• Disability adjusted life years
• life expectancy
• quality adjusted life years
• standardisation

QALYs and DALYs combine years of life and quality of life in a single measure.^1–3 In Arnesen and Nord’s words: “DALYs and QALYs are complementary concepts. QALYs are years of healthy life lived; DALYs are years of healthy life lost. Both approaches multiply the number of years (x axis) by the quality of those years (y axis). QALYs use “utility weights” of health states; DALYs use “disability weights” to reflect the burden of the same states. For example, if the utility of deafness is 0.67, the disability weight of deafness is 1−0.67 = 0.33. Disregarding age weighting and discounting, and assuming lifetime expectancy of 80 years, a deaf man living 50 years represents 0.67×50 = 33.5 QALYs gained and 0.33×50+1.0×(80−50) = 46.5 DALYs lost”.² We can see that 33.5+46.5 = 80.0—that is, QALYs+DALYs = lifetime expectancy.

If we would like to be more accurate, we had to put QALYs = 0.67×50y = 33.5y and DALYs = 0.33×50y+1.0×(80y−30y) = 46.5y. This means that the unit of measurement of QALYs and DALYs is years (y). As y is the unit of measurement of lifetime, using the same unit for the product “lifetime×lifequality” is confusing.

Saying that quality is rated on a scale from 0 to 1, we, in fact, have implicitly transformed the real but unknown scale of quality into a standard scale, where 0 denotes no quality at all and 1 the 100% of quality expected (lifequality expectancy). Therefore, QALYs and DALYs, combining actual years (axis x) and dimensionless quality (axis y), are, in fact, semi-standardised measures.

We can do the same with the dimension of time, assigning 0 to birth and 1 to lifetime expectancy. Continuing the example above, the dimensionless 1 is assigned to 80y, the dimensionless 0.625 to 50y (50y/80y) and the dimensionless 0.375 to 30y (30y/80y). Thus, fully standardised QALYs = SQALYs = 0.67×0.625 = 0.41875, and fully standardised DALYs = SDALYs = 0.33×0.625+1.00×0.375 = 0.58125; that is, 41.875% of the life expected to be lived was actually lived and 58.125% was lost. Again SQALYs+SDALYs = 1 = 100% =  life expectancy.

These transformed to fully dimensionless standardised measures seem to be more understandable: SQALYs are the percentage of life lived, and SDALYs the percentage of life lost; as their sum equals 1, they are complementary. They do not measure life as lifetime; therefore they are not misleading. And thirdly they permit comparisons between countries, nations, sub-nations, etc, with different lifetime expectancy.

In contrast, we could of course un-standardise both axes, by assigning lifequality its real scale, but it remains to be discovered.