# Disability-Adjusted Life Years II: Variations

Previously, I outlined the basics of the Disability-Adjusted Life Year (DALY) metric. It takes the approach of converting all health burdens into equivalent “years of healthy life lost”: a year of blindness is counted as .6 lost years, a year of severe malnutrition is counted as .053 lost years, etc.

This post discusses two common “variations” on DALYs, meant to deal with relatively thorny disagreements about how different years of life should be valued. As before, page numbers refer to the Global Burden of Disease 2000 report.

Age-weighting

One variation has to do with the intuition some people have that a 20-year-old’s death is more tragic than an infant’s. (I expressed this intuition myself back in November, and I still hold this view.) In an attempt to square with this intuition (which is common and well-documented, as Pg 400 shows), the DALY metric includes an optional age weighting feature that lowers the value of a healthy year of life lived at very young and very old ages, relative to the value of a healthy year of life around age 20. DALYs can be computed with or without age-weighting (“without” just means that all years of healthy life are valued the same).

Discounting

The other variation has to do with valuing present vs. future benefits of aid. DALY calculations apply a discount rate to future benefits; for example, when using a discount rate of 3%, one would count a year of healthy life saved ten years from now as being worth only 74% as much as a year of healthy life saved this year (74% = 1/1.03^10).

I confess that I don’t fully follow the justification for discounting given in the Global Burden of Disease Report, which claims that “the strongest argument for discounting is … [that] not discounting future health would lead to the conclusion that all of society’s health resources should be invested in research programs or programs for disease eradication” (400), which apparently is considered obviously wrong by the authors. Personally, the most appealing argument I can think of for discounting is that helping a person can help them help others, so helping a person sooner is literally “worth more” than helping a person later.

Notation

DALYs(0,0) refers to DALYs calculated with a 0% discount rate and no age-weighting. DALYs(3,1) refers to DALYs calculated with a 3% discount rate and age-weighting. (The first number in parentheses is the discount rate; the second is a 1 if age-weighting is being used, and a 0 if not.) See Pg 401 for the specifics of how varying these numbers affects the valuation of different years.

In theory, you can calculate DALYs using whatever parameters best fit your own philosophical values. In practice, the reports we’ve seen using this metric (Global Burden of Disease Report, Copenhagen Consensus, Disease Control Priorities Project) will give you, at most, DALYs(0,0), DALYs(3,0) and DALYs(3,1), and will rarely give you the inputs into these numbers so you can calculate your own versions. That means that if you want to use a 6% discount rate, you’re completely out of luck; there’s no way to convert DALYs(3,0) to DALYs(6,0) without having more information. More importantly, it means that:

• You can’t use your own version of age-weighting. Even the age-weighted version of DALYs still rates an infant death as about equally tragic to a 20-year-old death (it values a year more for a 20-year-old, but when you work it all out the value of a life comes out the same). There is evidence (see pg 401) that people find a 20-year-old’s death to be far worse; if you share that intuition, then DALYs as they are usually presented won’t reflect your values, and there will be no way to convert them into a unit that does.
• You can’t use your own disability weights. Personally, this is the area I’d most like to see some variation in – the official disability weights disagree violently with my personal intuitions about, for example, how bad it is to be severely malnourished (current weights put it at only 5.3% as bad as a year of life lost – see Pg 121) or how bad it is to go through an abortion (it appears that this is counted as “no cost” by DALYs – see Pg 121 again).

The DALY metric does have some flexibility to accommodate different personal values, but in practice it ends up being pretty rigid. More on this in a future post.

Next in series:

Previously in series:

### Comments

• Carl Shulman on August 11, 2008 at 11:12 pm said:

““the strongest argument for discounting is … [that] not discounting future health would lead to the conclusion that all of society’s health resources should be invested in research programs or programs for disease eradication””

Well, public health efforts to prevent the spread of infectious disease, provide vaccinations, and perform other very cheap effective health care interventions plausibly pay for themselves in increased productive activity, but I could easily endorse shifting 90%+ of current U.S. medical spending to research.

