Description Usage Arguments Details Value References See Also Examples

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

1 2 3 4 5 6 7 8 9 10 11 12 13 |

`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 |

`kranges` |
A vector of size two, giving the min and max of the |

`keep.lt` |
Logical. If |

`keep.rho` |
Logical. If |

`...` |
Additional arguments passed to the underlying function. For |

`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. |

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.

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.

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

`mortcast`

, `mortcast.blend`

, `PMDrho`

1 2 3 4 5 6 7 8 9 10 11 12 13 | ```
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")
``` |

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