gen_lifetable_parameters: Generate life table parameters

In ihmeuw-demographics/demCore: Core Functions for Demography

Generate life table parameters

Description

These functions perform life table calculations, to add selected life table parameters from others, using established demographic relationships.

Usage

gen_lx_from_qx(dt, id_cols, assert_na = T)

gen_qx_from_lx(dt, id_cols, assert_na = T)

gen_dx_from_lx(dt, id_cols, assert_na = T)

gen_nLx(dt, id_cols, assert_na = T)

gen_Tx(dt, id_cols, assert_na = T)

gen_ex(dt, assert_na = T)

Arguments

dt	[data.table()] Life table(s). Includes columns 'age_start', 'age_end', and all id_cols. Additionally: gen_lx_from_qx requires 'qx' gen_qx_from_lx requires 'lx' gen_dx_from_lx requires 'lx' gen_nLx requires 'lx', 'ax', 'dx' gen_Tx requires 'nLx' gen_ex requires 'lx', 'Tx'
id_cols	[character()] Columns that uniquely identify each row of dt. Must include 'age_start' and 'age_end'.
assert_na	[logical()] Whether to check for NA values in the generated variable.

Details

Parameter definitions:
For an age interval x to x+n:

• mx = mortality rate (deaths / person-years)

• qx = probability of death, conditional on survival to x-th birthday

• ax = average years lived of those who died in the age interval

• dx = number (or proportion of cohort) who died in the age interval

• lx = number (or proportion of cohort) alive at the beginning of the age interval

• ex = life expectancy, expected value for years lived after age x

• Tx = total person-years lived beyond age x

• nLx = total person-years lived in interval

gen_lx_from_qx: Use probability of death (qx) to get the proportion of survivors in the beginning of an age group (lx). l0 = 1; lx for ages > 0 is lx for previous age group times the probability of surviving the previous age group.

gen_qx_from_lx: Use survival proportion (lx) at age x and x+n to get probability of death between x and x+n (qx). This relationship is an algebraic equivalent to the gen_lx_from_qx relationship as described. Terminal age qx is set to 1.

gen_dx_from_lx: Calculate the proportion dying between age x and x+n (dx) as the difference between the proportion surviving (lx) at age x and the proportion surviving at age x+n. In the terminal age group all survivors die in the age group, so dx = lx.

gen_nLx: nLx is calculated as the sum of years lived by survivors and years lived by those who die between ages x and x+n. The first component is n times l(x+n). The second component is ax * dx. For terminal ages, assume that average person years lived equals number at the start of the age group divided by the mortality rate.

gen_Tx: Person-years lived above age x (Tx) is the cumulative sum of person-years lived by people in each age interval above age x (nLx). For the terminal age group, Tx = nLx.

gen_ex: Life expectancy (ex) at age x is based on person-years lived above the age group (Tx) and proportion of people alive at the start of age group (lx): ex = Tx / lx.

Value

dt with column added for new life table parameter. Modifies data.tables in place.

See Also

• mx_qx_ax_conversions

• lifetable

• vignette("introduction_to_life_tables", package = "demCore")

Examples

dt <- data.table::data.table(
  sex = rep("both", 4),
  age_start = c(0, 5, 10, 15),
  age_end = c(5, 10, 15, Inf),
  age_length = c(5, 5, 5, Inf),
  mx = c(0.1, 0.2, 0.3, 0.4),
  ax = c(2.5, 2.5, 2.5, 2.5)
)
dt[, qx := mx_ax_to_qx(mx, ax, age_length)]
gen_lx_from_qx(dt, id_cols = c("sex", "age_start", "age_end"))
gen_dx_from_lx(dt, id_cols = c("sex", "age_start", "age_end"))
gen_nLx(dt, id_cols = c("sex", "age_start", "age_end"))
gen_Tx(dt, id_cols = c("sex", "age_start", "age_end"))
gen_ex(dt)
gen_qx_from_lx(dt, id_cols = c("sex", "age_start", "age_end"))

ihmeuw-demographics/demCore documentation built on Feb. 24, 2024, 11:05 p.m.