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# 6. Calculation of DALYs for quantal health effects

The principles of the directly attributable health loss calculation are introduced first for DALYs and quantal effects (effects that are modelled as either absent or present, e.g. cancer). The following sections describe how the calculation differs for continuous effects (effects expressed as a change in a continuous variable, such as a change in body weight), and for QALYs.

The calculation takes account of three alternative outcomes of each effect: an individual may recover, die early as a result of the disease, or survive with the disease until the normal life expectancy. It allows for the possibility that the severity of the disease (represented by DALY weights,
*w*
) may differ between individuals who recover, individuals who die from the disease, and those who continue living with the disease until their normal life expectancy, although in many cases these are the same.

For an individual that recovers, the DALY loss is calculated as:

_{
}

where:

*YLD
_{
rec
}*
= duration of disease for those who recover

*w
_{
rec
}*
= DALY weight for disease, for those who recover.

For an individual that does not recover, but survives with the disease until their normal life expectancy, the DALY loss is:

_{
}

where:

*
CA
*
= current age of individual in year of disease onset

*LE*
= normal life expectancy
[1]
(generally a function of current age)

*w
_{
live
}*
= DALY weight for disease, for those who continue living with it until their normal life expectancy
.

For an individual that dies from the disease, the DALY loss is:

_{
}

where:

*YLD
_{
die
}*
= duration of disease (years lived with disease) for those who die of it

*w
_{
die
}*
= DALY weight for disease, for those who die from the disease.

Note that the loss for those who die comprises two parts: the DALY loss for the period prior to death (
_{
}
) and the loss of years due to dying earlier than would be expected without the disease.

The average DALY loss for individuals who get the disease can be obtained as a weighted average of the three contributions:

_{
}
where

*p
_{
rec
}*
= probability of recovery from the effect

*p
_{
die
}*
= probability this effect causes death.

The expected total DALY loss due to this disease can then be estimated as:

_{
}

(Equation 1)

where

*p
_{
effect
}*
= probability of onset of the disease in the current year

*
I
_{
sf
}
*
= individual scaling factor.

[1] Note: life expectancy is sometimes defined as the number of years of life remaining, but here it is defined as the expected age at death.