3 ms·

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 o

by wjnc 7y ago

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.

nkurz 7y ago
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-cities-towns-villages-by-population-size/ 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/audience/rare-cancers/what-is-rare-cancer.html 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: 1: 36393 2: 1831 3: 63 4: 1 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".
- hervature 7y ago
  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
- danieltillett 7y ago
  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 https://en.wikipedia.org/wiki/Health_effects_of_tobacco
  - nkurz 7y ago
    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?
    - danieltillett 7y ago
      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.
- wjnc 7y ago
  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 https://en.m.wikipedia.org/wiki/Binomial_distribution

by wjnc 7y ago

nkurz 7y ago

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-cities-towns-villages-by-population-size/ 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/audience/rare-cancers/what-is-rare-cancer.html 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: 1: 36393 2: 1831 3: 63 4: 1 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".

hervature 7y ago
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
danieltillett 7y ago
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 https://en.wikipedia.org/wiki/Health_effects_of_tobacco
- nkurz 7y ago
  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?
  - danieltillett 7y ago
    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.
wjnc 7y ago
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 https://en.m.wikipedia.org/wiki/Binomial_distribution