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Maths in a minute: QALYs

Public health can present us with stark choices. How much are we, as a society, prepared to pay for life-saving treatments for horrible diseases? How much economic loss are we prepared to accept to save a life from COVID-19 through measures such as lockdowns?

Money and pills

Is a treatment worth the extra cost?

To answer such difficult questions you need a common measuring instrument, a yardstick. A yardstick that is widely used is the quality adjusted life year — the QALY.

The QALY takes into account both the increase in life expectancy you get from a treatment or intervention and any change in quality of life. This reflects the value judgment that living longer, in itself, is an insufficient measure of success: the quality of life also needs to be considered. Of course many treatments (such as hip replacement surgery) may not directly increase longevity but give a better quality of life during a person's remaining years. Therefore, it is important to take both into account.

One QALY is equivalent to one year of life in perfect health. If a treatment or intervention gives you an additional QALY, then this could correspond to one year of life in perfect health, two years of life in 50% health, four years of life in 25% health, or any other combination. When bodies such as the National Institute for Clinical Excellence (NICE) compare two treatments, they compare the number of extra QALYs the treatments provide, and also how much those extra QALYs cost. In other words they compare the cost per QALY for the treatments.

Measuring the extra length of life provided by a treatment is easy, but it is more difficult to measure quality of life. To do this, people who have received a treatment are asked to fill out detailed questionnaires (such as the EQ-5D) about how they rate their quality of life. Those questionnaires have been designed to capture aspects of life that surveys have shown people find important, such as the level of pain they experience or how mobile they are. The combination of answers a person gives is then turned into a numerical score, from which the number of extra QALYs a treatment provides is calculated. Find out more in this article.

This article is an edited extract of The economics of health by Sarah Garner.

The article was produced as part of our collaborations with JUNIPER, the Joint UNIversity Pandemic and Epidemic Response modelling consortium, and the Isaac Newton Institute for Mathematical Sciences (INI).

JUNIPER comprises academics from the universities of Cambridge, Warwick, Bristol, Exeter, Oxford, Manchester, and Lancaster, who are using a range of mathematical and statistical techniques to address pressing question about the control of COVID-19. You can see more content produced with JUNIPER here.

The INI is an international research centre and our neighbour here on the University of Cambridge's maths campus. It attracts leading mathematical scientists from all over the world, and is open to all. Visit to find out more.

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