Package {demor}

Title:	Methods for Demographic Analysis
Version:	1.0.10
Description:	Implements life tables, fertility and mortality indicators, decomposition methods, Lee-Carter mortality forecasting, Leslie matrices, and population pyramids for demographic analysis. Methods are described in Preston et al. (2001, ISBN:1557864519) and Ustyuzhanin (2025) <doi:10.17323/demreview.v12i4.30415>.
License:	MIT + file LICENSE
Encoding:	UTF-8
RoxygenNote:	7.3.3
Imports:	dplyr, forecast, ggplot2, magrittr, tidyr, scales, splines
Depends:	R (≥ 4.0.0)
LazyData:	true
LazyDataCompression:	gzip
LazyLoad:	true
Suggests:	knitr, rmarkdown, stringr, testthat
URL:	https://vadvu.github.io/demor/, https://github.com/vadvu/demor
BugReports:	https://github.com/vadvu/demor/issues
Config/testthat/edition:	3
NeedsCompilation:	no
Packaged:	2026-05-18 16:41:59 UTC; vvust
Author:	Vadim Ustyuzhanin [aut, cre]
Maintainer:	Vadim Ustyuzhanin <vadim.v.ustyuzhanin@gmail.com>
Repository:	CRAN
Date/Publication:	2026-05-22 09:30:02 UTC

demor: Methods for Demographic Analysis

Description

Implements life tables, fertility and mortality indicators, decomposition methods, Lee-Carter mortality forecasting, Leslie matrices, and population pyramids for demographic analysis. Methods are described in Preston et al. (2001, ISBN:1557864519) and Ustyuzhanin (2025) doi:10.17323/demreview.v12i4.30415.

Author(s)

Maintainer: Vadim Ustyuzhanin vadim.v.ustyuzhanin@gmail.com (ORCID)

See Also

Useful links:

• https://vadvu.github.io/demor/

• https://github.com/vadvu/demor

• Report bugs at https://github.com/vadvu/demor/issues

Pipe operator

Description

See magrittr::%>% for details.

Usage

lhs %>% rhs

Arguments

Value

The result of calling rhs(lhs).

Life table

Description

Life table

Usage

LT(age, sex = "m", mx, ax = NULL, w = NULL, l0 = 1)

Arguments

Details

By default, a_x for age 0 (first entity in ax) is modeled as in Andreev & Kingkade (2015, p. 390, see table 3-2).

The weighted life expectancy is calculated as follows:

e_x^w = \frac{\sum_{i = x}^{\omega}L_x w_x}{l_x}

where \omega is the last age, w is weight s.t. w \in [0,1], and other variables are life table functions.

Value

A numeric matrix with one row per age group. Standard columns are age, mx, ax, qx, lx, dx, Lx, Tx, and ex. If w is supplied, additional columns w, wLx, and wex are appended, where wex is weighted life expectancy.

References

Andreev, E. M., & Kingkade, W. W. (2015). Average age at death in infancy and infant mortality level: Reconsidering the Coale-Demeny formulas at current levels of low mortality. Demographic Research, 33, 363-390.

See Also

MLT() for Multiple Decrement Life Table.

Examples

# Minimal toy example
age <- 0:5
mx <- c(0.02, 0.01, 0.012, 0.015, 0.02, 0.03)
LT(age = age, sex = "m", mx = mx)

if (interactive()) {
  # Real RosBris data via get_rosbris(): Russian males, 2010
  rus2010 <- subset(get_rosbris("mortality_5"),
    year == 2010 & code == 1100 & sex == "m" & territory == "t"
  )
  LT(age = rus2010$age, sex = "m", mx = rus2010$mx)
}

Multiple Decrement Life Table

Description

Multiple Decrement Life Table

Usage

MLT(age, mx, ...)

Arguments

Value

A numeric matrix extending the output of LT(). In addition to the standard life-table columns, for each cause i in mx[-1] it adds qx_i, dx_i, lx_i, and ex_no_i, corresponding to cause-specific death probabilities, deaths, survivors, and cause-deleted life expectancy.

