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Comment by psychometry | Hacker News Reader

As always, it's important to remember that even in the absence of environmental factors, the probability of a particular town of this size having cancer rates this high might be very low, but the probability of there existing such a town in the U.S. might actually be high. This is simply due to variance.

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Four one in a million events in 15k inhabitants. Yes in any ranked list of stochastic outcomes there must be a highest scorer and a lowest scorer, but in case of Wayland GA it's still off the charts. With these diseases for any given town in the US you'd expect 0 or 1, hardly ever 2, if independently distributed.

Your conclusion is probably correct, but you also need to know how many classes of events you looked at. The particular form of cancer wasn't set in advance, it arose out of the data, so you need to multiply the number of towns by the number of types "rare cancer".

There seem to be about 1500 towns in the US with populations between 10000 and 25000: https://www.statista.com/statistics/241695/number-of-us-citi...

There seem to be about 200 defined types of "rare cancer" (where rare is defined as affecting less than 1 in 100000 people[3]): https://www.macmillan.org.uk/information-and-support/audienc...

My programming is better than my math[1], so I brute forced it as a simulation. Using 2000 towns, each with a population of 10000, and testing for 200 different types of cancer with a prevalence of 1 in 100000, I got this distribution:

That is to say, in the single simulation I ran[2], with a higher prevalence of 1 in 100000 vs 1 in 1000000, but a lower population of 10000 rather than 15000, I found that 1 in 2000 towns had 4 incidences of one of the 200 types of cancer I considered. This proves nothing directly, and environment probably played a role in the town in the story, but it does imply to me that it's not absurd that a small town might have 4 incidences of a rare cancer merely by chance.

[1] What's the right way to calculate this mathematically?

[2] My slow Perl code took about 10 minutes to run while I was writing this, and I committed to showing the numbers generated regardless of what they came out as.

[3] Oops, reading more closely I now see that the linked article is distinguishing between "rare" and "very rare".

Probability of 1 town of 10^5 people having 4 people disease with 1 in 10^-6: (10^5 choose 4)x(10^-6)^4x(1-10^-6)^9996 ~= 3.77x10^-6

Assuming independence between diseases and towns (not a terrible assumption but definitely not true) we have:

2000x200x3.77x10^-6 ~= 1.5

Which agrees with your simulation [1].

[1] My slow brain and calculator took 2 minutes to calculate this ;)

EDIT: Changed asterisks to x to avoid formatting.

EDIT 2: Here are the numbers for all the cases you have:

0: 361934.8

1: 36913.8

2: 1809.5

3: 60.3

4: 1.5

Since you put in all the work! It's the binomial distribution [1]. What you've done is to simulate the distribution of a sum of binomial distributions.

Your point of there being more than two types of rare cancer and that any selection of outliers over all the types would give rise to the same sentiment is totally correct.

I did the quick mental calculation with one in a million. As you see in your simulation the difference between 1e-5 and 1e-6 makes all the difference here.

[1] https://en.m.wikipedia.org/wiki/Binomial_distribution

We know this must be a statistical artefact because of the way cancer arises in humans when they are exposed to a carcinogens. Take tobacco smoke for example, it does not cause just one type of cancer to rise in frequency (say lung cancer), but a whole range of cancers [0]. You just can’t expose people to a general carcinogen like “pollution” and end up with one kind of rare cancer. Cancer just doesn’t work this way.

0. https://en.wikipedia.org/wiki/Health_effects_of_tobacco

What I think you mean to say is that if these cancers were caused by environmental contamination, we would expect to see elevated levels of other cancers as well.

First, I'm not sure this is true for all forms of cancer and all types of carcinogens. While it's true that tobacco smoke contains a wide variety of carcinogens and causes a wide variety of cancers, it doesn't seem impossible that some particular chemical might cause an increase in rhabdomyosarcomas without producing a general increase. For example, I don't think that asbestos exposure leads to an across the board increase in all cancers, just an increase in lung cancer and mesothelioma. What makes you so sure that there cannot exist a more focused carcinogen that causes just rhabdomyosarcoma?

Second, you seem to be assuming that just because the article focuses on one particular type of cancer, that the town does not have elevated levels of other cancers. Do you have outside evidence that makes you so sure of this that you conclude that the increased rate of once type of cancer "must be a statistical artifact" rather than evidence of a greater underlying problem that merits further research?

I not only mean to say that, it is what I said.

Yes it is possible for some specific rare cancers to have some single specific cause (mesothelioma and asbestos are probably the best known example), but this is not what is seen with nearly all other carcinogens.

The reason is two fold:

1) Almost all carcinogens are not localised to a precise body location (asbestos is a rare example). Once inside a person the carcinogen is distributed everywhere. This is why exposure to tobacco smoke for example gives rise to cancers in distant locations to the lung.

2) Carcinogenic pollutants are almost never just a single chemical, but a wide range of compounds.

Cancer is not like infectious disease where you have one causative agent that gives rise to a distinct set of symptoms. The nature by which cancer arise (loss of cellular replication control), by its very nature rarely proceeds down the same path - expose one person to a specific carcinogen and they might get liver cancer and lung cancer in a different person.

