convert age-specific mortality rates to probabilities of dying

The standard life table conversion,

Usage

nmx_to_nqx(nmx, n = 5, nax = 2.6)

Arguments

nmx

age-specific mortality rates, as rates per person-year (so divide by 1,000 first if you have them per 1,000)

n

width of the age interval in years

nax

average years lived in the interval by those who die in it. The default of 2.6 is what both the DHS and the MICS tabulation code use; pass 2.5 for the textbook value. See Details

Value

a vector of probabilities, the same length as nmx

Details

$${}_nq_x = \frac{n \cdot {}_nm_x}{1 + (n - {}_na_x) \cdot {}_nm_x}$$

where nax is the average number of years lived in the interval by those who die in it.

Details

On the default. With n = 5, nax = 2.6 makes the denominator 1 + 2.4 * nmx, which is what Chap16_AM/AM_rates.do:1085 and the MICS6 TM.9 syntax both compute. AM_rates.do carries the comment "See DHS Guide to Statistics for use of 2.4 rather than 2.5", so it is deliberate on the DHS side; the MICS syntax uses the same value while its own header documents 2.5.

The difference is small — around 0.2 per 1,000 on a 35q15 of 200 — but it is free to get right, and published figures are rounded to integers, so it cannot be recovered by comparing against them.

Examples

  # Gambia 2019-20 DHS, women, Table 14.1, rates per 1,000
  nmx <- c(0.93, 1.55, 2.24, 3.27, 3.57, 6.27, 6.25) / 1000
  nmx_to_nqx(nmx)
#> [1] 0.004639644 0.007721277 0.011140111 0.016222684 0.017698360 0.030885239
#> [7] 0.030788177