See Also

LT() for usual life table calculation

Examples

data(asdtex)
mx_causes <- list(
  all = asdtex$all,
  neoplasms = asdtex$neoplasms,
  circulatory = asdtex$circulatory
)
MLT(age = asdtex$age, mx = mx_causes)[1:3, c("age", "mx", "qx_neoplasms", "ex_no_neoplasms")]

Split continuous ages to age groups

Description

Split continuous ages to age groups

Usage

ages(x, groups, char = FALSE, below_min_val = NA)

Arguments

Value

If char = TRUE, a factor of the same length as x with age-group labels. Otherwise, a numeric vector of the same length as x with the lower boundaries from groups; values below the first group receive below_min_val.

Examples

groups <- c(0, 1, 5, 10, 15, 20, 24, 45, 85)
x <- 0:100
ages(x, groups, TRUE)

Associated single decrement life table (ASDT) for causes of death (cause-deleted life table)

Description

Associated single decrement life table (ASDT) for causes of death (cause-deleted life table)

Usage

asdt(age, m_all, m_i, full = FALSE, method = "chiang1968", ...)

Arguments

Value

If full = TRUE, a data frame with the full associated single decrement life table, including the standard life-table columns and the cause-deleted columns r_not_i, p_not_i, l_not_i, a_not_i, d_not_i, L_not_i, T_not_i, and ex_without_i. If full = FALSE, a reduced data frame with columns age, r_not_i, lx, qx, ax, ex, p_not_i, l_not_i, a_not_i, and ex_without_i.

References

Chiang, L. (1968). Introduction to Stochastic Processes in Biostatistics. New York: John Wiley and Sons.

Examples

data(asdtex)
asdt(
  age = asdtex$age,
  m_all = asdtex$all,
  m_i = asdtex$circulatory
)[1:3, ]

Data on mortality of US men in 2002 by some causes

Description

Data on mortality of US men in 2002 by some causes

Usage

asdtex

Format

A dataframe

age

age

neoplasms

age specific mortality rate (asmr) from Neoplasms

circulatory

asmr from Diseases of the circulatory system

respiratory

asmr from Diseases of the respiratory system

digestive

asmr from Diseases of the digestive system

other

asmr from other causes

all

overall asmr

Source

Andreev & Shkolnikov spreadsheet, can be seen on this webpage

Cohort Component Model for Projecting Population.

Description

Cohort Component Model for Projecting Population.

Usage

ccm(
  Mx.f,
  Mx.m = NULL,
  Fx,
  Ix.f = NULL,
  Ix.m = NULL,
  age.mx,
  age.fx,
  N0.f,
  N0.m = NULL,
  srb = 100/205,
  ...
)

Arguments

Details

The model is calculated in matrix form as

\mathbf{N}_{t+h} = \mathbf{L}_t(\mathbf{N}_{t} + \mathbf{I}_{t}/2) + \mathbf{I}_{t}/2

where \mathbf{N}_t is a column vector of population for time t with h as a step of projection (it is the length of age interval), \mathbf{L}_t is Leslie matrix and \mathbf{I}_{t} is a column vector of net migration.

Note that the model assumes that in \mathbf{N} all age intervals are the same (i.e. age = \{0-1, 1-4, 5-9, ...\} is not permitted). Fortunately (and thanks to me), the function handles such situations automatically by transforming all age groups into a unified standard.

Value

If Mx.m is NULL, a numeric matrix with projected female population, where rows are age groups and columns are periods 0:h. If male mortality is supplied, a list with matrices female, male, and all, each with the same row/column structure.

Examples

age.mx <- seq(0, 80, 5)
age.fx <- seq(15, 45, 5)
Mx.f <- matrix(
  rep(seq(0.005, 0.12, length.out = length(age.mx)), 2),
  nrow = length(age.mx),
  ncol = 2
)
Fx <- matrix(
  rep(c(0.02, 0.08, 0.11, 0.09, 0.05, 0.02, 0.005), 2),
  nrow = length(age.fx),
  ncol = 2
)
N0.f <- round(100000 * exp(-0.04 * age.mx))
ccm(Mx.f = Mx.f, Fx = Fx, age.mx = age.mx, age.fx = age.fx, N0.f = N0.f)

