Derive Age-Specific Fertility Rates that Match Total Fertility Rates by Scaling

Turn total fertility rates (TFRs) into sets of age-specific fertility rates, by scaling a set of standard rates upwards or downwards.

Usage

tfr_to_asfr_scale(target, standard, suffix = NULL)

Arguments

target: A data frame containing a variable called "tfr", and possibly others. See Details.
standard: A data frame containing variables called age and asfr, and possibly others. See details.
suffix: Optional suffix added to asfr column in results.

Value

A tibble.

Method

The age-specific rates are derived by finding a value $\alpha$ such that

$$f_x = \alpha f_x^{\mathrm{std}}$$

and

$$sum_x f_x = F$$

where

$f_x$ is the age-specific fertility rate;
$f_x^{\mathrm{std}}$ is the standard schedule of rates;
$\alpha$ is a multiplier shared by all age groups; and
$F$ is the target total fertility rate.

`target` argument

target is a data frame specifying total fertility rates for each population being modelled, Values in target are not age-specific.

Variables in target:

A variable called "tfr". Can be an ordinary numeric variable, or an rvec().
Optionally, 'by' variables distinguishing populations, such as "region" or "time".

`standard` argument

standard is a data frame specifying standard fertility scedules to be used with each life expectancy in target. Values in standard are age-specific.

Variables in standard:

A variable called "age", with labels that can be parsed by reformat_age().
A variable called "value", containing non-negative values. Cannot be an rvec.
Additional variables used to match rows in standard to rows in target.

Internally, standard is merged with target using a left join from target, on any variables that target and standard have in common.

Examples

## create age-specific fertility rates
## based on the [Booth standard][booth_standard]
library(dplyr, warn.conflicts = FALSE)
target <- data.frame(region = c("A", "B"), 
                     tfr = c(5.5, 4.7))
asfr <- tfr_to_asfr_scale(target = target,
                          standard = booth_standard)
asfr
#> # A tibble: 16 × 3
#>    region age      asfr
#>    <chr>  <chr>   <dbl>
#>  1 A      10-14 0.00305
#>  2 A      15-19 0.146  
#>  3 A      20-24 0.266  
#>  4 A      25-29 0.254  
#>  5 A      30-34 0.206  
#>  6 A      35-39 0.147  
#>  7 A      40-44 0.0679 
#>  8 A      45-49 0.00893
#>  9 B      10-14 0.00260
#> 10 B      15-19 0.125  
#> 11 B      20-24 0.227  
#> 12 B      25-29 0.217  
#> 13 B      30-34 0.176  
#> 14 B      35-39 0.126  
#> 15 B      40-44 0.0580 
#> 16 B      45-49 0.00763

## check consistency with original TFRs
asfr |>
  tfr(asfr = asfr, by = region)
#> # A tibble: 2 × 2
#>   region   tfr
#>   <chr>  <dbl>
#> 1 A        5.5
#> 2 B        4.7