PAS a(x) rule of thumb. — lt_a

a(x) is calculated following the Coale-Demeny rules for ages 0 and 1-4, and assumes interval midpoints in higher ages. This is just a rule of thumb. This procedure is as found in the PAS spreadsheet LTPOPDTH.XLS.

lt_a_pas(
  nMx,
  AgeInt,
  a0rule = "ak",
  IMR = NA,
  Sex = "m",
  region = "w",
  SRB = 1.05,
  OAG = TRUE
)

Arguments

nMx	numeric. Event exposure mortality rates.
AgeInt	integer. Vector of age interval widths.
a0rule	character. Either `"ak"` (default) or `"cd"`.
IMR	numeric. Optional. q₀, the death probability in first year of life, in case available separately.
Sex	character. `"m"`, `"f"` or `"b"` for male, female, or both.
region	character. `"n"`, `"e"`, `"s"` or `"w"` for North, East, South, or West.
SRB	numeric. The sex ratio at birth (boys/girls), default 1.05.
OAG	logical. Whether or not the last element of `nMx` is the open age group Default `TRUE`.

Value

nax average contribution to exposure of those dying in the interval.

Details

If sex is given as both, "b", then female values are taken for a(0) and 4a1, per the PAS spreadsheet. If IMR is not given, the M(0) is used to estimate a(x) for ages < 5. This function is not vectorized. a(x) closeout assumes constant mortality hazard in the open age group. One safeguard is different from PAS: If assuming the interval midpoint implies a qx greater than 1, then we derive a(x) for the interval by assuming midpoint a(x) for each single age within the interval along with a constant death rate.

References

United Nations (1983). Manual X: Indirect Techniques for Demographic Estimation, number 81. United Nations Department of International Economic and Social Affairs, New York. United States Census Bureau (2017). “Population Analysis System (PAS) Software.” https://www.census.gov/data/software/pas.html, https://www.census.gov/data/software/pas.html.

Examples

 Exposures <- c(100958,466275,624134,559559,446736,370653,301862,249409,
     247473,223014,172260,149338,127242,105715,79614,53660,
     31021,16805,8000,4000,2000,1000)

 Deaths <- c(8674,1592,618,411,755,1098,1100,1357,
     1335,3257,2200,4023,2167,4578,2956,4212,
     2887,2351,1500,900,500,300)
 # lower age bounds
 Age    <- c(0, 1, seq(5, 100, by = 5))
 AgeInt <- c(diff(Age), NA)
 nMx <- Deaths/Exposures
 lt_a_pas(nMx = nMx,AgeInt = AgeInt,Sex = 'm',region = 'n',OAG = TRUE)
#>  [1] 0.299150 1.614835 2.500000 2.500000 2.500000 2.500000 2.500000 2.500000
#>  [9] 2.500000 2.500000 2.500000 2.500000 2.500000 2.500000 2.500000 2.500000
#> [17] 2.500000 2.500000 2.500000 2.500000 2.500000 3.333333
 lt_a_pas(nMx = nMx,AgeInt = AgeInt,Sex = 'm',a0rule = "cd",region = 'n',OAG = TRUE)
#>  [1] 0.2750276 1.6148347 2.5000000 2.5000000 2.5000000 2.5000000 2.5000000
#>  [8] 2.5000000 2.5000000 2.5000000 2.5000000 2.5000000 2.5000000 2.5000000
#> [15] 2.5000000 2.5000000 2.5000000 2.5000000 2.5000000 2.5000000 2.5000000
#> [22] 3.3333333