Age decomposition of mortality: single decrement process

Description

Age decomposition of mortality: single decrement process

Usage

decomp(mx1, mx2, sex = "m", age, method = "andreev", ax1 = NULL, ax2 = NULL)

Arguments

Details

Example of decomposition using Andreev (1982) formulas:

\Delta_x = l_x^2(e_x^2 - e_x^1) - l_{x+n}^2(e_{x+n}^2 - e_{x+n}^1), \ \ \ x \neq \omega

\Delta_{\omega} = l_{\omega}^2(e_{\omega}^2 - e_{\omega}^1)

where \Delta_x is an absolute contribution of age x to difference in e_0 between the second and the first population. e_x^i, l_x^i are life table functions for population i. \omega is the last age group. Note, e_0^2 - e_0^1 = \sum_{x}^{\omega}\Delta_x

Value

A data frame with one row per age group. It always contains age, ex12, and ex12_prc, where ex12 is the absolute age contribution to the life-expectancy difference and ex12_prc is the percentage contribution. Additional columns depend on method and contain intermediate life-table quantities used in the decomposition.

References

1. Arriaga, E. E. (1984). Measuring and explaining the change in life expectancies. Demography, 21, 83-96.

2. Andreev, E. M. (1982). Metod komponent v analize prodolzhitel'nosti zhizni. Vestnik statistiki, 9, 42-47.

3. Pollard, J. H. (1982). The expectation of life and its relationship to mortality. Journal of the Institute of Actuaries, 109(2), 225–240.

See Also

mdecomp() for age and cause decomposition

Examples

age <- 0:5
mx1 <- c(0.02, 0.01, 0.012, 0.015, 0.02, 0.03)
mx2 <- c(0.018, 0.009, 0.011, 0.014, 0.019, 0.028)
decomp(mx1, mx2, age = age)$ex12

e-dagger

Description

e-dagger

Usage

edagger(age, mx, ...)

Arguments

Value

A named numeric vector of the same length as age, where each element is ⁠e^\dagger_x⁠, the average remaining life years lost because of death from age x onward.

Examples

age <- 0:5
mx <- c(0.02, 0.01, 0.012, 0.015, 0.02, 0.03)
edagger(age, mx)[1:3]

Fertility models for ASFR approximation

Description

Fertility models for ASFR approximation

Usage

fert.approx(fx, age, model, start = NULL, se = FALSE, alpha = 0.05, bn = 1000)

Arguments

Details

This function runs least squares optimization (using default optim) of the selected fertility function with 1e-06 as tolerance parameter.

f_x is age-specific fertility rate for age x.

Hadwiger model

The model is as follows:

f_x = \frac{ab}{c} \frac{c}{x}^{3/2} exp[-b^2(\frac{c}{x}+\frac{x}{c}-2)]

where a,b,c are estimated parameters that do not have demographic interpretation. Sometimes c is interpreted as mean age at childbearing.

Gamma model

The model is as follows:

f_x = \frac{R}{\Gamma(b)c^b}(x-d)^{b-1} exp[-(\frac{x-d}{c})]

where R,b,c,d are estimated parameters. \Gamma is gamma function. R can be interpreted as fertility level (TFR) and d as mean age at childbearing.

Brass model

The model is as follows:

f_x = c(x-d)(d+w-x)

where c,d,w are estimated parameters.

Beta model

The model is as follows:

f_x = \frac{R}{B(A,C)}(\beta - \alpha)^{-(A+C-1)}(x-\alpha)^{(A-1)}(\beta-x)^{(B-1)}

where B(A, C) is beta function, R, \beta, \alpha are estimated parameters, which can be interpreted as fertility level (TFR) and max and min age of childbearing respectively. A,C are

C = (\frac{(v - \alpha)(\beta - v)}{\tau^2} - 1)\frac{\beta - v}{\beta - \alpha}

A = C\frac{v-\alpha}{v - \beta}

where v, \tau^2 are estimated parameters, where v can be interpreted as mean age at childbearing. Thus, Beta model uses 5 parameters R, \beta, \alpha, v, \tau^2, where only \tau^2 has no demographic interpretation.

Value

A list with two components: model, a list describing the fitted fertility model (type, fitted params, rmse, and, if se = TRUE, bootstrap covmat and parameter percentile intervals prc); and predicted, a data frame with observed and fitted age-specific fertility rates. When se = TRUE, predicted also includes bootstrap standard errors and percentile intervals.

