Quality Adjusted Life Years (QALY)

Quality Adjusted Life Years (QALYs) are a measure of the length of life adjusted for the quality of that life. The quality of life should be measured using utility, which is the extent to which a person values one health state over another. Utility values typically vary between 0 and 1, where 1 is perfect health and 0 is death. In principle, it is possible to have values below 0 (indicating a state worse than death).
There are a range of ways to measure utility such as time-trade-off (TTO). In practice, though, utility values as usually inferred from health-related quality of life scales such as the EQ-5D.
QALYs are useful because they allow us to draw together complex information in order to allow us to make decisions that involve choosing between lots of different health-states at the same time. This is necessary for us to make comprehensible, reasonably transparent, and consistent healthcare decisions in a complex world.
For example, when comparing 15 years of very poor quality life (utility: 0.2) with 5 years of relatively good health (utility: 0.8), we might do the following calculations:

Poor quality life: 15 years x 0.2 utility = 3 quality adjusted life-years
Good quality life: 5 years x 0.8 utility = 4 quality adjusted life-years

On the basis of this, a health economist might argue that a rational person would choose 5 healthy years over 15 years of very poor health. The aspect of choice is important because the purpose of QALYs is to help us make difficult decisions objectively.
There are some core challenges with this approach, particularly the question of who determines the utility values we use (a patient with the condition or the general public) and whether we value gains (e.g. extended life) equally to losses (e.g. loss of health).