980) · Leukemia Research · doi:10.1016/0145-2126(80)90061-2 · Cited by 45 · see citing works
Statistical approaches to experimental design and data analysis of in vivo studies
Hanfelt, J. (1997) · Breast Cancer Research and Treatment · doi:10.1023/a:1005946614343 · Cited by 36 · see citing works
The Assessment of Tumour Response to Treatment
Demidenko, E. (2006) · Journal of the Royal Statistical Society Series C (Applied Statistics) · doi:10.1111/j.1467-9876.2006.00541.x · Cited by 32 · see citing works
Self-citationHou, H. G., Khan, N. I., Grinberg, O. Y., Yu, H., Grinberg, S. A., Lu, S., Demidenko, E., Steffen, R. P., & Swartz, H. M. (2007) · Radiation Research · doi:10.1667/rr0962.1 · Cited by 32 · see citing works
Self-citationTomimaru, Y., Noura, S., Ohue, M., Okami, J., Oda, K., Higashiyama, M., Yamada, T., Miyashiro, I., Ohigashi, H., Yano, M., et al. (2008) · Digestive Surgery · doi:10.1159/000140693 · Cited by 24 · see citing works
The Response of a Mouse Sarcoma to Single and Divided Doses of X-rays and Fast Neutrons
Denekamp, J. (1974) · British Journal of Cancer · doi:10.1038/bjc.1974.69 · Cited by 19 · see citing works
Growth Laws in Cancer: Implications for Radiotherapy
Castorina, P., Deisboeck, T. S., Gabriele, P., & Guiot, C. (2007) · Radiation Research · doi:10.1667/rr0787.1 · Cited by 18 · see citing works
Papadopoulou, M. V., Ji, M. H., Ji, X., Bloomer, W. D., & Hollingshead, M. G. (2002) · Cancer Chemotherapy and Pharmacology · doi:10.1007/s00280-002-0521-8 · Cited by 16 · see citing works
Endpoints for agents that slow tumor growth
Yu, R., & Holmgren, E. B. (2006) · Contemporary Clinical Trials · doi:10.1016/j.cct.2006.05.011 · Cited by 14 · see citing works
A generalized "tumor growth delay" assay for quantifying alterations of tumor regrowth patterns.
Bassukas, I. D. (1993) · PubMed · Cited by 3 · see citing works
Nobody needs "relative tumour sizes" to compare tumour growth curves.
Bassukas, I. D., & Hofmockel, G. (2001) · PubMed · Cited by 1 · see citing works
Flagged first, then by citations
1 of the 31 references couldn’t be matched to a known paper.
Research works printed but not linked: 1
- Hall EJ Radiobiology for the radiobiologist 2000 5th ed. Philadelphia Lippincott
Cited by
Sorted by citations
Preclinical mouse solid tumour models: status quo, challenges and perspectives
Gengenbacher, N., Singhal, M., & Augustin, H. G. (2017) · Nature Reviews Cancer · doi:10.1038/nrc.2017.92 · Cited by 332 · see citing works
Statistical determination of synergy based on Bliss definition of drugs independence
Demidenko, E., & Miller, T. W. (2019) · PLOS ONE · doi:10.1371/journal.pone.0224137 · Cited by 187 · see citing works
Self-citationRAD51 Is a Selective DNA Repair Target to Radiosensitize Glioma Stem Cells
King, H., Brend, T., Payne, H. L., Wright, A., Ward, T., Patel, K., Egnuni, T., Stead, L. F., Patel, A., Wurdak, H., et al. (2017) · Stem Cell Reports · doi:10.1016/j.stemcr.2016.12.005 · Cited by 121 · see citing works
Wei, D., Parsels, L. A., Karnak, D. M., Davis, M. A., Parsels, J. D., Marsh, A. C., Zhao, L., Maybaum, J., Lawrence, T. S., Sun, Y., et al. (2013) · Clinical Cancer Research · doi:10.1158/1078-0432.ccr-13-0788 · Cited by 100 · see citing works
Shee, K., Yang, W., Hinds, J. W., Hampsch, R. A., Varn, F. S., Traphagen, N. A., Patel, K., Cheng, C., Jenkins, N. P., Kettenbach, A. N., et al. (2018) · The Journal of Experimental Medicine · doi:10.1084/jem.20171818 · Cited by 74 · see citing works
Self-citationBöhlen, T. T., Germond, J., Petersson, K., Özşahin, M., Herrera, F. G., Bailat, C. J., Bochud, F. O., Bourhis, J., Moeckli, R., & Adrian, G. (2023) · International Journal of Radiation Oncology*Biology*Physics · doi:10.1016/j.ijrobp.2023.05.045 · Cited by 51 · see citing works
