---
title: "Value of life-years lost"
output: rmarkdown::html_vignette
bibliography: resources/references.json
link-citations: true
vignette: >
  %\VignetteIndexEntry{Value of life-years lost}
  %\VignetteEngine{knitr::rmarkdown}
  %\VignetteEncoding{UTF-8}
---

```{r, include = FALSE}
knitr::opts_chunk$set(
  collapse = TRUE,
  comment = "#>"
)
```

This vignette explains how the value of lives lost due to infection in a pandemic scenario is calculated in _daedalus_.

The main focus is on explaining how the value of a statistical life (VSL, also referred to hereafter as 'life-value') is calculated in _daedalus_.
The VSL is multiplied by the number of deaths to get the total value of life-years lost due to the pandemic.

The methodology used here has been chosen so as to be generalisable for the widest possible range of countries and territories, while using publicly available data.

This approach balances the ability to run _daedalus_ scenarios for a large number of countries, and the effort required to obtain and update official life-values from national governments.

::: {.alert .alert-info}
**Note that** the VSL values used in a call to `daedalus()` for any country can always be substituted with values considered to be more appropriate (e.g., from a national health ministry).
:::

## Value of a life year

The value of a life year (VLY) in a country is assumed to be the gross national income (GNI) per capita scaled for purchasing power parity in international dollars.

Country GNI values are for the most recent year available, and are taken from the [World Bank's World Development Indicators](https://databank.worldbank.org/source/world-development-indicators).

::: {.alert .alert-info}
**Note that** there is no discounting applied to older age groups, that is, all remaining years of life are valued the same, and are not adjusted for disabilities or quality.
:::

## Life expectancy

Life-expectancy data in terms of years for each country and territory is initially accessed for age-bins and separated by sex.

The life-expectancy data is then aggregated by the DAEDALUS age bins: 0 -- 4, 5 -- 19 (school age), 20 -- 65 (working age), 65+ (retired or not working).

::: {.alert .alert-warning}
**Note that** the aggregation of is a simple mean across all age-bins in the raw data; a more appropriate approach which we aim to add in future would be a weighted mean that takes into account the size of each age-bin in the raw data.
:::

This results in four life-expectancy values for each country, each corresponding to one of the four DAEDALUS age groups.

## Value of a statistical life

::: {.alert .alert-info}
Many policies aim to improve longevity, decreasing the risk of death in each year.
The value of these risk reductions is often expressed as the value per statistical life (VSL); at times a value per statistical life year (VSLY) may be used.

The VSL concept is widely misunderstood. It is not the value that the analyst, the government, or the individual places on saving an identified life with certainty. Instead, it reflects individuals' willingness to exchange money for a small change in their own risk, such as a 1 in 10,000 decrease in the chance of dying in a specific year [@robinson2019].
:::

The value of a statistical life for an individual of country $c$ in age group $i$ denoted as $\text{VSL}_{c_i}$ is the product of the country-specific VLY ($\text{VLY}_{c}$) and the country- and age-specific life expectancy ($T_{c_i}$), and depends on the country and age-group of the individual; this can be expressed as:

$$\text{VSL}_{c_i} = \text{VLY}_c \times T_{c_i}$$

In _daedalus_, the country- and age-specifc VSL values can be accessed from the package data object `daedalus::life_value`.
These values are also automatically accessed and included when a `<daedalus_country>` object is created, under the name `vsl`.

```{r vsl_example}
# load library for examples
library(daedalus)

# create a <daedalus_country>
x <- daedalus_country("China")

# access VSL values using either a helper function or
# the subsetting operator
get_data(x, "vsl")

x$vsl
```

## Value of lives lost

In a `daedalus()` scenario, the total value of lives lost is the sum of the products of the country- and age-specific VSL and the number of deaths in each age-group in that country:

$$\Sigma_{i = 1}^{N} \text{VSL}_{c_i} \times D_i$$

where $D_i$ is the total number of deaths in age group $i$, with $i \in 1, 2, 3, 4$ (as detailed above).

For users' convenience, the total value of lives lost is reported in million dollars, to bring it in line with the scaling used for other pandemic costs.

## References