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

Let ${}_nf_x$ be the age-specific fertility rate for people aged between $x$ and $x+n$. Values for ${}_nf_x$ are obtained by scaling the standard rates ${}_nf_x^{\mathrm{std}}$ so that they agree with the target total fertility rate $F$. That is, tfr_to_asfr_scale() sets

$${}_nf_x = \alpha \times {}_nf_x^{\mathrm{std}}$$

where

$$\alpha = \frac{F}{\sum_x n \times {}_nf_x^{\mathrm{std}}}$$

The `target` argument

target is a data frame specifying total fertility rates for each population being modelled.

target contains the following variables:

A variable called "tfr". An ordinary numeric vector or an rvec().
Optionally, 'by' variables. Typical examples are time, region, and model variant.

The `standard` argument

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

standard contains the following variables:

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.

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

## target is an rvec
library(rvec, warn.conflicts = FALSE)
target_rvec <- data.frame(region = c("A", "B"), 
                          tfr = rnorm_rvec(n = 2,
                                           mean = c(5.5, 4.7),
                                           n_draw = 1000))
tfr_to_asfr_scale(target = target_rvec,
                  standard = booth_standard)
#> # A tibble: 16 × 3
#>    region age                      asfr
#>    <chr>  <chr>            <rdbl<1000>>
#>  1 A      10-14  0.003 (0.0019, 0.0041)
#>  2 A      15-19       0.15 (0.093, 0.2)
#>  3 A      20-24       0.27 (0.17, 0.36)
#>  4 A      25-29       0.25 (0.16, 0.35)
#>  5 A      30-34       0.21 (0.13, 0.28)
#>  6 A      35-39       0.15 (0.094, 0.2)
#>  7 A      40-44    0.068 (0.043, 0.092)
#>  8 A      45-49  0.0089 (0.0057, 0.012)
#>  9 B      10-14 0.0026 (0.0015, 0.0037)
#> 10 B      15-19      0.13 (0.072, 0.18)
#> 11 B      20-24       0.23 (0.13, 0.32)
#> 12 B      25-29       0.22 (0.13, 0.31)
#> 13 B      30-34        0.18 (0.1, 0.25)
#> 14 B      35-39      0.13 (0.073, 0.18)
#> 15 B      40-44    0.058 (0.034, 0.082)
#> 16 B      45-49  0.0076 (0.0044, 0.011)