Quantifying Pain Magnitude

A couple weeks ago I came across this interesting post by Alfredo Parra on the EA forum on quantifying pain from cluster headaches and I’ve been thinking about it a lot since, so I thought I’d write a bit about pain magnitude, one of its central ideas.

Pain Is Bad, and Sometimes Really Bad

The most intense pain I’ve experienced was from kidney stones. At the peak of their intensity, I was lying on the bathroom floor in between bouts of dry heaving from a pain that consumed my whole mind. But that’s far from the worst pain that anyone has experienced. If you ask people who suffer from cluster headaches how intense various types of pain they’ve experienced are, they give the headaches a mean score of 9.7, but only a 6.9 for kidney stones.

But how much worse is that? Sure, it’s 2.8 higher on the 10-point scale, but what does that mean?

If you’re a utilitarian, then how bad various types of pain are can in principle be quantified, with different levels leading to objective amounts of disutility. If you’re some other type of consequentialist it’s not quite as simple, but I think that magnitude of pain is still a useful concept in that case. Say you need a medical procedure and have two options. The first will take only one minute, but will be very painful, a 8 on the pain scale. The second takes five minutes, but is less painful at a 6. In order to decide which is better, you need to know not just that 8 is worse than 6 but how much worse it is. If you’re indifferent between the options, there’s some sense in which 8 is five times as bad as 6 per unit time. This is a little muddy because of quirks in how humans recall painful experiences, but I think it’s useful nevertheless.

Some Challenges

It would be really useful to be able to map the 0-10 pain scale to this idea of pain magnitude in order to quantify just how much suffering various types of pain cause. There are quite a few sources of inaccuracy that could lead to poor estimates:

• It’s not clear how magnitude of pain increases across the scale. A linear scale is the simplest, but this doesn’t seem to capture the top end of the scale well since a 10 seems more than 10/9ths as bad as a 9. A logarithmic scale seems more appropriate since each step is the same relative magnitude increase as the prior one, but it can’t represent an absence of pain. I like exponentials so I’m going to use them here, but it’s not the clear correct answer. Andrés Gómez-Emilsson has done some work on this topic, which seems consistent with using a logarithmic scale.

• We want pain intensity, but people’s reports of pain probably factor in length as well as intensity, leading to longer-lasting pain being overrated

• The scale is capped at 10, which could be censoring the most intense pain.

• The survey was offered on a site related to headache pain, so the respondents may have been disproportionately those with especially severe cluster headaches.

• Some pain conditions, like labor, have a mix of pain levels. When people report the value for labor pain, are they thinking of the peak pain during contractions, or the average pain throughout the experience?

Because of all of these concerns, any estimates we come up with should be taken as very rough approximations.

A Simple Model

As a first stab at the problem, let’s assume that each point on the pain scale represents twice as much pain magnitude as the one before it. If we apply this scale, here’s what pain magnitudes for each of the pain conditions look like:

Whew, this puts cluster headache pain pretty far above the rest! Is a base of 2 in the exponential transformation reasonable though? This suggests a gunshot wound is about 3 times the pain of a stab wound, kidney stones are about 2.5 times as painful as a migraine, and that the difference in a 3 and an 8 on the pain scale is 32x. That seems reasonable to me, but not obviously right. The choice of base makes a big difference, here are magnitudes using 1.4 (~sqrt(2)), 2, and 4.

1.4 seems too small to me, and 4 seems too big, but that still leaves a pretty big range of uncertainty, since the cluster headache:arthritis ratio differs by about 500x between those. I think somewhere around 2 is probably “right” in the sense that it gets close to how the median person feels about pain tradeoffs and intensity on the 10-point scale. There’s still certainly variability between how different people map pain magnitude to the scale, and the logarithmic fit may not be appropriate especially at the edges of the scale, but I think it’s a reasonable starting point.