References

Peristera, P., & Kostaki, A. (2007). Modeling fertility in modern populations. Demographic Research, 16, 141-194.

Examples

age <- seq(15, 45, 5)
fx <- c(0.03, 0.10, 0.14, 0.12, 0.07, 0.03, 0.01)
fert.approx(fx = fx, age = age, model = "Hadwiger", se = FALSE)

Download RosBris Data

Description

Download age-specific mortality, fertility, and population data from the Russian Fertility and Mortality Database (RosBris) and return them as long-format data frames for use in demor.

Usage

get_rosbris(
  dataset = c("mortality_1", "mortality_5", "fertility_1", "fertility_5"),
  refresh = FALSE
)

Arguments

Details

The function downloads official .zip archives from the RosBris website, stores them in a user cache directory created by tools::R_user_dir(), reads .txt tables from the archives, and converts them to long-format data frames.

Returned data have the following structure:

• "mortality_1": year, code, territory, sex, age, mx, N, Dx, name.

• "mortality_5": year, code, territory, sex, age, mx, N, Dx, name.

• "fertility_1": year, code, territory, age, fx, N, Bx, name.

• "fertility_5": year, code, territory, age, fx, fx1, fx2, fx3, fx4, fx5, N, Bx, Bx1, Bx2, Bx3, Bx4, Bx5, name.

At the moment, get_rosbris() uses the legacy RosBris series corresponding to the periods 1989-2014 and 2015-2022. Updated post-census series are not used by this function.

Value

A data frame with one row per year-region-age combination. Column structure depends on dataset; see Details.

Source

Russian Fertility and Mortality Database. Center for Demographic Research, Moscow (Russia). Available at https://www.nes.ru/research-main/research-centers/demogr/demogr-fermort-data

See Also

rosbris.codes

Examples

if (interactive()) {
  mort <- get_rosbris("mortality_5")
  rus2010 <- subset(
    mort,
    year == 2010 & code == 1100 & sex == "m" & territory == "t"
  )
  head(rus2010)
}

Gini coefficient of a life table

Description

Gini coefficient of a life table

Usage

gini(age, mx, ...)

Arguments

Value

A list with two components: Gini, itself a list with the relative Gini coefficient G0 and the absolute Gini coefficient G0_abs; and plot, a data frame with columns Fx and Phix for drawing the Lorenz curve.

Examples

age <- 0:5
mx <- c(0.02, 0.01, 0.012, 0.015, 0.02, 0.03)
gini(age, mx)$Gini

The Human Life Indicator (HLI)

Description

The Human Life Indicator (HLI)

Usage

hli(age, mx, ...)

Arguments

Details

It is calculated as

HLI = \prod_{x=\alpha}^{\omega}(x + a_x)^{d_x}

where \alpha, \omega are the first and last age groups, x is age, a_x, d_x are life table functions (s.t. \sum_{x=\alpha}^{\omega} d_x = 1).

Value

A length-1 numeric value giving the Human Life Indicator, i.e. the geometric mean age at death implied by the life table.

References

Ghislandi, S., Sanderson, W.C., & Scherbov, S. (2019). A Simple Measure of Human Development: The Human Life Indicator. Population and Development Review, 45, 219–233.

Examples

age <- 0:5
mx <- c(0.02, 0.01, 0.012, 0.015, 0.02, 0.03)
hli(age, mx)

Lee-Carter model

Description

Lee-Carter model

Usage

leecart(
  data,
  n = 10,
  alpha = 0.05,
  model = "RWwD",
  ax_method = "classic",
  bx_method = "classic",
  boot = FALSE,
  bn = 1000,
  ktadj = "none",
  ...
)

Arguments

Details

The model argument specifies the forecasting method.

• model ="RWwD" – classic random walk option

• model = "ARIMA" for selecting a more complex time series model

The ax_method argument allows to control how a_x is calculated.

• ax_method = "classic" – classic option with the average of the logarithm of mortality rates (but there is so-called "jump-off bias").

• ax_method = "last" uses the logarithm of mortality for the last available year (as proposed in Lee & Miller, 2001).

