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THE MATHEMATICAL ANALYSIS OF
CANCER RISK IN A STATISTICS CLASS
Vera Hu-Hyneman and Alexander Atwood
SUNY Suffolk County Community College
JMM 2016- Seattle
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.
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
Variation in cancer risk among tissues can be explained by the number of
stem cell divisions.
Tomasetti C, 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
Cancer’s Random Assault
By DENISE GRADYJAN. 5, 2015
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.
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…….
Overview of Argument by Tomasetti and Vogelstein
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
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.
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.
Overview of Argument by Tomasetti and Vogelstein
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:
r2 = 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.
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.
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
Questions?
[email protected]
[email protected]
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
Jennifer Couzin-Frankel Science 2015;347:12
Published by AAAS