the DALY Calculator
a generic tool for stochastic DALY calculation in R

## Definition & Interpretation

The disability-adjusted life year or DALY is a summary measure of population health widely used in disease burden assessment studies and cost-utility analyses (Murray and Lopez, 1996; Lopez et al., 2006). DALYs represent the incident number of healthy life years lost due to disease or disability, and do so by incorporating non-fatal and fatal health outcomes, calculated as the years of life lived with disability (YLD) and the years of life lost due to premature death (YLL), respectively.

Since DALYs measure the losses from disability or death, diseases accounting for more DALYs have a higher public health impact than diseases accounting for less DALYs. Likewise, health measures will be beneficial if they are able to reduce the number of DALYs.

DALYs can be expressed as an absolute number, thereby giving an idea of the total burden suffered by the population. They can also be expressed relative to the population, e.g., as the number of DALYs lost per 1000 population. This enables a direct comparison of the burden suffered by different populations or different population subgroups. Finally, DALYs may also be expressed relative to the number of incident cases. This allows to assess and compare the impact of diseases at the patient-level, instead of at the population-level.

The DALY has become a key measure employed by the World Health Organization in its Global Burden of Disease project. Moreover, more and more nations are performing national DALY calculations to assess and monitor their population's health and to set priorities within their health sector.

## Basic formulas

DALYs are the sum of YLDs and YLLs, per disease category or outcome, and per age and sex class:

````DALY = YLD + YLL`
```

The YLDs are the morbidity component of the DALYs, and are proportional to the number of incident cases and the severity of the disease:

````YLD = Number of Cases * Disease Duration * Disability Weight`
```

The Disability Weights are a crucial component of the DALY calculation, as they enable the direct comparison of morbidity and mortality. The Disability Weight of a disease category or health outcome reflects its severity, on a scale from zero (perfect health) to one (worst possible health state). The higher the disease severity is, the higher the reduction in healthy life is for people suffering from the disease.

The YLLs are the mortality component of the DALYs, and are proportional to the number of deaths and the average age of death:

````YLL = Number of Deaths * Life expectancy at age of death`
```

## Social weighting

The basic formulas for YLDs, YLLs and DALYs may be extended by applying so-called social weighting functions. Unlike the basic formulas, the application of social weighting implies that not all life years lost are valued equally. Social weighting is therefore not accepted by all authors.

### Age weighting

The initial Global Burden of Disease study, and many ensuing studies, applied non-uniform age weights, implying that the value of life depends on age. A higher weight is given to the healthy life years lived between the age of 9 and 54, as this period of life is considered to be socially more important than the younger and older life spans (Murray, 1994).

The standard age weighting formula is as follows:

````Weight = 0.1658 * age * e(-0.04 * age)`
```

### Time discounting

Time discounting discounts the years of healthy life lived in the future, at a rate of (usually) 3%. The incorporation of a time discount rate reflects similar practices in economic assessments, and would prevent policy makers from saving resources for a possible future eradication program, instead of investing in currently available, but less effective, intervention measures (the so-called "disease eradication and research paradox"; Murray, 1994).

The standard time discounting formula is as follows:

````Weight = e(-0.03 * [age - a])`
```

Where a is the age at onset or death.