• ax_method = "last_smooth" uses data for the last year with smoothing (see Ševčíková et al., 2016, p. 288).

The bx_method argument allows to control how b_x is calculated.

• bx_method = "classic" for the original method.

• bx_method = "rotate" for the rotational variant (see Li et al., 2013).

The ktadj argument allows to control how k_t is calculated.

• ktadj = "none" for no adjustment.

• ktadj = "Dmin" for minimizing the deviance of predicted/actual annual deaths (as proposed in the original Lee-Carter paper). This method requires data on the age-specific number of deaths (Dx column in the data) and the age-specific population (N column in the data).

• ktadj = "e0min" for minimizing the deviance of predicted/actual life expectancy (as proposed in Lee & Miller, 2001).

• ktadj = "poisson" for minimizing the deviance from a Poisson model, where the dependent variable is the age-specific annual number of deaths (as proposed in Booth et al., 2002). This method requires data on the age-specific number of deaths (Dx column in the data) and the age-specific population (N column in the data).

• ktadj = "edaggermin" for minimizing the deviance of predicted/actual edagger (see edagger()) as proposed in Rabbi & Mazzuco, 2021.

Value

A list with four components: model, the fitted time-series model used to forecast kt; kt, a data frame with historical and forecast mortality index values and confidence intervals; ex0, a data frame with observed, fitted, and forecast life expectancy at birth and confidence intervals; and mx, a data frame with observed, fitted, and forecast age-specific mortality rates and confidence intervals.

References

Booth, H., Maindonald, J., & Smith, L. (2002). Applying Lee-Carter under conditions of variable mortality decline. Population Studies, 56(3), 325-336. doi:10.1080/00324720215935

Lee, R. D., & Carter, L. R. (1992). Modeling and forecasting US mortality. Journal of the American Statistical Association, 87(419), 659–671. doi:10.1080/01621459.1992.10475265

Lee, R., & Miller, T. (2001). Evaluating the performance of the Lee-Carter method for forecasting mortality. Demography, 38(4), 537–549. doi:10.1353/dem.2001.0036

Li, N., Lee, R., & Gerland, P. (2013). Extending the Lee-Carter Method to Model the Rotation of Age Patterns of Mortality Decline for Long-Term Projections. Demography, 50(6), 2037–2051. doi:10.1007/s13524-013-0232-2

Rabbi, A. M. F., & Mazzuco, S. (2021). Mortality forecasting with the Lee-Carter method: Adjusting for smoothing and lifespan disparity. European Journal of Population, 37(1), 97-120. doi:10.1007/s10680-020-09559-9

Ševčíková, H., Li, N., Kantorová, V., Gerland, P., & Raftery, A. E. (2016). Age-Specific Mortality and Fertility Rates for Probabilistic Population Projections. In R. Schoen (Ed.), Dynamic Demographic Analysis (Vol. 39, pp. 285–310). Springer International Publishing. doi:10.1007/978-3-319-26603-9_15

Examples

age <- 0:20
year <- 2000:2009
lc_data <- expand.grid(age = age, year = year)
lc_data$mx <- exp(-7 + 0.09 * lc_data$age - 0.02 * (lc_data$year - min(year)))
fit <- leecart(lc_data, n = 2)
head(fit$kt)

Leslie Matrix

Description

Leslie Matrix

Usage

leslie(mx, fx, age.mx, age.fx, srb = 100/205, fin = TRUE, ...)

Arguments

Value

A square numeric matrix of class leslie with one row and one column per age group. The first row contains fertility contributions and the subdiagonal contains survival ratios.

See Also

summary.leslie() for leslie output that calculates \lambda, r, w and v.

Examples

mx <- c(0.02, 0.01, 0.012, 0.015, 0.02)
fx <- c(0.05, 0.08)
leslie(mx = mx, fx = fx, age.mx = 0:4, age.fx = 1:2)

Mean Age at Childbearing (MAC)

Description

Mean Age at Childbearing (MAC)

Usage

mac(fx, age)

Arguments

Value

A length-1 numeric value giving the mean age at childbearing implied by fx.

