Cluster Headache Frequency Follows a Long-Tail Distribution

[Warning: Disturbing content ahead. Why talk about it? This is an ethically very serious topic and it deserves more attention. But please beware that thinking about this might be bad for one’s mental health.]

One of the key insights that shows why Effective Altruism is so important is that the positive effect on the world that results from donating to various charities follows a long-tail distribution:

health interventionsCost-effectiveness of health interventions as found in the Disease Controls Priorities Project 2. See “The moral imperative towards cost-effectiveness in global health” by Toby Ord for more explanation. [Taken from: The world’s biggest problems and why they’re not what first comes to mind]

It is for this, among other, reasons why focusing on the best interventions really pays off. Where else can we expect long-tails to appear?

In Get-Out-Of-Hell-Free Necklace we discussed how introducing a new metric into the Effective Altruist ecosystem could shed light on neglected cost-effective interventions. We presented the Hell-Index:

A country’s Hell-Index could be defined as the yearly total of people-seconds in pain and suffering that are at or above 20 in the McGill Pain Index (or equivalent)*. This index captures the intuition that intense suffering can be in some ways qualitatively different and more serious than lesser suffering in a way that isn’t really captured by a linear pain scale.

In a future article we will discuss how the quality of suffering as a function of different medical and psychological conditions very likely follows a long-tail distribution. That is, some conditions such as Cluster Headaches (which affect about 1 in 1000 people worldwide) produce pain that is orders of magnitude worse than the pain experienced in other kinds of medical conditions, such as migraines (which are themselves already described as orders of magnitude worse than tension headaches). In other words, a 0-10 pain-scale is better thought of as a logarithmic compression of the true levels of pain rather than a linear scale. So concentrating on the worst conditions could really pay off for reducing suffering in bulk amounts.

Now: the long-tailed nature of suffering may extend beyond the quality of suffering, and show up also in its quantity. That is, the frequency with which people experience episodes of intense suffering, even among those who experience the same kind of suffering, is unlikely to be normally distributed.

Intuitively, one may think that how much suffering people endure on a given year follows a normal distribution. This intuition says that if the median number of hell-seconds people endure in a year is, say, 1,000, then people who are at the 90% percentile of hell-seconds experienced per year will be experiencing something like 1,500 or at most 2,000. If suffering follows a long-tail distribution, in reality the 90% percentile might be experiencing something more akin to 10,000 hell-seconds per year, the 99% percentile something akin to 100,000, and the 99.9% something akin to 1,000,000. If true, such a heavy skew of the distribution would suggest that we should concentrate our energies on addressing the problems of the people who are unlucky to be on the upper ranges, rather than be overly concerned with “the typical person”*.

Unfortunately, I come to share the bad news that suffering probably follows a very long-tail distribution:

It is generally acknowledged that Cluster Headaches are some of the most painful experiences that people endure. Having a single Cluster Headache, lasting anywhere between 15 minutes to 4 hours, is already an ethically unacceptable situation that should never happen to begin with. It is disheartening to know that 1 in 1,000 people experience such extreme pain. But the truth of the matter is yet much worse than we intuitively think…

We recently analyzed a survey** of Cluster Headache patients that was conducted with the intention of determining the reasons why sufferers do or do not use psychedelics to relieve their pain. As it turns out, LSD, psilocybin, and DMT all get rid of Cluster Headaches in a majority of sufferers. Given the safety profile of these agents, it is insane to think that there are millions of people suffering needlessly from this condition who could be nearly-instantly cured with something as simple as growing and eating some magic mushrooms.

We will get back to this in more depth in later articles, but for the time being what we want to highlight is the responses to the question “About how many cluster headaches do you get in a typical year?”.

After cleaning the data***, we end up with 270 participants. We then ranked the values from smallest to largest, and visualize them:


Honestly I am a bit suspicious of the very top numbers (I do not know how you can fit 25,000 Cluster Headaches in a year, so perhaps the participant interpreted the question as “lifetime number of Cluster Headaches”). So, just to be safe, we cut the top 20 highest numbers and visualize the bottom 250 values:


This is clearly a long-tail distribution. And since many people online do claim to have 3 or more Cluster Headaches a day, I am inclined to believe this curve. To zoom in on some parts of the distribution, here are some additional histograms that focus on the lower percentiles:

If we take the logarithm of the number of yearly Cluster Headaches, the distribution looks remarkably normal:


Natural log of the responses to the question “About how many cluster headaches do you get in a typical year?”

Using a Shapiro-Wilk normalcy test does not rule out a Gaussian distribution (p >0.05). Although this in no way shows that that the distribution is log-normal (which would require more specialized statistical analysis), it is at least suggestive of it.