Thanks. So you think that apart from very special cases like asbestos, any chemical cause would cause other cancers as well, and there is no reasonable chance that a particular chemical could cause only rhabdomyosarcoma. I'll defer to your expertise here.

I was partly confused by one of the links from the article[1], which says "These cancers are derived from similar cellular lineage; therefore, these sarcomas are closely related in cellular composition. It is biologically plausible that a common exposure exists." Is there a way in which this might make sense? Are they suggesting that it might be biologically contagious rather than chemically induced?

And the second question? When you conclude that the prevalence of this particular must be a statistical artifact rather than a reproducible effect, do you have reason to believe that there are not elevated levels of other cancers in the area? Or is this not actually necessary to show?

[1] https://www.facebook.com/notes/jason-c-spencer/response-to-w...

I don't think it is biologically plausible at all that a common chemical exposure exists. It is possible, just unlikely. It also doesn't match up with what we know about pollutant chemicals being a wide range of compounds, nor the broad range of cancers seen with other known pollutant chemicals.

I would be far more likely to believe that a large number of unrelated cancers in an area were caused by pollutant carcinogens, than a small number of rare cancers.

I don't know if there is an elevated rate of cancer in this area, but I assume not since it would be the first thing that anyone looking at this rare cancer cluster would look for.

Some quick Googling and bad math (let me know where I screw up):

36,000 people in Ware County, GA.

3 cases of RMS, 1 of Ewing's.

327,000,000 people in the US.

400-500 cases of RMS in the US per year.

Chance of a case: 0.0000015

Chance of 4 cases: 5.5e-24

...in Ware County: 2.0e-19

...in any Ware County-sized population: 1.8e-15 [edit; I'm an idiot] [think I was right the first time]

Bonus: number of cases in US based on Ware Cty: 36,000 (weird, eh?) or about 73× more common.

Wait, how can the chance of 4 cases in any population be lower than the chance of 4 cases in a specific population? That can't be right can it?

Yep, it can't.

"Variance" does not give people cancer. But pollution does. The nuance is lost in your comment, and what you might more accurately say is "statistics/variance predicts that there is a high probability that somewhere in the US there is a town that has enough pollution (or other cause) to create cancer rates this high. It happens to be Waycross, GA"

No, that's not what "statistics/variance predicts". What statistics predicts is that even if there was no pollution whatsoever in the entire country we would still see some towns with increased cancer rates.

That said, I didn't do the math and it's entirely possible that the rates in Waycross are way above what one might expect by chance.

Your original comment was still valuable though because it makes people consider another, and important angle. Someone will probably do the math and show that even after considering statistical variance, this is still an outlier, but I feel like I have a more complete view with your comment.

Genetics also gives people a chance. There is some probability that somewhere in the US there is a town that has enough people with cancer-prone genetics to create cancer rates this high.

they would be getting the same set of rare cancers

I think you are referring to the Law of Large numbers. "with a large enough number of samples, any outrageous thing is likely to be observed" https://en.wikipedia.org/wiki/Law_of_truly_large_numbers

> This is simply due to variance.

"This" == "a possibility", not "this" == "Waycross cancer rate". What matters is what the probabilities/frequencies are.

https://en.wikipedia.org/wiki/Multiple_comparisons_problem

http://cms.web.cern.ch/news/should-you-get-excited-your-data...

https://xkcd.com/882/

"The more inferences are made, the more likely erroneous inferences are to occur."

Whoa. :-)

Your logic has some flaws. Allow me to elucidate:

The probability of you randomly selecting a sample of people who happen to have a high rate of cancer is very low.

The probability of you EVENTUALLY selecting a sample of people who have a high rate of cancer after selecting many samples is actually very high.

The probability of you eventually selecting a sample of people who happen to have a high rate of cancer AND happen to live in the same town AND happen to have cancers that are classified as rare is very very low.

There is no doubt this is an anomaly by every logical measure and not a statistical quirk.

This is an example of where your gut notion of a cancer cluster actually trumps the statistical logic. While logic is always correct and the logic you were using was technically wrong, this is a good example of how your intuitive gut feeling of what a cluster is, trumps your logical mind. Don't ignore your gut feelings, don't ignore your intuitions. The logical part of the human mind is just as flawed as your intuitions and it can build an incorrect scaffold of compositions that support an incorrect conclusion.

When your logic collides with your intuitions, do not automatically assume that logic trumps all. Evaluate both.

Your reliance on "logic" and not statistical training (it appears you don't have much) has lead you astray. Read the other replies to my comment to understand why you haven't understood.

I read it and it appears to me you are still wrong. You are better served to explain to me explicitly why you think you are not wrong then for me to read your mind.

There are events that contain so much information that the probability of the event occurring due to entropy are basically impossible. The event fitting those 3 conditions I mentioned is one example.

Let me add one more conditional to the cancer-cluster event: Happening within the same time-frame.

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