In this prior report it was found, with 99% confidence, that the suspected 10 brain tumors, out of an estimated 750 total nurses working at Newton-Wellesley Hospital in Massachusetts, over the estimated course of 4 years to accrue cases, met statistical thresholds for a cancer cluster. A new apparent total of 17 tumors is suspected.
For this additional analysis, state-specific expected rates will be used for brain tumors. Here was the amount of total brain tumors (benign and malignant) expected in the state, according to the National Brain Tumor Society (NBTS):
And here is the population of Massachusetts (bottom-left):
After putting them together, you develop the expected rate of yearly brain tumor incidence per 100,000 population in the state of Massachusetts (cell B27 at bottom-left):
[click image to enlarge]
In the middle set with yellow highlights, three scenarios are covered: an accrual time for brain tumors that was either 2 years long, 3 years long, or 4 years long. The expectation on the rate for the whole period rises as you lengthen the observation window. Even at the longest window (4 years) the observed rate is at least 11x expected.
The 99% lower bound on the observed rate was 11 times higher than the 99% upper bound of the expected rate. The attempt to compute the probability of witnessing 17 events in either of the 3 time periods exceeded the software’s ability to compute. In other words, the baseline chance was so low that the probability did not even compute.
Reference
[expected yearly total brain tumors (malignant + benign) in Massachusetts] — https://braintumor.org/wp-content/uploads/2022/06/MA-NBTS_State.Factsheet.2022-final.pdf