Let me try to do a rough calculation myself: if you world-wide banned sugary drinks, each person would lose 0.001 DALYs total over the rest of their lives [EDIT: this is wrong, it’s per annum, see this comment for a corrected version of the following calculation].
What’s the disease burden caused by DMT2? Your report says roughly 90 million DALYs, I’m going to assume that’s per year (you probably say this somewhere or it’s probably an obvious convention, but I couldn’t find it easily and don’t know the conventions in this field). The global average age is ~30 and average life expectancy is ~70, so let’s multiply that by 40 remaining years to say 3,600 million DALYs of total DMT2 burden for the present population over the rest of their lives. Banning sugary drinks would reduce that burden by 5%, for a gain of 180 million DALYs. There are ~8 billion people on earth, so that’s 0.02 DALYs per person gained by banning sugary drinks.
So loss of freedom of 0.001 DALYs reduces the benefit of 0.02 DALYs by 0.001 / 0.02 = 5%, agreeing with my guesstimate above (assuming that the ratio is the same for a tax vs an all-out ban, which seems right to first order).
FWIW I’m also suspicious of the 0.001 DALYs per person number.
AFAICT, the way you get it is by combining two methods: method 1 is to ask people a chain of questions like “as a fraction of death, how bad is life imprisonment”, “as a fraction of life imprisonment, how bad is not being able to eat tasty stuff”, “as a fraction of not being able to eat tasty stuff, how bad is not being able to have sugary drinks”, multiply their answers to get how bad losing sugary drinks is as a fraction of dying, and then multiply by the fraction 64⁄74 (for remaining life years? this was opaque to me), to get a DALY loss of 0.016 +/- 0.009 [1]. You then do method 2: ask people how much of their annual income they’d give up to get a 1-year exemption from a ban on drinking sugary drinks, take the binary logarithm of 1 + that fraction, and multiply by 2 to get DALY loss. This gives you a loss of 0.0012 +/- 0.0009 [1]. You then average each respondent’s result from each method to get a per-respondent DALY loss estimate, before aggregating that accross respondents. Because the standard deviation of responses from method 1 is 10 times higher than that of method 2 [2], you weight method 2 10x higher in the per-respondent average, meaning that the overall loss is basically just that of method 2.
But I don’t think you’re right to conclude that method 2 is more accurate than method 1: it’s just that method 2 gives ~10x smaller results for whatever reason, so it makes sense that its error is also ~10x smaller. If you look at the spread in responses as a fraction of the mean response, methods 1 and 2 are pretty close (if anything, it looks like method 1 is a bit more precise). If you instead weighted the methods equally, you would get 3x the per-person DALY loss [3], and if I’m right in the parent comment, that would net out to a 15% reduction in the value of the program.
(also more fundamentally, the fact that the methods give 10x different values suggests that they plausibly are just measuring different things, and we should be unsure which (if either) is actually measuring the disvalue of the loss of freedom to drink sugary drinks)
[1] My error here is the standard error of the mean of each result: basically, how much we’d expect our calculated mean to vary if we resampled. It’s equal to the empirical standard deviation divided by the square root of the number of samples (which is 4).
[2] You also list one benefit of method 1 and one benefit of method 2, which I’m assuming cancel out in your considerations.
[3] Sanity check: the mean of the first method is 10x bigger than the second method, previously we were ~ignoring the first method, now we’re taking the geometric mean, and the geometric mean of 1 and 10 is 3 (because 3^2 is about 10), so this looks right.
Wait: your survey numbers are for DALYs lost per year. So if the disease burden is 90 million DALYs per year, banning sugary drinks gives a benefit of 0.0006 DALYs per person-year, compared to 0.001 DALYs lost per person-year, meaning that the loss of freedom reduces the benefit by 167% (or 500% if you believe this comment). So now I’m really curious how your adjustments are bringing that down so much.
EDIT: reading the full report, the 0.02% reduction in diabetes burden is from eliminating sugary drink consumption in a single country. I’ve updated my comments below to correct for that
Overall, we expect a 100% reduction in sugar-sweetened beverages consumption in a single country to reduce the global disease burden of diabetes mellitus type 2 by 0.02%.
I’m also confused here, but I get different numbers than you do.
My BOTEC:
For 100% elimination of sugary beverages in all countries, the benefits seem like they’d be 0.0002*193*90,000,000 = 3,474,00 DALYs averted /year
For 100% elimination of sugary drinks, the costs in reduced freedom seem like they’d be 8,100,000,000 * 0.001 = 8,100,000 DALYs/year
Sounds like you roughly agree with me − 8.1 / 3.5 = 230%, which is close to 167%. Difference is I use the 5% reduction number for proportion of burden due to sugary drinks, getting 90 mil / 20 = 4.5 mil, 8.1 / 4.5 = 180%, and the rest is error built into these calcs.
Another way to look at this is that according to the report’s numbers, a 100% reduction in sugary beverages would prevent 0.02%*193 = 1 in 26 cases of diabetes. But it would also make life 1/1000th worse for everyone.