Leung, C. N., Canter, B. S., Rajon, D. A., Bäck, T. A., Fritton, J. C., Azzam, E. I., & Howell, R. W. (2019) · Journal of Nuclear Medicine · doi:10.2967/jnumed.119.227835 · Cited by 44 · see citing works
Hampsch, R. A., Shee, K., Bates, D. J. P., Lewis, L. D., Désiré, L., Leblond, B., Demidenko, E., Stefan, K., Huang, Y. H., & Miller, T. W. (2017) · Oncotarget · doi:10.18632/oncotarget.15586 · Cited by 40 · see citing works
Self-citationIntracellular Delivery System for Antibody–Peptide Drug Conjugates
Berguig, G. Y., Convertine, A. J., Frayo, S. L., Kern, H. B., Procko, E., Roy, D., Srinivasan, S., Margineantu, D. H., Booth, G. C., Palanca-Wessels, M. C., et al. (2015) · Molecular Therapy · doi:10.1038/mt.2015.22 · Cited by 37 · see citing works
Sagers, J. E., Beauchamp, R. L., Zhang, Y., Vasilijić, S., Wu, L., DeSouza, P., Seist, R., Zhou, W., Xu, L., Ramesh, V., et al. (2020) · Scientific Reports · doi:10.1038/s41598-020-60156-6 · Cited by 36 · see citing works
Role of Interleukin-6 in the Radiation Response of Liver Tumors
Chen, M., Hsieh, C., Chen, W., & Lai, C. (2012) · International Journal of Radiation Oncology*Biology*Physics · doi:10.1016/j.ijrobp.2012.07.2360 · Cited by 34 · see citing works
Yang, W., Hosford, S. R., Dillon, L. M., Shee, K., Liu, S. C., Bean, J. R., Salphati, L., Pang, J., Zhang, X., Nannini, M., et al. (2016) · Clinical Cancer Research · doi:10.1158/1078-0432.ccr-15-2276 · Cited by 33 · see citing works
Self-citationYang, W., Hosford, S. R., Traphagen, N. A., Shee, K., Demidenko, E., Liu, S., & Miller, T. W. (2017) · The FASEB Journal · doi:10.1096/fj.201700477r · Cited by 33 · see citing works
Self-citationMao, B., & Guo, S. (2023) · Cancer Research Communications · doi:10.1158/2767-9764.crc-23-0243 · Cited by 27 · see citing works
Hamity, M. V., White, S. R., Blum, C., Gibson-Corley, K. N., & Hammond, D. L. (2020) · Pain · doi:10.1097/j.pain.0000000000001924 · Cited by 24 · see citing works
Oberg, A. L., Heinzen, E. P., Hou, X., Hilli, M. M. A., Hurley, R. M., Hendrickson, A. E. W., Goergen, K. M., Larson, M. C., Becker, M. A., Eckel‐Passow, J. E., et al. (2021) · Scientific Reports · doi:10.1038/s41598-021-87470-x · Cited by 24 · see citing works
Design, analysis and reporting of tumor models
Shaw, R. A., Miller, S., Curwen, J., & Dymond, M. (2017) · Lab Animal · doi:10.1038/laban.1257 · Cited by 22 · see citing works
Picchini, U., & Forman, J. L. (2019) · Journal of the Royal Statistical Society Series C (Applied Statistics) · doi:10.1111/rssc.12347 · Cited by 20 · see citing works
Hou, H. G., Mupparaju, S. P., Lariviere, J. P., Hodge, S., Gui, J., Swartz, H. M., & Khan, N. I. (2013) · Radiation Research · doi:10.1667/rr2811.1 · Cited by 19 · see citing works
Fu, W. Y., CHIU, Y., Huang, S.-C., Huang, W., Hsu, F.-T., Lee, H. Y., Wang, T., & Keng, P. Y. (2024) · Biomacromolecules · doi:10.1021/acs.biomac.4c00298 · Cited by 17 · see citing works
Zhao, L., Feng, D., Neelon, B., & Buyse, M. E. (2015) · Statistics in Medicine · doi:10.1002/sim.6445 · Cited by 12 · see citing works
Brüning‐Richardson, A., Shaw, G. C., Tams, D. M., Brend, T., Sanganee, H. J., Barry, S. T., Hamm, G. R., Goodwin, R. J. A., Swales, J. G., King, H., et al. (2021) · Cancers · doi:10.3390/cancers13235939 · Cited by 11 · see citing works
Liatsou, I., Fu, Y., Li, Z., Hasan, M., Guo, X., Yu, J., Piccolo, J., Cartee, A., Wang, H., Du, Y., et al. (2023) · European Journal of Nuclear Medicine and Molecular Imaging · doi:10.1007/s00259-023-06528-2 · Cited by 10 · see citing works
Nath, K., NELSON, D. S., Putt, M. E., Leeper, D. B., Garman, B., Nathanson, K. L., & Glickson, J. D. (2016) · PLoS ONE · doi:10.1371/journal.pone.0157125 · Cited by 10 · see citing works