• Toby Ord on August 12, 2008 at 8:06 am said:

Holden,

I’m enjoying this series of posts. I agree that there are some serious issues with the DALY approach, though I’m supportive of it as a ‘best attempt so far’ at a single number metric. If there really are strongly convincing arguments that it should be tweaked in way X or Y, then presumably it will be and will continue to evolve. As to the candidates for X and Y…

The cost of blindness really does seem overvalued if it is considered in a western context. I would prefer 20 years of life while blind to 10 years sighted. The early years might be as bad as suggested, but people adapt. However, there are a lot of additional complications in developing countries. One is that blindness dramatically reduces life-span. Hopefully they take that into account separately and the 60% isn’t a strange fudge to accommodate that fact. Also, in developing countries being blind will often have a significant impact on the ability to earn a living and thus cause its own malnutrition etc. The 60% number might fudge some of this.

In any event, I agree that the number for malnutrition is puzzlingly low.

Your point about the death of an infant vs the death of a 20 year old is a good one. There are several things that could explain why the death of the 20 year old might be quite a bit worse. A major one is that for the early years of life, far more resources are spent on someone than they produce. Thus it is particularly bad for a community if people are dying at the age when they have not yet produced more than they have consumed. I’ve heard that there has been a study of this effect and that it had a very good correlation with the age-at-death that produced the most grief, but I was not given a citation and wouldn’t completely trust it.

Discounting is a controversial kettle of fish and my opinion is that it is not intrinsically valid, but only useful when it is a fudge for other effects such as the one you mention. Another is that the lot of the poor might improve even without a given intervention, so we can’t claim 200 years of benefits for building a well that lasts 200 years as one probably would have been built anyway.

A good way to think of DALYs is as a way to get order of magnitude estimates for effectiveness (and sadly these are often useful…). Taking them with this much salt accounts for some of their unreliability, although you would still need to make adjustments in some cases where they are systematically at odds with your estimates of harm.

I’m looking forward to your further posts and your multidimensional metric.

• Holden on August 13, 2008 at 12:51 pm said:

Toby, interesting comments – thanks. I think you make a particularly good point about disability weights, which is that a disability means different things in different parts of the world (for example, blindness probably lowers quality of life much more in the developing world than in the U.S.) This is an argument not only against the particular disability weights used in the Global Burden of Disease reports, but against region-invariant disability weights in general.

We will be discussing alternatives to DALYs in future posts.

• Ron Noble on August 13, 2008 at 2:03 pm said:

I read the GBD explanation and agree it could have been written more clearly. What they are referring to is the “Keeler-Cretin paradox.” If you were faced with the choice of spending X dollars now to achieve a certain health benefit, or investing it and spending it a year later, you should invest it because a year from now you’ll have more money to spend and can achieve a greater benefit. But then why not delay two years, etc? The paradox is that infinite delay is called for by this logic. Discounting of health future health benefits potentially solves the problem. You have more money to spend, but if future health benefits are valued less, you aren’t necessarily getting more for your dollar by delaying. Obviously this is debatable and is debated, but that’s the crux of the issue as I understand it.

As to age weighting, if I understand both your intuition and the GBD report correctly, you have slightly misstated the rationale, but this slight misstatement is crucial: The GBD report does not say that people value the life of a 20-year old more than an old person or an infant. It says they value a year of life of a 20 year old more than a year of life of an old person or an infant. Saving an infant’s life is still more valuable, because they still have all of their childhood up to age 20 to gain by living, plus the high quality life at age 20, in addition to life after that, which the 20 year old and the infant both have to gain by living.

As to only the a couple of discount rates being reported, that is standard in journal reports but they sometimes contain enough information for you to do your own discounting.

