LawTable: Compute Life Tables from Parameters of a Mortality Law

In mpascariu/MortalityLaws: Parametric Mortality Models, Life Tables and HMD

Compute Life Tables from Parameters of a Mortality Law

Description

Compute Life Tables from Parameters of a Mortality Law

Usage

LawTable(x, par, law, sex = NULL, lx0 = 1e+05, ax = NULL)

Arguments

x	Vector of ages at the beginning of the age interval.
par	The parameters of the mortality model.
law	The name of the mortality law/model to be used. e.g. gompertz, makeham, ... To investigate all the possible options, see availableLaws function.
sex	Sex of the population considered here. Default: NULL. This argument affects the first two values in the life table ax column. If sex is specified the values are computed based on the Coale-Demeny method and are slightly different for males than for females. Options: NULL, male, female, total.
lx0	Radix. Default: 100 000.
ax	Numeric scalar. Subject-time alive in age-interval for those who die in the same interval. If NULL this will be estimated. A common assumption is ax = 0.5, i.e. the deaths occur in the middle of the interval. Default: NULL.

Details

The "life table" is also called "mortality table" or "actuarial table". This shows, for each age, what the probability is that a person of that age will die before his or her next birthday, the expectation of life across different age ranges or the survivorship of people from a certain population.

Value

The output is of the "LifeTable" class with the components:

lt	Computed life table;
call	Call in which all of the specified arguments are specified by their full names;
process_date	Time stamp.

Author(s)

Marius D. Pascariu

See Also

LifeTable MortalityLaw

Examples

# Example 1 --- Makeham --- 4 tables ----------
x1 = 45:100
L1 = "makeham"
C1 = matrix(c(0.00717, 0.07789, 0.00363,
              0.01018, 0.07229, 0.00001,
              0.00298, 0.09585, 0.00002,
              0.00067, 0.11572, 0.00078),
            nrow = 4, dimnames = list(1:4, c("A", "B", "C")))

LawTable(x = 45:100, par = C1, law = L1)

# WARNING!!!

# It is important to know how the coefficients have been estimated. If the
# fitting of the model was done over the [x, x+) age-range, the LawTable
# function can be used to create a life table only for age x onward.

# What can go wrong?

# ** Example 1B - is OK.
LawTable(x = 45:100, par = c(0.00717, 0.07789, 0.00363), law = L1)

# ** Example 1C - Not OK, because the life expectancy at age 25 is
# equal with life expectancy at age 45 in the previous example.
LawTable(x = 25:100, par = c(0.00717, 0.07789, 0.00363), law = L1)

# Why is this happening?

# If we have a model that covers only a part of the human mortality curve
# (e.g. adult mortality), in fitting the x vector is scaled down, meaning
# age (x) becomes (x - min(x) + 1). And, the coefficients are estimated on
# a scaled x in ordered to obtain meaningful estimates. Otherwise the
# optimization process might not converge.

# What can we do about it?

# a). Know which mortality laws are rescaling the x vector in the fitting
# process. If these models are fitted with the MortalityLaw() function, you
# can find out like so:
A <- availableLaws()$table
A[, c("CODE", "SCALE_X")]

# b). If you are using one of the models that are applying scaling,
# be aware over what age-range the coefficients have been estimated. If they
# have been estimated using, say, ages 50 to 80, you can use the
# LawTable() to build a life tables from age 50 onwards.


# Example 2 --- Heligman-Pollard -- 1 table ----
x2 = 0:110
L2 = "HP"
C2 = c(0.00223, 0.01461, 0.12292, 0.00091,
       2.75201, 29.01877, 0.00002, 1.11411)

LawTable(x = x2, par = C2, law = L2)

# Because "HP" is not scaling down the x vector, the output is not affected
# by the problem described above.

# Check
LawTable(x = 3:110, par = C2, law = L2)
# Note the e3 = 70.31 in both tables

mpascariu/MortalityLaws documentation built on Jan. 17, 2024, 3:43 a.m.