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 were left thinking, “that can’t be a coincidence.” As a Stanford University Ph.D. who studied statistics, 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 share a statistical point of view.
Let’s assume the null hypothesis that working at MHS had nothing to do with the odds, and see how likely are the observed results.
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.
The odds of getting exactly three “heads” out of 80 coin flips, when repeatedly flipping a weighed coin of known probability, is governed by the binomial distribution formula. Free online “Cumulative Binomial Calculators” help with the calculation. Plugging in 80 for the “number of trials,” three for the “number of successes” and 0.000129 for the “probability of success” you get 0.00000018. That is less than one in 5.5 million.
Getting one thyroid cancer diagnosis out of eighty people in a year would happen roughly one percent of the time (One 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 five percent or one percent. Getting two diagnoses drops the odds to one in over 18,000. Getting three or more drops the odds to one in over 5.5 million.
These findings demonstrate that there is a statistically significant “relationship” between spending your days at MHS and thyroid cancer. Hopefully the search for the “relationship” continues until it is identified and remedied.