LifeTable: Compute Life Tables from Mortality Data

Description

Construct either a full (single-year age intervals) or an abridged (wider age intervals) life table from a variety of input data types. The function accepts:

Death counts and mid-interval population estimates (Dx, Ex)
Age-specific death rates (mx)
Death probabilities (qx)
Survivorship curve (lx)
Distribution of deaths (dx)

Only one of these input options needs to be provided; the others are ignored if present. The input can be a numeric vector, matrix, or data.frame. When a matrix or data.frame with multiple columns is supplied, the function computes one life table per column.

Usage

LifeTable(x, Dx = NULL, Ex = NULL,
             mx = NULL,
             qx = NULL,
             lx = NULL,
             dx = NULL,
             sex = NULL,
             lx0 = 1e5,
             ax  = NULL)

Value

An object of class "LifeTable" containing the following components:

lt: A data.frame with the complete life table, including columns for age interval (x.int), exact age (x), death rate (mx), death probability (qx), person-years lived by decedents (ax), survivorship (lx), death distribution (dx), person-years lived (Lx), total person-years remaining (Tx), and life expectancy (ex).
call: The matched function call.
process_date: Timestamp of when the life table was computed.

Arguments

x: Numeric vector of ages at the beginning of each age interval. For a full life table, use single-year ages (e.g., 0:110). For an abridged life table, use the lower bound of each interval (e.g., c(0, 1, 5, 10, ..., 110)).
Dx: Death counts. Each element represents the total number of deaths during the calendar year to persons aged x to x + n (where n is the length of the age interval). Must be provided together with Ex.
Ex: Exposure-to-risk in the period. This is usually approximated by the mid-year population aged x to x + n. Must be provided together with Dx.
mx: Age-specific death rate in the age interval [x, x+n). Defined as Dx / Ex.
qx: Probability of dying within the age interval [x, x+n).
lx: Probability of surviving to exact age x (if lx0 = 1), or the number of survivors at exact age x (if lx0 > 1). When lx is the sole input, the values are re-scaled to the chosen radix lx0.
dx: Number of deaths in the life-table population occurring in the age interval [x, x+n). When dx is the sole input, the values are re-scaled to sum to lx0.
sex: Sex of the population. Options are NULL (default), "male", "female", or "total". When specified, the first two entries of the ax column are adjusted using Coale-Demeny coefficients, producing more accurate life-table values at the youngest ages. The adjustment differs slightly between males and females.
lx0: Radix, the starting population (or probability scale) at age 0. Default is 100,000. All subsequent life-table columns (lx, dx, Lx, Tx) are scaled accordingly.
ax: Numeric vector representing the average number of person-years lived in the age interval by those who die in that interval. If NULL (the default), ax is estimated internally using a standard formula. You may supply a single value (applied to all intervals) or a vector of the same length as x. A common assumption is ax = 0.5, which places deaths at the midpoint of each interval.

Author

Marius D. Pascariu

Details

A life table (also called a mortality table or actuarial table) summarises the mortality experience of a population. For each age (or age interval) it reports:

Death rates (mx) and death probabilities (qx)
Survivorship (lx)
Distribution of deaths (dx)
Person-years lived (Lx) and total person-years remaining (Tx)
Life expectancy (ex)

The life table is constructed sequentially: from the input data the function derives mx, then qx, then lx, dx, Lx, Tx, and finally ex. The constant-force-of-mortality (CFM) assumption is used to convert between mx and qx. If the sex argument is supplied, the first two values of the ax column are adjusted using the Coale-Demeny method, which accounts for the different infant mortality patterns between males and females.

Examples

Run this code

# Example 1 --- Full life tables with different inputs ------------

y  <- 1900
x  <- as.numeric(rownames(ahmd$mx))
Dx <- ahmd$Dx[, paste(y)]
Ex <- ahmd$Ex[, paste(y)]

LT1 <- LifeTable(x, Dx = Dx, Ex = Ex)
LT2 <- LifeTable(x, mx = LT1$lt$mx)
LT3 <- LifeTable(x, qx = LT1$lt$qx)
LT4 <- LifeTable(x, lx = LT1$lt$lx)
LT5 <- LifeTable(x, dx = LT1$lt$dx)

LT1
LT5
ls(LT5)

# Example 2 --- Compute multiple life tables at once ------------

LTs <- LifeTable(x, mx = ahmd$mx)
LTs
# A warning is printed if the input contains missing values.
# Some of the missing values can be handled automatically.

# Example 3 --- Abridged life table -----------------------------

x  <- c(0, 1, seq(5, 110, by = 5))
mx <- c(.053, .005, .001, .0012, .0018, .002, .003, .004,
        .004, .005, .006, .0093, .0129, .019, .031, .049,
        .084, .129, .180, .2354, .3085, .390, .478, .551)
LT6 <- LifeTable(x, mx = mx, sex = "female")
LT6

# Example 4 --- Abridged life table using a custom 'ax' --------
# This example reuses the ages (x) and death rates (mx) from Example 3.
# Note that 'ax' must have the same length as 'x', otherwise an error
# will be returned.

my_ax <- c(0.1, 1.5, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,
           2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1)

LT7 <- LifeTable(x = x, mx = mx, ax = my_ax)

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