I should also point out that the distribution is really close to the 80/20 Pareto principle – we see that the top 20% of the participants contain about 83% of the CH incidents per year. Below you will find the percent of the total number of incidents accounted for by the bottom x% of the respondents:

  1. The bottom 10% accounts for .06% of incidents
  2. The bottom 20% accounts for 0.36% of incidents
  3. The bottom 30% accounts for .95% of incidents
  4. The bottom 40% accounts for 1.82% of incidents
  5. The bottom 50% accounts for 3.17% of incidents
  6. The bottom 60% accounts for 5.54% of incidents
  7. The bottom 70% accounts for 9.56% of incidents
  8. The bottom 80% accounts for 17% of incidents
  9. The bottom 90% accounts for 30% of incidents
  10. The bottom 95% accounts for 43% of incidents

Below we also include the number of yearly Cluster Headaches experiences at different percentiles:

  1. 10% percentile experiences 5 CH/year
  2. 20% percentile experiences 17 CH/year
  3. 30% percentile experiences 30 CH/year
  4. 40% percentile experiences 45 CH/year
  5. 50% percentile experiences 70 CH/year
  6. 60% percentile experiences 105 CH/year
  7. 70% percentile experiences 200 CH/year
  8. 80% percentile experiences 365 CH/year
  9. 90% percentile experiences 730 CH/year
  10. 95% percentile experiences 1095 CH/year
  11. 98% percentile experiences 2190 CH/year

I believe that this information is crucial to consider when assessing cost-effective interventions to help people who endure intense suffering.

Here are some additional results from the survey.


The following graphs are about the beliefs and attitudes of Cluster Headache sufferers who do not use tryptamines (LSD, psilocybin, DMT, etc.) to treat their condition:


I think it is fair to say that the survey shows that one of the biggest barriers preventing CH patients from using tryptamines to treat their condition is simply the difficulty of acquiring them. Since a number of interviews we’ve conducted have shown that even sub-hallucinogenic doses of DMT can abort cluster headaches (writeup coming soon), more education could easily address the barrier of being concerned about hallucinogenic side effects. The social stigma seems like a minor problem, and the legal implications (the hardest to change, perhaps), are a big concern to about half of the participants (ratings of 4 or 5/5). Hence the importance of passing new laws allowing people with this condition to use them without repercussions.

Do CH sufferers who do not use tryptamines think they would work?


And do they work? Here is what the CH sufferers who do use them say:




Tryptamines used

If we interpret a 2 or 3 in the 0 to 5 scale as an equivalent to a “maybe”, and a 4 or 5 as a “yes” to the question “do they work?” we see a big difference between non-users beliefs in their effectiveness and their reported effectiveness by users. 24% of people who use tryptamines to treat their CHs report that “They have completely eliminated the cluster headaches” and in total 68% mark it as either a 4 or a 5 in the scale (which we can interpret as “working” even if not “completely eliminating them”). This is compared to only 30% of non-users who believe the tryptamines would work. This large discrepancy also suggests that outreach and education could help sufferers give this approach a try.

Finally, we also looked at whether the users and non-users had different number of incidents per year (reasoning that perhaps those who experience more incidents would be more desperate to try legally and socially risky treatments). We notices that there is a very slight difference in the mean (and mean-log) for the number of CH incidents a year between the 20% of sufferers who treat their CHs with tryptamines and those who don’t. I won’t report the difference in the mean because the skew of the distribution makes such a metric deceptive, but the log-mean of yearly incidents of tryptamine users is 4.73 whereas for all the rest it is 4.10 (which reaches statistical significance of p < 0.05 based on a t-test). That said, we don’t think this is a very practically relevant difference. The distributions look roughly the same:


The similarity between these two distributions also suggests that there is a long way to go to make sure that those who are the worse off get prompt access to tryptamines.

The End.

See also, which is an organization that aims to make psychedelics legally available to people who suffer from this condition. Please consider donating to them to help this very important cause. Also consider donating to MAPS which is championing the use of psychedelics for mental health applications. Finally, consider also donating to organizations that care and strategize about how to reduce intense suffering, such as: QRI, FRIOPIS, and The Neuroethics Foundation.

*There are instrumental considerations here – if experiencing more than, say, 5,000 hell-seconds in a year is very likely to make you depressed and ineffective, then it might pay-off to also spend resources on keeping as many people as possible below that level. In particular, to be an effective Effective Altruist it pays off not to be heavily depressed and nihilistic.

**Thanks to Harlan Stewart for taking the initiative to conduct this survey. He advertised it on the Facebook groups and subreddits of Cluster Headache sufferers and got 371 responses.

***Some people provided numerical answers, which we used directly. Some other people provided ranges, in which case we used the middle point between the values provided (e.g. “200 to 300” was coded as “250”). Some people provided lower bounds, in which case we simply used such lower bound (e.g. “500+” was coded as “500”). We discarded the data of people who didn’t provide an answer in any of those formats – which left 270 participants. A more strict analysis that uses *only* the numerical responses results in the same observations listed above (e.g. the distribution is equally long-tailed and it appears to be log-normal).

[Cross-posted in Effective Altruism Forum]


  1. Pingback: Every Qualia Computing Article Ever | Qualia Computing
  2. Pingback: Treating Cluster Headaches Using N,N-DMT and Other Tryptamines | Qualia Computing
  3. Anthony Garner · August 3

    Anecdotally I can tell you that my use of psilocybyn has greatly reduced the number of very severe headaches I have suffered from for many years.

Leave a Reply