Today I am celebrating my first publication in my new job, and since it’s about a topic I’ll probably be coming back to a lot in the next year, I thought I’d cover it here. It’s not much of a publication – just a letter in the journal Addiction – but it covers what I think is an interesting topic, and it shows some of the complexity of modern health policy analysis. The article, entitled Equity Considerations in the Calculation of Cost-Effectiveness in Substance Use Disorder Populations[1], can be found here[2]. It’s only 400 words, but I thought I’d give an explanation in more detail here, and explain what I’m trying to say in more detail. The background I’m presenting here may be useful for some future material I’m hoping to post up here. I’ll give a brief overview of the “cost effectiveness” concept, explain what the problem is that I’m addressing in this paper, and then give a (slightly) mathematical example in extremis to show where cost-effectiveness analysis might lead us. I’ll also add some final thoughts about cost-effectiveness analysis (CEA) in fantasy populations, with perhaps a final justification for genocide. Or at least an argument for why Elves should always consider it purely on cost-effectiveness grounds.

Cost-Effectiveness Analysis, QALYs and the IDU Weight

Traditional epidemiological analysis of interventions is pretty simple: cholera, for example, kills X people, so let’s prevent it. However, we run into problems when we have limited resources and need to compare two different interventions (e.g. turning off a pump vs. handing out disinfectant pills). In this situation we need to compare which intervention is more effective, and we do this by assessing the cost per life saved under each intervention – if turning off the pump is cheaper and saves more lives, then it’s better. This is usually represented mathematically as the ratio of the cost difference between the intervention and some control (the incremental cost) and the effect difference (the incremental effects). The ratio of the two is the incremental cost effectiveness ratio (ICER). This is what I used in assessing clerical interventions to prevent infant mortality. However, when we are dealing with chronic diseases the incremental effects become harder to measure, because a lot of interventions for chronic illness don’t actually save lives: they extend life, or they improve the quality of life a person experiences before they die. In this case we use Quality-Adjusted Life Years (QALYs). These are usually defined by conducting a study in which people are asked how they would weight a year of their life under some condition relative to fully healthy – or, more usually, relative to their health as it is now. For example, blindness in one eye might be rated a QALY of 0.9 relative to being fully-sighted. There is some interesting debate about whether these ratings should be assessed by those who have the condition or the community as a whole; the logic here can be perverse and complex and is best avoided[4].

So in essence, you rate one year of life as having the value of 1 when fully healthy, and then other states are rated lower. We can use the issue of Voluntary Testing and Counselling as an HIV intervention to see how this works.

Example: Voluntary Testing and Counselling

It’s fairly well-established that good post-test counselling can successfully reduce a person’s risk behavior, so if you can get people at high risk of HIV (e.g. men who have sex with men (MSM)) to undergo voluntary testing, you can catch their HIV disease at an early stage and get them to change their behavior. In theory, doing this fast enough and effectively will reduce the rate at which HIV spreads. Furthermore, catching HIV earlier means initiating treatment earlier (before it becomes symptomatic), and early treatment with anti-retroviral drugs leads to longer survival[5]. However, discovering one is HIV positive is not a pleasant experience and knowing you are HIV positive lowers your overall quality of life, even if the disease is asymptomatic. So if the survival benefits of early testing don’t outweigh the loss of utility, then it’s not worth it. So 10 years ago, when treatment extended your life by perhaps 10%, but testing reduced your remaining QALYs from 1 to 0.9, then the benefits might not outweigh the costs. Additionally, treatment is expensive, and it might be more cost effective on a population level to run health promotion campaigns that reduce risk behavior: reduced risk behavior means less infections, means less QALYs lost to HIV.

In essence, it’s a kind of rigorous implementation of the old bar room logic: sure I’d live longer if I didn’t drink, but why would I want to?

Recently, however, some analysts have introduced a sneaky new concept, in which they apply a weight to all QALY calculations involving injecting drug users (IDUs). The underlying logic for this is that IDU is a mental illness, and people with a mental illness have a lower utility than people without. This weight is applied to all QALY calculations: so a year of life as a “healthy” IDU is assigned a value of, e.g. 0.9, and all other HIV states (for example) are given a value of 0.9 times the equivalent values for a non-IDU.

