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:


Cost-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 rea­son 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:

(Bins of 1, re­sponses be­tween 1 and 10 CHs per year.)

(Bins of 1, re­sponses be­tween 1 and 100 CHs per year.)

(Bins of 10, re­sponses be­tween 1 and 1000 CHs per year.)

(Bins of 100, re­sponses be­tween 1 and 2000 CHs per year.)

(Bins of 10, re­sponses be­tween 1 and 5000 CHs per year.)

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

(Above: 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 8020 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:

(Difficulty get­ting. 0 – Ex­tremely easy to ac­quire, 5 – Nearly im­pos­si­ble to ac­quire)

(Le­gal risk. 0 – Not con­cerned at all, 5 – Ex­tremely con­cerned)

(Side effects. 0 – Not con­cerned at all, 5 – Ex­tremely con­cerned)

(So­cial stigma. 0 – Not con­cerned at all, 5 – Ex­tremely con­cerned)

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 55). 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:


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 no­ticed 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 https://​​cluster­busters.org/​​, 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, FRI, OPIS, 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 Qualia Com­put­ing]