Duval, K. E. A., Tavakkoli, A. D., Kheirollah, A., Soderholm, H. E., Demidenko, E., Lines, J. L., Croteau, W., Zhang, S. C., Wagner, R. J., Aulwes, E. F., et al. (2023) · International Journal of Molecular Sciences · doi:10.3390/ijms241813742 · Cited by 9 · see citing works
Self-citationAssessment of Antitumor Activity for Tumor Xenograft Studies Using Exponential Growth Models
Wu, J. (2011) · Journal of Biopharmaceutical Statistics · doi:10.1080/10543406.2010.481802 · Cited by 9 · see citing works
Using First-Passage Times to Analyze Tumor Growth Delay
Román‐Román, P., Roman‐Roman, S., Serrano-Pérez, J. J., & Torres‐Ruiz, F. (2021) · Mathematics · doi:10.3390/math9060642 · Cited by 5 · see citing works
Duval, K. E. A., Petryk, J. D., Crary-Burney, M., Demidenko, E., Wagner, R. J., & Hoopes, P. J. (2020) · International Journal of Hyperthermia · doi:10.1080/02656736.2020.1802070 · Cited by 4 · see citing works
Self-citationBrložnik, M., Boc, N., Cemazar, M., Bošnjak, M., Savarin, M., Kejžar, N., Serša, G., Pavlin, D., & Kranjc, S. (2021) · Bioelectrochemistry · doi:10.1016/j.bioelechem.2021.107932 · Cited by 3 · see citing works
DiPRO1 distinctly reprograms muscle and mesenchymal cancer cells
Rich, J., Bennaroch, M., Notel, L., Patalakh, P., Alberola, J., Issa, F., Opolon, P., Bawa, O., Rondof, W., Marchais, A., et al. (2024) · EMBO Molecular Medicine · doi:10.1038/s44321-024-00097-z · Cited by 2 · see citing works
Subashi, E., Qi, Y. P., & Johnson, G. A. (2015) · Medical Physics · doi:10.1118/1.4917525 · Cited by 2 · see citing works
Moon, J. Y., Park, J. B., Lee, K. W., Park, D., Yoo, G. S., Choi, C., Park, S., Yu, J. I., Lim, D. H., Kim, J. E., et al. (2025) · International Journal of Radiation Biology · doi:10.1080/09553002.2024.2447509 · Cited by 1 · see citing works
Demidenko, E. (1987) · Wiley series in probability and statistics · doi:10.1002/9781118651537.refs
Self-citationRosenzweig, E., Axelrod, D. E., & Gordon, D. (2025) · PLoS ONE · doi:10.1371/journal.pone.0324141
Schmalenstroer, L., Chen, H., Rockne, R. C., & Farahpour, F. (2026) · Bulletin of Mathematical Biology · doi:10.1007/s11538-026-01740-1
Kisamore, C. O., Kisamore, C. A., Boyd, J. M., Owolabi, P. J., Kadri, D. B., Mizener, A. D., Pistilli, E. E., & Walker, W. H. (2026) · Brain Behavior & Immunity - Health · doi:10.1016/j.bbih.2026.101262
- Authors
- Demidenko, E.
- Affiliations
- Dartmouth College (US)
- Corresponding author
- Demidenko, Eugene
- ORCID
- Demidenko, Eugene
- Venue
- International Journal of Radiation Biology
- Publisher
- Informa UK Limited
- Published
- 2010-02
- Volume
- 86
- Issue
- 2
- Pages
- 164-173
- ISSN
- 0955-3002 (ISSN-L)
- 1362-3095
- PMC
- PMC2900851
- OpenAlex
- W2135761571
- Cited by
- 37
- References
- 31
- Citations by year
- 2026: 2 · 2025: 2 · 2024: 2 · 2023: 5 · 2021: 4 · 2020: 3 · 2019: 3 · 2018: 1 · 2017: 5 · 2016: 2 · 2015: 3 · 2013: 2 · 2012: 1
- FWCI
- 1.37
- Type
- journal article
- Language
- en
- Open access
- green
- www.ncbi.nlm.nih.gov
- Locations
- International Journal of Radiation Biology (publishedVersion)
- PubMed (publishedVersion)
- PubMed Central (acceptedVersion)
- Funders
- National Institutes of Health
- National Cancer Institute (R01CA130880, P30CA023108)
- Topics
- Physical Sciences › Mathematics › Modeling and Simulation › Mathematical Biology Tumor Growth
- Health Sciences › Medicine › Radiology, Nuclear Medicine and Imaging › Effects of Radiation Exposure
- Health Sciences › Medicine › Pulmonary and Respiratory Medicine › Radiation Therapy and Dosimetry
- Keywords
- tumour growth delay, tumor doubling time, surviving fraction, tumor regrowth, exponential growth model, geometric mean, mixed modeling, statistical power, tumor volume
- MeSH terms
- Animals, Cell Survival, Models, Biological, Neoplasms, Experimental, Photochemotherapy, Radiobiology, Models, Statistical, Endpoint Determination
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review