Examples

age <- seq(15, 45, 5)
fx <- c(0.03, 0.10, 0.14, 0.12, 0.07, 0.03, 0.01)
mac(fx, age)

Age and cause decomposition of differences in life expectancies

Description

Age and cause decomposition of differences in life expectancies

Usage

mdecomp(mx1, mx2, age, method = "andreev", ...)

Arguments

Details

The contribution of each cause c to the absolute difference in life expectancies between the first and second population is caculated as

\Delta_{x,c} = \frac{m^1_{x,c} - m^2_{x,c}}{m^1_{x} - m^2_{x}} \times \Delta_{x}

where \Delta_{x} is contribution of age x to difference e_0^2 - e_0^1 from function decomp(), m^i_{x,c} is age-specific mortality rate for population i from cause c, and m^i_x is total age-specific mortality rate.

Value

A data frame of class c("mdecomp", "data.frame") with one row per age group. Column age contains ages, ex12 contains the overall age contribution to the life-expectancy difference, and the remaining columns contain cause-specific contributions named after the cause-specific elements of mx1 and mx2.

See Also

decomp() for just age decomposition and plot.mdecomp() for graph of mdecomp results

Examples

data(mdecompex)
usa <- subset(mdecompex, cnt == "usa")
eng <- subset(mdecompex, cnt == "eng")
dec <- mdecomp(
  mx1 = list(
    all = usa$all,
    neoplasms = usa$neoplasms,
    circulatory = usa$circulatory
  ),
  mx2 = list(
    all = eng$all,
    neoplasms = eng$neoplasms,
    circulatory = eng$circulatory
  ),
  age = usa$age
)
dec[1:3, ]

Data on mortality of US and England and Wales men in 2002 by some causes

Description

Data on mortality of US and England and Wales men in 2002 by some causes

Usage

mdecompex

Format

A dataframe

age

age

neoplasms

age specific mortality rate (asmr) from Neoplasms

circulatory

asmr from Diseases of the circulatory system

respiratory

asmr from Diseases of the respiratory system

digestive

asmr from Diseases of the digestive system

other

asmr from other causes

all

overall asmr

cnt

country: usa - US, eng - England and Wales

Source

Andreev & Shkolnikov spreadsheet, can be seen on this webpage

Median age calculation

Description

Median age calculation

Usage

med.age(N, age)

Arguments

Value

A length-1 numeric value giving the estimated median age of the population represented by N.

Examples

N <- c(100, 90, 80, 70, 60)
age <- seq(0, 20, 5)
med.age(N, age)

Mortality models for mx approximation

Description

Mortality models for mx approximation

Usage

mort.approx(mx, age, model = c("Brass", "Gompertz"), standard.mx = NULL, ...)

Arguments

Details

This function runs least squares optimization of the selected mortality function using Gauss-Newton algorithm algorithm with 2000 maximum iterations and 1e-07 as tolerance parameter. For "Gompertz" usual OLS estimator is used.

Gompertz model

The model is as follows:

m(age) = \alpha e^{\beta age}

Brass model

The model is as follows:

y(age) = \alpha + \beta y^{S}(age)

where

y(age) = \frac{1}{2} ln[\frac{q(age)}{1-q(age)}]

and subscript S defines that function is for standard population. To get mx from qx usual formula is used:

m(age) = \frac{q(age)}{n-q(age)(n-a(age))}

where n is the size of age interval and a(x) is a parameter from life table.

Value

A list with two components: model, the fitted lm or nls object; and predicted, a data frame with columns age and mx.pred containing the fitted mortality schedule.

References

Preston, S. H., Heuveline, P., & Guillot, M. (2001). Demography: Measuring and Modeling Population Processes. Blackwell Publishers.

Examples

age <- seq(40, 80, 10)
mx <- c(0.003, 0.005, 0.009, 0.018, 0.036)
standard.mx <- c(0.0025, 0.004, 0.007, 0.014, 0.03)
mort.approx(mx = mx, age = age, model = "Gompertz")
mort.approx(mx = mx, age = age, model = "Brass", standard.mx = standard.mx)

Plot for mdecomp function

Description

Plot for mdecomp function

Usage

## S3 method for class 'mdecomp'
plot(x, return.data = FALSE, ...)

Arguments

Value

If return.data = FALSE, a ggplot2 object with stacked bars of age- and cause-specific contributions. If return.data = TRUE, a data frame with columns age, ex12, and group used to build the plot.

