My family asked me if they should be worried about external causes. Generally, a communities response to cluster cases can be rash, and so I'm inclined to downplay the problem. I really didn't know though, so I considered this simple model:

Approximately 400 people under the age of 20 get osteosarcoma each year, that gives 2000 cases over 5 years. There are roughly 80 million individuals under the age of 20 in the United States. Approximately 1700 students attend West Salem high school each year - so over 5 years approximately 4000 unique students go through West Salem High School.

I'm curious what the probability is for 5 or more cases of osteosarcoma to crop up at some school. I'll assume all schools can be binned into 4000 students, and that every person under the age of 20 is a student.

The probability of a student getting osteosarcoma is, p=P(O) = 2000/8 10

^{7}= .25 10

^{-4}.

The probability of n kids getting osteosarcoma at a school is f(n) = p

^{n}(1-p)

^{4000-n}(4000 choose n)

The probability of 4 or less kids getting osteosarcoma at a school is f(0) + f(1) + f(2) + f(3) + f(4).

The probability of 4 or less kids getting osteosarcoma for all schools is K=(f(0) + f(1) + f(2) + f(3) + f(4))

^{2*10^4}

Finally the probability of some school having 5 or more kids with osteosarcoma is 1 - K.

Putting this into a TI I calculate 1-K to be 0.002.

So the probability that this happens with no unusual causal factor is 0.002. Is my reasoning sensible, and is this number "small"? This event is definitely unusual, but doesn't seem impossible either. I'm curious what other more statistically minded folks might have to say.