pmdgroup: Pattern of Mortality Decline Prediction

Description Usage Arguments Details Value References See Also Examples

Description

Predict age-specific mortality rates using the Pattern of mortality decline (PMD) method (Andreev et al. 2013).

Usage

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pmd(
  e0,
  mx0,
  sex = c("male", "female"),
  nx = 5,
  interp.rho = FALSE,
  kranges = c(0, 25),
  keep.lt = FALSE,
  keep.rho = FALSE,
  ...
)

copmd(e0m, e0f, mxm0, mxf0, nx = 5, interp.rho = FALSE, keep.rho = FALSE, ...)

Arguments

e0

A vector of target life expectancy, one element for each predicted time point.

mx0

A vector with starting age-specific mortality rates.

sex

Either "male" or "female".

nx

Size of age groups. Should be either 5 or 1.

interp.rho

Logical controlling if the ρ coefficients should be interpolated (TRUE) or if the raw (binned) version should be used (FALSE), as stored in the dataset PMDrho.

kranges

A vector of size two, giving the min and max of the k parameter which is estimated to match the target e0 using the bisection method.

keep.lt

Logical. If TRUE additional life table columns are kept in the resulting object.

keep.rho

Logical. If TRUE the ρ coefficients are included in the resulting object.

...

Additional arguments passed to the underlying function. For copmd, in addition to kranges and keep.lt, it can be sexratio.adjust which is a logical controlling if a sex-ratio adjustment should be applied to prevent crossovers between male and female mx. In such a case it uses coefficients from the PMDadjcoef dataset. However, if the argument adjust.with.mxf is set to TRUE (in addition to sexratio.adjust), the adjustment is done using the female mortality rates as the lower constraint for male mortality rates. If the argument adjust.sr.if.needed is set to TRUE, a sex-ratio adjustment is performed dynamically, using the sex ratio in the previous time point. In such a case, an adjustment in time t is applied only if there was a drop of sex ratio below one at time t-1.

e0m

A time series of target male life expectancy.

e0f

A time series of target female life expectancy.

mxm0

A vector with starting age-specific male mortality rates.

mxf0

A vector with starting age-specific female mortality rates.

Details

These functions implements the PMD method introduced in Andreev et al. (2013). It assumes that the future decline in age-specific mortality will follow a certain pattern with the increase in life expectancy at birth (e0):

\log mx(t) = \log mx(t-1) - k(t) ρ_x(t)

Here, ρ_x(t) is the age-specific pattern of mortality decline between t-1 and t. Such patterns for each sex and various levels of e0 are stored in the dataset PMDrho. The pmd function can be instructed to interpolate between neighboring levels of e0 by setting the argument interp.rho to TRUE. The k parameter is estimated to match the e0 level using the bisection method.

Function pmd evaluates the method for a single sex, while copmd does it coherently for both sexes. In the latter case, the same ρ_x (namely the average over sex-specific ρ_x) is used for both, male and female.

Value

Function pmd returns a list with the following elements: a matrix mx with the predicted mortality rates. If keep.lt is TRUE, it also contains matrices sr (survival rates), and life table quantities Lx and lx. If keep.rho is TRUE, it contains a matrix rho where columns correpond to the values in the e0 vector and rows correspond to age groups.

Function copmd returns a list with one element for each sex (male and female) where each of them is a list as described above. In addition if keep.rho is TRUE, element rho.sex gives the sex-dependent (i.e. not averaged) ρ_x coefficient.

References

Andreev, K., Gu, D., Gerland, P. (2013). Age Patterns of Mortality Improvement by Level of Life Expectancy at Birth with Applications to Mortality Projections. Paper presented at the Annual Meeting of the Population Association of America, New Orleans, LA. https://paa2013.princeton.edu/papers/132554.

Gu, D., Pelletier, F., Sawyer, C. (2017). Projecting Age-sex-specific Mortality: A Comparison of the Modified Lee-Carter and Pattern of Mortality Decline Methods, UN Population Division, Technical Paper No. 6. New York: United Nations. https://population.un.org/wpp/Publications/Files/WPP2017_TechnicalPaperNo6.pdf

See Also

mortcast, mortcast.blend, PMDrho

Examples

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data(mxF, e0Fproj, package = "wpp2017")
country <- "Hungary"
# get initial mortality for the current year
mxf <- subset(mxF, name == country)[,"2010-2015"]
names(mxf) <- c(0,1, seq(5, 100, by=5))
# get target e0
e0f <- subset(e0Fproj, name == country)[-(1:2)]
# project into future
pred <- pmd(e0f, mxf, sex = "female")
# plot first projection in black and the remaining ones in grey 
plot(pred$mx[,1], type = "l", log = "y", ylim = range(pred$mx),
    ylab = "female mx", xlab = "Age", main = country)
for(i in 2:ncol(pred$mx)) lines(pred$mx[,i], col = "grey")

PPgp/MortCast documentation built on Aug. 8, 2021, 5:17 p.m.