See Also

mdecomp()

Examples

data(mdecompex)
usa <- subset(mdecompex, cnt == "usa")
eng <- subset(mdecompex, cnt == "eng")
dec <- mdecomp(
  mx1 = list(
    all = usa$all,
    neoplasms = usa$neoplasms,
    circulatory = usa$circulatory
  ),
  mx2 = list(
    all = eng$all,
    neoplasms = eng$neoplasms,
    circulatory = eng$circulatory
  ),
  age = usa$age
)
plot(dec)

Plot population pyramid

Description

Plot population pyramid

Usage

plot_pyr(
  popm,
  popf,
  popm2 = NULL,
  popf2 = NULL,
  age,
  prc = FALSE,
  sexn = c("Males", "Females"),
  sexc = c("#ED0000B2", "#00468BB2"),
  age.cont = NULL,
  un.intervals = TRUE
)

Arguments

Value

A ggplot2 object representing a population pyramid. If popm2 and popf2 are supplied, the plot also includes dashed comparison lines for the second population.

Examples

plot_pyr(
  popm = c(100, 90, 80, 70, 60),
  popf = c(95, 92, 85, 75, 65),
  age = seq(0, 20, 5)
)

Rosbris' Region codes

Description

Rosbris' Region codes

Usage

rosbris.codes

Format

A dataframe

n

number of Region (sequence number)

name

Region name

code

Region unique code

Source

Russian Fertility and Mortality Database. Center for Demographic Research, Moscow (Russia). Available at https://www.nes.ru/demogr-fermort-data

Data on Standard Life expectancies that is used for YLL calculations

Description

Data on Standard Life expectancies that is used for YLL calculations

Usage

sle_stand

Format

A dataframe

stand

Standard: 1 - World Health Organization Standard Life Expectancy by single-age; 2 - Global Burden of Disease studies (GBD) and WHO Global Health Estimates (WHO GHE) Standard Life Expectancy by 5-year age groups.

age

age

ex

Standard Life Expectancy

Source

Martinez, R., Soliz, P., Caixeta, R., Ordunez, P. (2019). Reflection on modern methods: years of life lost due to premature mortality-a versatile and comprehensive measure for monitoring non-communicable disease mortality. International Journal of Epidemiology, 48, 1367-1376. doi:10.1093/ije/dyy254

Leslie matrix summary

Description

Leslie matrix summary

Usage

## S3 method for class 'leslie'
summary(object, d = 1, ...)

Arguments

Details

The function calculates \lambda, r, w and v.

• \lambda – asymptotic growth factor that is dominant eigenvalue.

• r – asymptotic growth rate that is ln \lambda / \delta t.

• w – stable age distribution normalized to 1 s.t. \sum_x^{\omega} w_x = 1 where x is age.

• v – reproductive values normalized s.t. v'w = 1.

Value

A list of class summary.leslie with four components: lambda (dominant eigenvalue / asymptotic growth factor), r (intrinsic growth rate), w (stable age distribution summing to 1), and v (reproductive values normalized so that sum(v * w) = 1).

See Also

leslie()

Examples

mx <- c(0.02, 0.01, 0.012, 0.015, 0.02)
fx <- c(0.05, 0.08)
les <- leslie(mx = mx, fx = fx, age.mx = 0:4, age.fx = 1:2)
summary(les)

Tempo-adjusted total fertility rate (TFR')

Description

Tempo-adjusted total fertility rate (TFR')

Usage

tatfr(past_fx, present_fx, post_fx, age)

Arguments

Details

This indicator is calculated as follows

TFR_{i,t}' = \frac{TFR_{i,t}}{1-(M_{i,t+1} - M_{i,t-1}) / 2}

where TFR_{i,t}', TFR_{i,t} are tempo-adjusted and usual total fertility rate for parity i and time t respectively, M_{i,t} is mean age at childbearing for parity i and time t. The tempo-adjusted total fertility rate is a sum of parity-specific TFR_i'.

