Thanks for sharing this Alfredo, I hadn’t really thought about trying to map subjective pain scales to a pain magnitude, but it seems very important to be able to do so! If using an exponential scale, what is your intuitive sense of what ranges of base to use seem reasonable? If you’re modeling magnitude as base^(1-10 pain scale value), the relative importance of extreme pain is pretty sensitive to the base used. I see e is used as the default in the paper, but I assume that’s partly arbitrary. A value more like 2 seems most reasonable to me, but that is a weakly held view. Has any other work tried to look at suffering magnitude across the pain scale?
I wish we could have more confidence in the pain intensity data. I’m not sure how exactly we should compare the 5-point scale in Russell to the 10-point one in Torelli & Manzoni, in the mapping you’ve done in the code to a shared 10-point scale, they suggest very different intensities.
Indeed, the choice of e is arbitrary and used for illustration purposes. And the base 6 is simply the choice for which the total burden of CH is larger than that of migraines, so it’s also not derived from first principles. This footnote is relevant:
The resulting scaling as 6x would mean that the 0–10 scale would have to span 4 orders of magnitude. While Gómez-Emilsson & Percy (2023) suggest the scale spans “at least two orders of magnitude”, private communication with the authors indicates their central estimates might be closer to 4 orders of magnitude, with uncertainty ranging from 2 to 8 OOMs.
The paper cited also mentions the possibility of a linear relationship for lower pain intensities and an exponential relationship at higher intensities (a “kinked” distribution), highlighting the fact that there are more possibilities beyond a uniform exponential increase.
I personally don’t have a good intuition for what the base should be but might do more work on this specific question.
I’m also not sure what the optimal mapping of intensities for the Russell vs Torelli & Manzoni scales is, also considering the fact that the two studies had different methodologies. I think there’s no correct answer, so that was my best guess (though I could also imagine “Very slight” being more intense than a 1.5). Do let me know if you have other suggestions! (Or feel free to fork the code and play around with the parameters. :) )
Thanks, that’s helpful! I think that footnote may have an error though. 6^10 is 60 million, implying nearly 8 OOMs from 0 to 10. The 1-10 gap would be closer to 4 OOMs if linear from 0-5 and exponential with base 6 from 0-10 though. 2-8 OOMs seems like a reasonable range to me, it’s comically broad but highlights our uncertainty about pain magnitude. I’ll definitely give Gómez-Emilsson & Percy (2023) a read, and will fork your cose and play around with the numbers as well!
Thanks for sharing this Alfredo, I hadn’t really thought about trying to map subjective pain scales to a pain magnitude, but it seems very important to be able to do so! If using an exponential scale, what is your intuitive sense of what ranges of base to use seem reasonable? If you’re modeling magnitude as base^(1-10 pain scale value), the relative importance of extreme pain is pretty sensitive to the base used. I see e is used as the default in the paper, but I assume that’s partly arbitrary. A value more like 2 seems most reasonable to me, but that is a weakly held view. Has any other work tried to look at suffering magnitude across the pain scale?
I wish we could have more confidence in the pain intensity data. I’m not sure how exactly we should compare the 5-point scale in Russell to the 10-point one in Torelli & Manzoni, in the mapping you’ve done in the code to a shared 10-point scale, they suggest very different intensities.
Thank you for your comment, Tim!
Indeed, the choice of e is arbitrary and used for illustration purposes. And the base 6 is simply the choice for which the total burden of CH is larger than that of migraines, so it’s also not derived from first principles. This footnote is relevant:
The paper cited also mentions the possibility of a linear relationship for lower pain intensities and an exponential relationship at higher intensities (a “kinked” distribution), highlighting the fact that there are more possibilities beyond a uniform exponential increase.
I personally don’t have a good intuition for what the base should be but might do more work on this specific question.
I’m also not sure what the optimal mapping of intensities for the Russell vs Torelli & Manzoni scales is, also considering the fact that the two studies had different methodologies. I think there’s no correct answer, so that was my best guess (though I could also imagine “Very slight” being more intense than a 1.5). Do let me know if you have other suggestions! (Or feel free to fork the code and play around with the parameters. :) )
Thanks, that’s helpful! I think that footnote may have an error though. 6^10 is 60 million, implying nearly 8 OOMs from 0 to 10. The 1-10 gap would be closer to 4 OOMs if linear from 0-5 and exponential with base 6 from 0-10 though. 2-8 OOMs seems like a reasonable range to me, it’s comically broad but highlights our uncertainty about pain magnitude. I’ll definitely give Gómez-Emilsson & Percy (2023) a read, and will fork your cose and play around with the numbers as well!
Gee, not sure what happened there—thanks for pointing that out! I’ve edited the footnote.