CalcRemainLifeExp {paramDemo}

Calculating Remaining Life Expectancy.

Description

CalcRemainingLifeExp calculates remaining life expectancy from parametric models of age-specific mortality.

Usage

CalcRemainLifeExp (theta, x = NULL, dx = NULL, xmax = NULL,
                              atAllAges = FALSE, model = "GO", 
                              shape = "simple", checkTheta = TRUE)

Arguments

theta

Numerical vector of age-specific mortality parameters (see details).

x

Numerical vector of ages at which to calculate mortality.

dx

Numerical value for the width of age intervals used for integration. If NULL, default is dx = 0.01

xmax

Numerical value for the maximum age. If NULL, the value is obtain as the age when the surviva

atAllAges

Logical to indicate whether ageing rates should be provided between ages 0 and xmax

model

The underlying mortality model to be used. "EX" = exponential,"GO" = Gompertz, "WE" = Weibull and "LO" = logistic (see details).

shape

The overall shape of the model. Values are: simple = no extra parameters added; Makeham = a constant parameter is added to the mortality; and bathtub = a Gompertz declining mortality for early ages and a constant parameter are added to the mortality model (see details).

checkTheta

Logical to verify that the beta parameters conform with the model's specification (see details).

Details

The function CalcAgeingRate uses parametric functions to calculate the actuarial (i.e., survival) rate of ageing. The function follows the conventions from package BaSTA (Colchero and Clark 2012, Colchero et al. 2012, Colchero et al. 2021) to select the parametric model of mortality. The mortality function describes how the risk of mortality changes with age, and is defined as

\mu(x | \theta) = \lim_{\Delta x \rightarrow 0} \frac{\Pr[x < X < x + \Delta x | X > x]}{\Delta x},

where X is a random variable for ages at death, x \geq 0 are ages and \theta is the vector of mortality parameters. From the mortality function, the survival function is then given by

S(x | \theta) = \exp[-\int_0^x \mu(t | \theta) dt].

(For further details on the mortality and survival models see CalcMort).

Given a vector of ages x_1, x_2, \dots, x_n specified by the user with argument x, the function calculates the remaining life expectancy at age x_i as

e_{x_i} = \frac{\int_{x_i}^{\infty} S(t) dt}{S(x_i)}

for i = 1, 2, \dots, n.

Value

The function outputs a matrix with the ages from which remaining life expectancies were calculated, and the values for the remaining life expectancy.

Author(s)

Fernando Colchero [e-mail]

See Also

CalcSurv to calculate age-specific survival, CalcMort to calculate age-specific mortality, CalcFert to calculate age-specific fertility.

CalcAgeMaxFert to calculate the age at maximum fertility from parametric models of age-specific fertility. CalcAgeingRateMort to calculate ageing rates from parametric models of age-specific mortality.

Examples

# Calculate ageing rate from Gompertz model:
rle <- CalcRemainLifeExp(theta = c(b0 = -5, b1 = 0.1), x = 10)

# Calculate ageing rate from Siler model:
rle <- CalcRemainLifeExp(theta = c(a0 = -1, a1 = 1, c = 0.0001, 
                          b0 = -6, b1 = 0.15), x = 10,
                     model = "GO", shape = "bathtub")