Note, the calculation are done as in footnote 1 in (Bongaarts & Feeney, 2000, p. 563). Unfortunately, the original 1998 article does not provide the exact formula, which has caused some confusion in academic circles.

Value

A list with four components: tatfr (overall tempo-adjusted total fertility rate), tatfr_i (parity-specific tempo-adjusted rates), tfr (overall conventional TFR), and tfr_i (parity-specific conventional rates).

References

Bongaarts, J., & Feeney, G. (1998). On the Quantum and Tempo of Fertility. Population and Development Review, 24(2), 271–291. doi:10.2307/2807974

Bongaarts, J., & Feeney, G. (2000). On the Quantum and Tempo of Fertility: Reply. Population and Development Review, 26(3), 560–564. doi:10.1111/j.1728-4457.2000.00560.x

See Also

tfr() for TFR and mac() for mean age at childbearing calculation.

Examples

age <- seq(15, 45, 5)
past_fx <- list(
  c(0.02, 0.05, 0.07, 0.05, 0.03, 0.01, 0.00),
  c(0.01, 0.03, 0.04, 0.03, 0.02, 0.01, 0.00)
)
present_fx <- list(
  c(0.03, 0.06, 0.08, 0.06, 0.03, 0.01, 0.00),
  c(0.01, 0.03, 0.05, 0.04, 0.02, 0.01, 0.00)
)
post_fx <- list(
  c(0.03, 0.05, 0.08, 0.07, 0.04, 0.02, 0.00),
  c(0.01, 0.03, 0.04, 0.04, 0.03, 0.01, 0.00)
)
tatfr(past_fx, present_fx, post_fx, age)

Total Fertility Rate (TFR)

Description

Total Fertility Rate (TFR)

Usage

tfr(fx, age.int = 1)

Arguments

Value

A length-1 numeric value equal to the sum of age-specific fertility rates multiplied by age.int.

Examples

fx <- c(0.02, 0.08, 0.12, 0.09, 0.04, 0.01, 0.001)
tfr(fx, age.int = 5)

Years of Life Lost (YLL) calculation

Description

Years of Life Lost (YLL) calculation

Usage

yll(
  Dx,
  type = c("yll", "yll.p", "yll.r", "asyr"),
  age.int = 5,
  Dx_all = NULL,
  pop = NULL,
  w = NULL,
  standard = NULL
)

Arguments

Details

Computes four types of Years of Life Lost (YLL) indicators:

• Absolute YLL (type = "yll"):

  YLL_{x,t,c} = D_{x,t,c} \times SLE_x

  where x,t,c are age, time, and cause respectively, D_{x,t,c} is deaths in age x at time t from cause c and SLE_x is standard life expectancy at age x

• YLL proportion (type = "yll.p"):

  YLL_{x,t,c}^p = \frac{YLL_{x,t,c}}{YLL_{x,t}}

  where YLL_{x,t} = \sum_{c} YLL_{x,t,c} (total YLL across causes)

• YLL rate (type = "yll.r"):

  YLL_{x,t,c}^r = \left( \frac{YLL_{x,t,c}}{N_{x,t}} \right) \times 100'000

  where N_{x,t} is population in age group x at time t

• Age-standardized YLL rate (type = "asyr"):

  ASYR_{t,c} = \sum_{x=\alpha}^{\omega} \left( YLL_{x,t,c}^r \times w_x \right)

  where \alpha to \omega corresponds to first to last age group, w_x is standard population weight for age x.

Value

A list whose components depend on type. For type = "yll", the list contains yll_all (overall YLL) and yll (age-specific YLL). For type = "yll.p", it contains yll.p_all and yll.p (overall and age-specific YLL proportions). For type = "yll.r", it contains yll.r_all and yll.r (overall and age-specific YLL rates). For type = "asyr", it contains asyr_all and asyr (overall and age-specific age-standardized YLL rates).

References

Martinez, R., Soliz, P., Caixeta, R., & Ordunez, P. (2019). Reflection on modern methods: years of life lost due to premature mortality—a versatile and comprehensive measure for monitoring non-communicable disease mortality. International Journal of Epidemiology, 48, 1367–1376.

Examples

yll(Dx = rep(1, 19), type = "yll", age.int = 5)$yll_all