1. THE MATHEMATICAL ANALYSIS OF CANCER RISK IN A STATISTICS CLASS Vera Hu-Hyneman and Alexander Atwood SUNY Suffolk County Community College JMM 2016- Seattle

2. In January of 2015, Tomasetti and Vogelstein published in Science Magazine a revolutionary, provocative and rigorous statistical analysis which strongly suggests that the accumulation of random mutations during division in healthy stem cells can explain two-thirds of cancers. Their mathematical analysis is a wonderful subject for exploration by students in an Introductory Statistics Class. Mathematics faculty will be able to directly use the information in our presentation to design a stimulating classroom activity about the risk for cancer. In particular, students will be able to see how linear regression can be used to understand the correlation between cancer risk in an organ and the number of cumulative stem cell divisions within that organ, and students will be able to understand how this correlation can lead to a quantitative understanding of some of the causes of cancer. Furthermore, this classroom activity can open the door to further discussion and debate about the many possible causes of cancer and the role that statistics can play in understanding cancer.

3. What is Cancer? -Uncontrolled Growth of Human Body Cells after successive mutations. -Cancer is not one disease, but many. -Many Possible Causes of Cancer: -Smoking (lung cancer) and other potent mutagenic carcinogens -Viruses (e.g. Hepatitis B and liver cancer, Human Papilloma Virus and cervical cancer) -Ionizing Radiation, Sunlight (basal cell carcinoma) -Inherited Genetic Variation. -Accumulated Random Mutations in the Division of Normal Stem Cells. -Unknown

4. Variation in cancer risk among tissues can be explained by the number of stem cell divisions. Tomasetti CTomasetti C, Vogelstein B.Vogelstein B Abstract Some tissue types give rise to human cancers millions of times more often than other tissue types. Although this has been recognized for more than a century, it has never been explained. Here, we show that the lifetime risk of cancers of many different types is strongly correlated (0.81) with the total number of divisions of the normal self-renewing cells maintaining that tissue's homeostasis. These results suggest that only a third of the variation in cancer risk among tissues is attributable to environmental factors or inherited predispositions. The majority is due to "bad luck," that is, random mutations arising during DNA replication in normal, noncancerous stem cells. This is important not only for understanding the disease but also for designing strategies to limit the mortality it causes. Science: 2 January 2015: 78-81

5. Cancer’s Random Assault By DENISE GRADYJAN. 5, 2015DENISE GRADY It may sound flippant to say that many cases of cancer are caused by bad luck, but that is what two scientists suggested in an article published last week in the journal Science. The bad luck comes in the form of random genetic mistakes, or mutations, that happen when healthy cells divide.cancerarticle published last week in the journal Science Random mutations may account for two-thirds of the risk of getting many types of cancer, leaving the usual suspects — heredity and environmental factors — to account for only one-third, say the authors, Cristian Tomasetti and Dr. Bert Vogelstein, of Johns Hopkins University School of Medicine. “We do think this is a fundamental mechanism, and this is the first time there’s been a measure of it,” said Dr. Tomasetti, an applied mathematician…….

6. Observations: 1.) Extreme Variation in Cancer Incidence Across Different Organs. Lifetime Risk: 6.9% for Lung 1.08% for Thyroid 0.003% for Pelvic Bone 0.00072% for Laryngeal Cartilage 2.) Only 5-10% of Cancers have a Heritable Component. 3.) Exposure to Mutagenic Carcinogens is important for some cancers but is not important for most cancers. 4.) As we age (and our cells keep dividing) our risk for cancer increases. 5.) A series of Mutations, starting with a normal cell, results in cancerous cells. (somatic mutation theory of cancer, verified by genome-wide analyses) Overview of Argument by Tomasetti and Vogelstein

7. Do this: 1.) Identify the number of stem cells within a particular organ. 2.) Calculate the total number of cell divisions that occur in a lifetime in those stem cells. 3.) Identify the lifetime risk of cancer associated with that particular organ. 4.) Plot the total number of stem cell divisions in the organ versus the lifetime risk of cancer for that organ. 5.) A log-log scatter plot results when 31 different organs are analyzed. Overview of Argument by Tomasetti and Vogelstein

8. The relationship between the number of stem cell divisions in the lifetime of a given tissue and the lifetime risk of cancer in that tissue.

9. What they found: 1.) A Correlation between the number of stem cell divisions and the lifetime risk of cancer in an organ. 2.) The Pearson Linear Correlation is 0.81 for this data. (r = 0.81) 3.) Coefficient of Determination: r 2 = 0.65 4.) Suggestion is that “65% of the difference in the cancer risk among different tissues can be explained by the total number of stem cell divisions in those tissues.” 5.) “The stochastic effects of DNA replication appear to be the major contributor to cancer in humans” This is revolutionary, profound, and very controversial! Note: Does not include Breast Cancer and Prostate Cancer. Overview of Argument by Tomasetti and Vogelstein

10. Why Look at this Analysis in a Statistics Class? -Analysis of Cancer is a “Real Life” problem. - Tomasetti and Vogelstein’s paper in Science is very accessible to students. -Even if you gloss over the technical details, the conclusions are understandable and possibly profound. -This analysis and the resulting discussion will raise more questions than it answers……..which is always good.

11. Stochastic (replicative) factors versus environmental and inherited factors: R-tumor versus D-tumor classification. Cristian Tomasetti, and Bert Vogelstein Science 2015;347:78-81 Published by AAAS

12. Questions? atwooda@sunysuffolk.edu huhynev@sunysuffolk.edu

13. The relationship between the number of stem cell divisions in the lifetime of a given tissue and the lifetime risk of cancer in that tissue. Cristian Tomasetti, and Bert Vogelstein Science 2015;347:78-81 Published by AAAS

14. Jennifer Couzin-Frankel Science 2015;347:12 Published by AAAS