u5mr (version 0.1.1)

u5mr_trussell: Estimating under-five mortality using Coale-Demeny life table models

Description

u5mr_trussell() uses the Trussell version of the BRASS method and calculates under-five mortality estimates.

Usage

u5mr_trussell(
  data,
  women = "women",
  child_born = "child_born",
  child_dead = "child_dead",
  agegrp = "agegrp",
  model = "west",
  svy_year = 1976.5,
  sex
)

Arguments

data

processed data

women

total number of women

child_born

children ever born

child_dead

children dead

agegrp

age grouping

model

Coale-Demeny life table model: north, south, east, and west

svy_year

end of the survey

sex

indicates sex-specific estimates: both, male, and female

Value

data.frame

• agegrp - five-year age groups

• women - total number of women

• child_born - total number of children ever born

• child_dead - number of children dead

• pi - average parity

• di - proportion of dead among children ever born

• ki - multipliers

• qx - probabilities of dying at age x

• ti - time between survey year and interpolated year

• year - reference year

• h - interpolation factor

• q5 - under-five mortality

Details

T. J. Trussell developed the Trussell version of the Brass method to estimate child mortality using summary birth history (United Nations, 1983b, Chapter III). It is based on the Coale-Demeny life table models of either North, South, East, or West.

Computational Procedure

Step 1. Preparing the dataset

The function needs four variables from the input data:

a) agegrp: age groups representing 15-19, 20-24, 25-29, 30-34, 35-39, 40-44, and 45-49.

b) women: the total number of women in the age group irrespective of their marital or reporting status

c) child_born: the total number of children ever borne by these women

d) child_dead: the number of children dead reported by these women

Step 1.1. Calculation of average parity per woman P(i)

$$P(i) = CEB(i) / FP(i)$$

• CEB(i) is the total number of children ever borne by these women

• FP(i) is the total number of women in the age group irrespective of their marital or reporting status.

Step 1.2. Calculation of the proportions dead among children ever borne D(i)

$$D(i) = CD(i) / CEB(i)$$

• CD(i) is the number of children dead for women of age group i

Step 2. Calculating the multipliers k(i) and probabilities of dying by age x q(x)

$$k(i) = a(i) + b(i) P(1)/P(2) + c(i) P(2)/P(3)$$

where a(i), b(i), and c(i) are coefficients estimated by regression analysis of simulated model cases, and P(1)/P(2) and P(2)/P(3) are parity ratios.

$$q(x) = k(i) x D(i)$$

Step 3. Calculating the reference dates for q(x) and interpolating q5

Under conditions of steady mortality change over time, a reference time t(i) can be estimated for each q(x).

$$t(i) = a(i) + b(i) P(1)/P(2) + c(i) P(2)/P(3)$$

Actual dates can be obtained by subtracting t(i) from the reference date of the survey or census, expressed in decimal terms.

Step 4. Interpolating between q(x) and model life table

A common index, in this case, under-five mortality q(5) can be obtained by conversions of corresponding q(x) values to the specified family of the Coale-Demeny life table models. In a given life table family and sex, the first step is to identify the mortality levels with q(x) values that enclose the estimated value \(q^e(x)\).

$$q^j(x) > q^e(x) > q^j+1(x)$$

where \(q^j(x)\) and \(q^j+1(x)\) are the model values of q(x) for levels j and j+1, and \(q^e(x)\) is the estimated value.

The desired common index \(q^c(5)\), or q5 is given by

$$q^c(5) = (1.0 - h) x q^j(5) + h x q^e(5)$$

where h is the interpolation factor calculated in the following way:

$$h = q^e(x) - q^j(x) / q^j+1(x) - q^j(x)$$

Step 5. Finalizing the calculation

The final output is combined into a data.frame, which contains original dataset as well as statistics produced during the computational procedure.

References

1. United Nations (1990) "Step-by-step guide to the estimation of the child mortality" https://www.un.org/en/development/desa/population/publications/pdf/mortality/stepguide_childmort.pdf

2. United Nations (1983) "Manual X indirect techniques for demographic estimation" https://www.un.org/en/development/desa/population/publications/pdf/mortality/stepguide_childmort.pdf

Examples

# NOT RUN {
## Using Bangladesh survey data to estimate child mortality
data("bangladesh")
bang_both <- u5mr_trussell(bangladesh, sex = "both", model = "south", svy_year = 1974.3)
bang_male <- u5mr_trussell(bangladesh, child_born = "male_born",
                 child_dead = "male_dead", sex = "male",
                 model = "south", svy_year = 1974.3)
bang_female <- u5mr_trussell(bangladesh, child_born = "female_born",
                 child_dead = "female_dead", sex = "female",
                 model = "south", svy_year = 1974.3)

## plotting all data points
with(bang_both,
    plot(year, q5, type = "b", pch = 19,
         ylim = c(0, .45),
         col = "black", xlab = "Reference date", ylab = "u5MR",
         main = paste0("Under-five mortality, q(5) in Bangladesh, estimated\n",
                       "using model South and the Trussell version of the Brass method")))
with(bang_both, text(year, q5, agegrp, cex=0.65, pos=3,col="purple"))
with(bang_male,
    lines(year, q5, pch = 18, col = "red", type = "b", lty = 2))
with(bang_female,
    lines(year, q5, pch = 18, col = "blue", type = "b", lty = 3))
legend("bottomright", legend=c("Both sexes", "Male", "Female"),
      col = c("Black", "red", "blue"), lty = 1:3, cex=0.8)


## Using panama survey data to estimate child mortality
data("panama")
pnm_both <- u5mr_trussell(panama, sex = "both", model = "west", svy_year = 1976.5)
pnm_male <- u5mr_trussell(panama, child_born = "male_born",
                child_dead = "male_dead", sex = "male",
                model = "west", svy_year = 1976.5)
pnm_female <- u5mr_trussell(panama, child_born = "female_born",
                child_dead = "female_dead", sex = "female",
                model = "west", svy_year = 1976.5)

## plotting all data points
with(pnm_both,
    plot(year, q5, type = "b", pch = 19,
        ylim = c(0, .2), col = "black", xlab = "Reference date", ylab = "u5MR",
         main = paste0("Under-five mortality, q(5) in Panama, estimated\n",
                       "using model West and the Trussell version of the Brass method")))
with(pnm_both, text(year, q5, agegrp, cex=0.65, pos=3,col="purple"))
with(pnm_male,
    lines(year, q5, pch = 18, col = "red", type = "b", lty = 2))
with(pnm_female,
    lines(year, q5, pch = 18, col = "blue", type = "b", lty = 3))
legend("bottomleft", legend=c("Both sexes", "Male", "Female"),
      col = c("Black", "red", "blue"), lty = 1:3, cex=0.8)

# }