What is Wrong with the IDU Weight

This has serious ramifications for cost-effectiveness and, as I observe in my article, fucks up any attempt to get a cost-effectiveness analysis past the British NICE, since it breaks their equity rule (for good reason). In addition to its fundamentally discriminative nature, it’s also technically a bit wonky, and in my opinion it clouds cost effectiveness analysis (“which treatment for disease X provides better value for money?”) with cost-benefit analysis (“who should we spend our money on?”). It’s cool to do the latter vs. the former, but to cloud them together implicitly is very dangerous.

Technical Wonkiness

Suppose you have a population of IDUs with a weight of 0.9, and you need to compare two interventions to prevent the spread of HIV. One possible intervention you could use is methadone maintenance treatment (MMT), which is very good at reducing the rate at which IDUs take injecting risks. You want to compare this with some other, broader-based intervention (e.g. voluntary testing and treatment, VTT, which also affects MSM and low-risk people).  Then the average QALY for an MSM with asymptomatic HIV is about 0.9 (to pick a common value). Because you’ve applied the weight to IDUs but not to (e.g.) MSM, the average QALY for an IDU with asymptomatic HIV is 0.9*0.9=0.81. Now suppose that you implement MMT: this intervention reduces the risk of transmission of HIV, but it also treats IDU’s mental illness, so the weight for all the successfully-treated IDUs drops away and you gain 0.09 QALYs per IDU you treat; but then you gain 0.1 additional QALYs for every case of HIV prevented by the MMT intervention. This means that VTT has to be almost twice as effective as MMT to be considered cost effective, if they cost roughly the same amount. That is, in this case the cost-effectiveness of MMT is exaggerated relative to VTT by dint of your weighting decision – even though half of the benefits gained don’t actually have anything to do with reducing the spread of HIV (which implies you can prevent half as much HIV for the same QALY gains). On the other hand, if you implement an intervention that doesn’t treat IDU but does prevent HIV in IDU (such as needle exchange), its effectiveness will be under-estimated due to the IDU weight. In both cases, introducing the cost-benefit element to the analysis has confused your outcome.

Opening Pandora’s Box

The real problem with this IDU weight, though, is if we decided to extend the logic to all cost-effectiveness analysis where identifiable groups exist. For example, we could probably argue that very old people have lower QALYs than younger people, and any intervention which affects older people would gain less benefit than one which affects young people. An obvious example of this is anything to do with road accidents: consider, for example, mandatory eye testing vs. raising the minimum driving age. Both would result in lower rates of injury (and thus gain QALYs) but the former would primarily affect older people, and so would be assigned lower effectiveness, even if it prevented a hugely greater number of injuries[6]. When we start considering these issues, we find we’ve opened Pandora’s box, and particularly we’ve taken ourselves to a place that no modern health system is willing to contemplate: placing a lower value on the lives of the old, infirm, or mentally ill. As is often the case with social problems, the marginalized and desperate (in this case, IDUs) are the canaries in the coalmine for a bigger problem. I don’t think any health system is interested in going down the pathway of assigning utility weights to otherwise healthy old people (or MSM, or people with depression, or…)

An Example in Extremis

Let’s consider an obscene example of this situation. Suppose we apply a weight, let’s call it beta, to some group of recognizable people, who we call “the betamaxes.” Now imagine that these people are the “carriers” for a disease that doesn’t afflict them at all (i.e doesn’t change their quality of life) but on average reduces the quality of life of those who catch it to a value alpha. Suppose the following conditions (for mathematical simplicity):

  • The people who catch the disease are on average the same age as the betamaxes (this assumption makes comparison of life years easier; breaking it simply applies some ratio effects to our calculation)
  • The disease is chronic and incurable, so once a member of the population gets the disease their future quality of life is permanently reduced by a factor of alpha
  • One betamax causes one case of disease in his or her life
  • Preventing the disease is possible through health promotion efforts, but costs (e.g.) $10000 per disease prevented
  • Betamaxes are easily identifiable, and identifying and killing a betamax costs $10000

I think we can all see where I’m going here. Basically, under these (rather preposterous) conditions, identifying and killing betamaxes is a more cost-effective option than the health promotion campaign whenever alpha>1-beta. Obviously permanent quarantine (i.e. institutionalization) could also be cost-effective.