I think you are right to question the disability weight that WHO uses. I’m surprised they’ve been so widely accepted with so little question. On the other hand, it is likely that a fair amount of research did do into determining them. My dissertation focused on trying to measure QALYs (essentially the same thing as DALYs) at different levels of depression. All the weights in the literature can and should be criticized, but weights also shouldn’t be dismissed because they don’t match our off the cuff intuitions. It’s a hard problem!

• Toby Ord on August 15, 2008 at 4:48 am said:

There are other ways around that paradox that Ron mentioned. For example, as Holden mentioned, some benefits to the developing world cause their own exponential returns in the developing world and it seems quite plausible to me that their effective returns are higher than market rates. Another example is that (I believe) the marginal impact of a real dollar spent on poverty in a century will be lower than that now as we will find and complete the low hanging fruit. As an example, if within 1,000 years poverty has been pretty much neutralized, then that puts a ceiling on how long it is worth saving up for and dispels the paradox. I know there are technical details and assumptions needed, but I’m just trying to sketch the solutions here.

• Doug S. on August 15, 2008 at 3:09 pm said:

Perhaps one should embrace the paradox and choose to fund the project that, if successful, could very well solve everyone’s problems forever, but probably won’t pay off in your lifetime.

You think I’m joking, but that project does exist, and it is looking for money.

• Holden on August 18, 2008 at 6:23 pm said:

Ron –

• Your explanation of the rationale for discounting makes sense. Thanks.
• The parts of GBD that I’m getting my interpretation from are:
• “the DALY values the life of a newborn about equally to that of a 20-year-old, whereas the empirical data suggest a
fourfold difference” (401)
• “The ratio of the DALY loss from a death at age 20, say, to that at birth is close to 1 for any reasonable set of parameter values in the current DALY formulation. Many people’s ethical judgments would give this ratio a value substantially greater than 1.” (439)
• Table on pg 402 shows that even with age-weighting, the DALY values the lives of an infant & 20-year-old about the same. This reinforces my sense that the complaints they’re referring to are about the relative value of lives, not years.
• I don’t have a very clear understanding of how exactly disability weights were determined, but the most important point to me is that subjective weights can be expected to vary significantly from donor to donor. Even if these weights correctly state the “average” philosophical values for some population, the way DALYs are used still causes lost relevant information for individuals.
• Daniel on January 4, 2011 at 9:36 pm said:

The infinite delay paradox only works if you assume that society will last forever, and interest will make the value of your money increase without limit.

Let’s just assume the first one. This means that the expected utility of helping and not helping are both infinite. Also, depending on the order in which you add the utilities, you could even set it to an arbitrary number. There are far worse things.

It might be that this implies that the correct action is to invest your money for millennia. If this is the case, the correct action is to invest your money for millennia. The fact that it’s counterintuitive means little.

• Holden on January 10, 2011 at 4:02 pm said:

Daniel, I agree that counterintuitiveness alone means little. However, I’m not sure that the kind of argument being discussed here (“If you can earn interest, then you can always accomplish more by waiting a year than by spending now, thus you should wait forever”) ought to carry more weight than intuition. It has a logical feel to it, but it is not a proof, and it does not address the intuition that “we shouldn’t wait indefinitely” with any facts. Rather, it invokes various implicit assumptions about completely unknown parameters (in particular, the extent to which human empowerment “compounds” via the person you empowered being able to contribute back to society and help others). Thus it is more of a shift from one intuition than another, rather than a reliable counter to intuition.

I think the observation that “argument X implies we should wait forever” is a powerful argument, not because it demonstrates a logical paradox, but because it highlights argument X’s lack of grounding in contingent empirical reality. I.e., when an argument endorsing a specific human action (donating vs. waiting) seems equally powerful regardless of time and place, I think that’s good reason to be suspicious of it, and to suspect that there’s an insufficiently examined assumption buried in there (which I think is the case here).

Comments are closed.