probability of dying between exact ages 15 and 50 — q15_to

Converts seven five-year age-specific mortality rates into ${}_{35}q_{15}$, the probability that someone alive at exact age 15 dies before exact age 50, under the synthetic-cohort assumption that these rates hold constant.

Usage

q15_to_50(nmx, n = 5, nax = 2.6, per = 1000)

Arguments

nmx: seven age-specific mortality rates for the groups 15–19 through 45–49, in the order returned by siblingsurvival::reproductive_age_groups(), as rates per person-year
n: width of each age interval in years
nax: see nmx_to_nqx; the default matches the DHS and MICS implementations
per: express the result per this many people. 1000 is the convention in both DHS and MICS reports

Value

a single number

Details

$${}_{35}q_{15} = 1 - \prod_{x} (1 - {}_5q_x)$$

nmx must be rates, not counts, and must not already be multiplied by 1,000 — a common way to get an answer that is wrong by orders of magnitude.

Examples

  # Gambia 2019-20 DHS, Table 14.1 rates per 1,000; report gives 114 and 124
  women <- c(0.93, 1.55, 2.24, 3.27, 3.57, 6.27, 6.25) / 1000
  men   <- c(1.44, 2.30, 2.29, 3.40, 4.91, 6.11, 6.11) / 1000
  q15_to_50(women)
#> [1] 113.4885
  q15_to_50(men)
#> [1] 124.4195