Thyroid Cancer at MHS: What Are the Odds?

With the news that three teachers at Malibu High School were diagnosed with Thyroid Cancer within a six-month period last year, many of us in the community were alarmed and left thinking, “that can’t be a coincidence.” But at least one expert seems to suggest that it isn’t that uncommon.

In the March 20, 2014 LA Weekly article “Cancer Scare at Malibu High Turns Messy,” Marcia Brose, Director of the Thyroid Cancer Therapeutics Program at the University of Pennsylvania, states: “It’s not surprising that you might discover some people who have had thyroid cancer, and they might know somebody [who has it] nearby. Unless there’s really clear radiation risks in the area, I don’t think that there’s any evidence for thinking that their thyroid cancer is caused by an environmental toxin, particularly.”

That statement did not sit well with me. We are talking about threecases, not one, and in a very limited sample group of teachers working at MHS. Characterizing that outcome as “not surprising” did not appear to fit the facts of the situation.

As a Stanford University Ph.D. who studied Statistics, as an aspiring Cancer Epidemiology Researcher, and as the father of two students who will be spending their days on the MHS campus, I feel compelled to make some sense of this for myself, and for the community, from a probability and statistical point of view.

The question I want to answer is: How likely is it that there would be three Thyroid Cancer diagnoses within a calendar year from a group of approximately eighty people (an estimate of the employees working full time in the MHS buildings), while assuming that the probability of being diagnosed is the same as it is for the U.S. population in general? That is, assume that working at MHS had nothing to do with the odds, or in the language of statistics, was “statistically independent,” and let’s see what the odds are.

The definitive source for Cancer diagnosis rates in the U.S. is the Surveillance, Epidemiology, and End Results Program (“SEER”) database of the National Cancer Institute. According to SEER, The number of new cases of Thyroid Cancer is 12.9 per 100,000 men and women per year. We will use the number 0.000129 as the probability that an adult is diagnosed with thyroid cancer in a particular year.

A common problem in statistics is figuring out the odds of a particular outcome, such as getting exactly 3 “heads” out of 80 coin flips, when repeatedly flipping a weighed coin of known probability. Rather than bore you with the foundational work needed in the explanation, let me just jump to the solution: the Binomial Distribution Formula, which you can google yourself for background. It shows the odds of getting an exact number of “success” results, in our case 3 out of 80 repeated trails, where the probability of an individual “success” is know to be 0.000129. It is ironic to call getting a diagnosis of thyroid cancer a “success,” but this is the language of the many free online “Cumulative Binomial Calculators” which are available. The term “cumulative” refers to expressing the results as “3 or more” - rather than “exactly 3.”

Plugging in 80 for the “number of trials,” 3 for the “number of successes,” and 0.000129 for the “probability of success” you get: 0.00000018. That is less than 1 in 5.5 million. To put it into perspective, this is less likely than flipping a fair coin 22 times and getting heads each and every time.

Getting one Thyroid Cancer diagnosis out of eighty people in a year would happen roughly one percent of the time (1 in 97). This alone could be used to argue that the null hypothesis of “no relationship” is false, as the rejection level is usually set at either 5 percent or 1 percent. Getting 2 diagnoses drops the odds to 1 in over 18,000. Getting 3 or more drops the odds to 1 in over 5,500,000. To me, there is no question about whether the results are “surprising.” They are. There is no question about whether the results are “statistically significant.” They are.

These findings demonstrate that there is a statistically significant “relationship” between spending your days at MHS and Thyroid Cancer. We all need adequate answers about the nature of that relationship, and some sense that it has been adequately addressed. In their July 27, 2014 release, SMMUSD indicates that PCB levels are safe now, and were safe prior to testing. If true, all that tells me is that we haven’t found what we are looking for yet. Hopefully the search for the “relationship” continues until it is identified and remedied.

Patrick Witting