This may seem like a preposterous example (it is), but there’s something cruel about these calculations that makes me think this weighting process is far from benign. Imagine, for example, the relative QALY weights of people with dementia and their carers; schizophrenia and the injuries caused by violence related to mental health problems; or paedophilia. I think this is exactly why health systems avoid applying such weights to old people or the mentally ill. So why apply them to IDUs?

Cost-Effectiveness Analysis in Fantasy Communities

There’s an obvious situation where this CEA process breaks down horribly: if you have to apply it to elves. Elves live forever, so theoretically every elf is worth an infinite amount of QALYs. This means that if a chronic disease is best cured by drinking a potion made of ground up human babies, it’s always cost-effective for elves to do it, no matter how concentrated the baby souls have to be. If a human being should ever kill an elf due to some mental health problem, then it’s entirely reasonable for the elven community to consider exterminating the entire human community just in case[7]. Conversely, any comparison of medical interventions for chronic disease amongst elves on cost-effectiveness grounds is impossible, because all treatments will ultimately produce an infinite gain in QALYs: this means that spending the entire community’s money on preventing a single case of HIV has an incremental cost effectiveness of 0 (it costs a shitload of money, but saves an infinite number of QALYs). But so does spending the entire community’s money to prevent a single case of diabetes. How to compare?

Similar mathematical problems arise for Dwarves, who have very long lives: you’d have to give them a weight of 0.25 (for being beardy bastards) or less to avoid the same problems vis a vis the use of humans in medicinal treatment that arise with elves.

This might explain why these communities have never gone for post-scarcity fantasy. When you have an infinite lifespan, no intervention of any kind to improve quality of life is cost-effective. You might as well just live in squalor and ignorance, because doing anything about it is a complete waste of money.

Cost Effectiveness Analysis as a Justification for Goblin Genocide

Furthermore, we can probably build a mathematical model of QALYs in an AD&D world: some people have better stats than others, so they probably have better quality of life. We could construct a function in terms of the 6 primary stats, and obviously goblins come out of this equation looking pretty, ah, heavily downward weighted. Given that they lead short and brutish lives, and are prone to kill humans when the two communities interact, the obvious effect of weighting their QALYs from this mathematical model is pretty simple: kill the fuckers. The QALY gains from this (and the low cost, given the ready availability and cheap rates of modern adventurers) makes it a guaranteed investment. In fact, compared to spending money paying clerics to prevent infant mortality, it could even be cost-effective.


Cost-effectiveness analysis needs to be applied very carefully to avoid producing perverse outcomes, and the logical consequences of applying weights to particular groups on the basis of their health state are not pretty. We should never weight people “objectively” to reflect their poor health in dimensions other than that under direct consideration in the cost-effectiveness analysis, in order to avoid the risk of applying a cost-benefit analysis to a cost-effectiveness situation. Furthermore, even if we are comfortable with a “discriminatory” weight, of the “oh come on! they’re just junkies!” sort, it can still have perverse outcomes, leading to over-estimates of the cost-effectiveness of treatments for the mental illness compared to other interventions. Furthermore, we should never ever ever allow this concept to become popular amongst elven scholars.

I’ll be coming back to this topic over the next few months, I think, in a way I hope is quite entertaining for my reader(s). Stay tuned…

fn1: The slightly cumbersome title arose because the journal now doesn’t like to refer to “substance abuse” or “substance abusing populations” so I had to change it to the un-verbable “Substance Use Disorder”

fn2: If you download the pdf version it comes with a corker of a letter about French tobacco control policy[3]

fn3: Which is a contradiction in terms, surely?

fn4: For a full explanation of this and other matters you can refer to the famous text by Drummond, which is surprisingly accessible

fn5: In fact we are now looking at very long survival times for HIV – up towards 30 years, I think – provided that we initiate good quality treatment early, and so it is no longer necessarily a death sentence, if one assumes a cure will be available within the next 30 years

fn6: This applies even if you ignore deaths and focus only on short-term minor injuries, and thus avoid the implicit bias in comparing old people with young people (interventions that save life-years in old people will always be less “effective” than those that save life years in young people, unless the effect of the intervention is very short-lived, because old people have less years of life to save).

fn7: In fact you can go further than this. All you need is for an elven propagandist to argue that there is a non-zero probability that a single crazy human will kill a single elf at any point in the future, and the expected value of QALYs lost will always be greater than the QALY cost of killing all humans on earth, no matter how small the probability that the human would do this