International Journal of Mathematical, Engineering and Management Sciences

ISSN: 2455-7749

Age Dependent Analysis of Colon Cancer Tumours Using Mathematical and Statistical Modelling

Vidya Bhargavi Machavaram
GITAM Institute of Science, GITAM (deemed to be) University, Visakhapatnam, Andhra Pradesh, India.

Sireesha Veeramachaneni
GITAM Institute of Science, GITAM (deemed to be) University, Visakhapatnam, Andhra Pradesh, India.


Received on September 18, 2020
Accepted on March 07, 2021


Colon cancer is the third most commonly diagnosed cancer and the second leading cause of cancer death in men and women combined in the United States. In this work, we performed mathematical and statistical modelling of Tumour sizes as a function of age for four different races. Mathematically, based on the behaviour of the data for each race, we partitioned ages of subjects into several intervals. The mathematical function that characterizes the size of the Tumour as a function of age was determined for each age interval. Statistically, using quantile regression, we designed models that are more robust at specific quantiles using Tumour size and age as dependent and predictor variables.

Keywords- Colon cancer, Line plots, Quantile regression, Statistical modelling, Mathematical modelling.


Machavaram, V. B., & Veeramachaneni, S. (2021). Age Dependent Analysis of Colon Cancer Tumours Using Mathematical and Statistical Modelling. International Journal of Mathematical, Engineering and Management Sciences, 6(3), 944-960.

Conflict of Interest

The authors confirm that there is no potential conflict of interest to publish the paper in the journal.


We would like to thank Stanley College of Engineering-Hyderabad, GITAM (deemed to be) University-Visakhapatnam, our families and colleagues for their unconditional support in completing this research article.


Altrock, P.M., Liu, L.L., & Michor, F. (2015). The mathematics of cancer: integrating quantitative models. Nature Reviews Cancer, 15(12), 730-745.

Anderson, A.R., & Quaranta, V. (2008). Integrative mathematical oncology. Nature Reviews Cancer, 8(3), 227-234.

Augustus, G.J., & Ellis, N.A. (2018). Colorectal cancer disparity in African Americans: risk factors and carcinogenic mechanisms. The American Journal of Pathology, 188(2), 291-303.

Bergin, R.J., Emery, J., Bollard, R.C., Falborg, A.Z., Jensen, H., Weller, D., Menon, U., Vedsted, P., Thomas, R.J., Whitfield, K., & White, V. (2018). Rural-urban disparities in time to diagnosis and treatment for colorectal and breast cancer. Cancer Epidemiology and Prevention Biomarkers, 27(9), 1036-1046.

Bhargavi, M.V., Mudunuru, V.R., & Veeramachaneni, S. (2020). Colon cancer stage classification using decision trees. In: Raju, K.S., Senkerik, R., Lanka, S.P., Rajagopal, V. (eds.) Data Engineering and Communication Technology. Springer, Singapore, pp. 599-609.

Bonsu, N.O. (2013). Age dependent analysis and modelling of prostate cancer data. Tampa: University of South Florida Scholar Commons.

Byrne, H.M. (2010). Dissecting cancer through mathematics: from the cell to the animal model. Nature Reviews Cancer, 10(3), 221-230.

Daley, D.J., & Jones, D.V. (2003). An introduction to the theory of point processes: elementary theory of point processes. Springer.

DePillis, L.G., Savage, H., & Radunskaya, A.E. (2013). Mathematical model of colorectal cancer with monoclonal antibody treatments. arXiv preprint arXiv:1312.3023.

Favoriti, P., Carbone, G., Greco, M., Pirozzi, F., Pirozzi, R.E.M. & Corcione, F. (2016) Worldwide burden of colorectal cancer: a review. Updates in Surgery, 68(1), 7-11.

Few, S., & Edge, P. (2008). Line graphs and irregular intervals: an incompatible partnership. Visual Business Intelligence Newsletter, 12(11), 16-29.

Hong, H.G., Christiani, D.C., & Li, Y. (2019). Quantile regression for survival data in modern cancer research: expanding statistical tools for precision medicine. Precision Clinical Medicine, 2(2), 90-99.

Howlader, N., Noone, A.M., Krapcho, M. (2016). SEER cancer statistics review. Bethesda, MD: National Cancer Institute, 1975-2013.

Huang, Q., Zhang, H., Chen, J., & He, M. (2017). Quantile regression models and their applications: a review. Journal of Biometrics & Biostatistics, 8(3), 2155-6180.

Jacobs, D., Zhu, R., Luo, J., Grisotti, G., Heller, D.R., Kurbatov, V., Johnson, C.H., Zhang, Y., & Khan, S.A. (2018). Defining early-onset colon and rectal cancers. Frontiers in Oncology, 8, 504.

Keim, D.A. (2002). Information visualization and visual data mining. IEEE Transactions on Visualization and Computer Graphics, 8(1), 1-8.

Koenker, R., & Bassett, Jr.G. (1978). Regression quantiles. Journal of the Econometric Society, 46(1), 33-50.

Koenker, R., & Kevin, F.H. (2001). Quantile regression. Journal of Economic Perspectives, 15(4) 143-156.

Le Cook, B., & Manning, W.G. (2013). Thinking beyond the mean: a practical guide for using quantile regression methods for health services research. Shanghai Archives of Psychiatry, 25(1), 55-59. doi:10.3969/j.issn.1002-0829.2013.01.011.

Olsen, C.S., Clark, A.E., Thomas, A.M., & Cook, L.J. (2012). Comparing least‐squares and quantile regression approaches to analyzing median hospital charges. Academic Emergency Medicine, 19(7), 866-875.

Pages, F., Berger, A., Camus, M., Sanchez-Cabo, F., Costes, A., Molidor, R., Mlecnik, B., Kirilovsky, A., Nilsson, M., Damotte, D., Meatchi, T., Bruneval, P., Cugnenc, P., Trajanoski, Z., Fridman, W., Galon, J. (2005). Effector memory T cells, early metastasis, and survival in colorectal cancer. New England Journal of Medicine, 353(25), 2654-2666.

Paterson, C., Clevers, H., & Bozic, I. (2020). Mathematical model of colorectal cancer initiation. In Proceedings of the National Academy of Sciences. Cold Spring Harbor Laboratory, bioRxiv.

Proctor, B.D., Semega, J.L., Kollar, M.A. (2016). Income and poverty in the United States: 2016. U.S. Government Printing Office, Washington. DC: U.S. Census Bureau.

Ratnapradipa, K.L., Lian, M., Jeffe, D.B., Davidson, N.O., Eberth, J.M., Pruitt, S.L., & Schootman, M. (2017). Patient, hospital, and geographic disparities in laparoscopic surgery use among surveillance, epidemiology, and end results–medicare patients with colon cancer. Diseases of the Colon & Rectum, 60(9), 905-913.

Yang, X., Narisetty, N.N., & He, X. (2018). A new approach to censored quantile regression estimation. Journal of Computational and Graphical Statistics, 27(2), 417-425. doi: 10.1080/10618600.2017.1385469.

Xu, Y., Wu, M., Zhang, Q., & Ma, S. (2019). Robust identification of gene-environment interactions for prognosis using a quantile partial correlation approach. Genomics, 111(5), 1115-1123.

Privacy Policy| Terms & Conditions