Let me try to do a rough calculation myself: if you world-wide banned sugary drinks, each person would lose 0.001 DALYs total over the rest of their lives [EDIT: this is wrong, it’s per annum, see this comment for a corrected version of the following calculation].
What’s the disease burden caused by DMT2? Your report says roughly 90 million DALYs, I’m going to assume that’s per year (you probably say this somewhere or it’s probably an obvious convention, but I couldn’t find it easily and don’t know the conventions in this field). The global average age is ~30 and average life expectancy is ~70, so let’s multiply that by 40 remaining years to say 3,600 million DALYs of total DMT2 burden for the present population over the rest of their lives. Banning sugary drinks would reduce that burden by 5%, for a gain of 180 million DALYs. There are ~8 billion people on earth, so that’s 0.02 DALYs per person gained by banning sugary drinks.
So loss of freedom of 0.001 DALYs reduces the benefit of 0.02 DALYs by 0.001 / 0.02 = 5%, agreeing with my guesstimate above (assuming that the ratio is the same for a tax vs an all-out ban, which seems right to first order).
FWIW I’m also suspicious of the 0.001 DALYs per person number.
AFAICT, the way you get it is by combining two methods: method 1 is to ask people a chain of questions like “as a fraction of death, how bad is life imprisonment”, “as a fraction of life imprisonment, how bad is not being able to eat tasty stuff”, “as a fraction of not being able to eat tasty stuff, how bad is not being able to have sugary drinks”, multiply their answers to get how bad losing sugary drinks is as a fraction of dying, and then multiply by the fraction 64⁄74 (for remaining life years? this was opaque to me), to get a DALY loss of 0.016 +/- 0.009 [1]. You then do method 2: ask people how much of their annual income they’d give up to get a 1-year exemption from a ban on drinking sugary drinks, take the binary logarithm of 1 + that fraction, and multiply by 2 to get DALY loss. This gives you a loss of 0.0012 +/- 0.0009 [1]. You then average each respondent’s result from each method to get a per-respondent DALY loss estimate, before aggregating that accross respondents. Because the standard deviation of responses from method 1 is 10 times higher than that of method 2 [2], you weight method 2 10x higher in the per-respondent average, meaning that the overall loss is basically just that of method 2.
But I don’t think you’re right to conclude that method 2 is more accurate than method 1: it’s just that method 2 gives ~10x smaller results for whatever reason, so it makes sense that its error is also ~10x smaller. If you look at the spread in responses as a fraction of the mean response, methods 1 and 2 are pretty close (if anything, it looks like method 1 is a bit more precise). If you instead weighted the methods equally, you would get 3x the per-person DALY loss [3], and if I’m right in the parent comment, that would net out to a 15% reduction in the value of the program.
(also more fundamentally, the fact that the methods give 10x different values suggests that they plausibly are just measuring different things, and we should be unsure which (if either) is actually measuring the disvalue of the loss of freedom to drink sugary drinks)
[1] My error here is the standard error of the mean of each result: basically, how much we’d expect our calculated mean to vary if we resampled. It’s equal to the empirical standard deviation divided by the square root of the number of samples (which is 4).
[2] You also list one benefit of method 1 and one benefit of method 2, which I’m assuming cancel out in your considerations.
[3] Sanity check: the mean of the first method is 10x bigger than the second method, previously we were ~ignoring the first method, now we’re taking the geometric mean, and the geometric mean of 1 and 10 is 3 (because 3^2 is about 10), so this looks right.
Wait: your survey numbers are for DALYs lost per year. So if the disease burden is 90 million DALYs per year, banning sugary drinks gives a benefit of 0.0006 DALYs per person-year, compared to 0.001 DALYs lost per person-year, meaning that the loss of freedom reduces the benefit by 167% (or 500% if you believe this comment). So now I’m really curious how your adjustments are bringing that down so much.
EDIT: reading the full report, the 0.02% reduction in diabetes burden is from eliminating sugary drink consumption in a single country. I’ve updated my comments below to correct for that
I’m also confused here, but I get different numbers than you do.
My BOTEC:
For 100% elimination of sugary beverages in all countries, the benefits seem like they’d be 0.0002*193*90,000,000 = 3,474,00 DALYs averted /year
For 100% elimination of sugary drinks, the costs in reduced freedom seem like they’d be 8,100,000,000 * 0.001 = 8,100,000 DALYs/year
So this looks net negative in expectation
Sounds like you roughly agree with me − 8.1 / 3.5 = 230%, which is close to 167%. Difference is I use the 5% reduction number for proportion of burden due to sugary drinks, getting 90 mil / 20 = 4.5 mil, 8.1 / 4.5 = 180%, and the rest is error built into these calcs.
Gotcha, makes sense!
Another way to look at this is that according to the report’s numbers, a 100% reduction in sugary beverages would prevent 0.02%*193 = 1 in 26 cases of diabetes. But it would also make life 1/1000th worse for everyone.