Title: | Under-Five Child Mortality Estimation |
---|---|
Description: | Contains functions for calculating under-five child mortality estimates using the Trussell version of the Brass method (United Nations (1990) <https://www.un.org/en/development/desa/population/publications/pdf/mortality/stepguide_childmort.pdf> and United Nations (1983) <https://www.un.org/en/development/desa/population/publications/pdf/mortality/stepguide_childmort.pdf>) as well as applying the cohort-derived methods by Rajaratnam and colleagues (Rajaratnam JK, Tran LN, Lopez AD, Murray CJL (2010) "Measuring Under-Five Mortality: Validation of New Low-Cost Methods" <doi:10.1371/journal.pmed.1000253>). |
Authors: | Myo Minn Oo [aut, cre] |
Maintainer: | Myo Minn Oo <[email protected]> |
License: | GPL (>= 2) |
Version: | 0.1.2 |
Built: | 2025-01-25 03:03:01 UTC |
Source: | https://github.com/myominnoo/u5mr |
agegroup_as_map()
converts age
variable into a character vector named
agegroup
with two yearly intervals between 14 and 50.
agegroup_as_map(data, age = "age")
agegroup_as_map(data, age = "age")
data |
processed data |
age |
age of women |
data.frame
## demonstrating using microdata data("microdata") ## get only female md <- subset(microdata, sex == 2) ## get those aged between 14 and 50 md <- subset(md, age >= 15 & age < 50) ## create age group into 2-yearly intervals md <- agegroup_as_map(md, age = "age") summary(md$agegroup) table(md$agegroup)
## demonstrating using microdata data("microdata") ## get only female md <- subset(microdata, sex == 2) ## get those aged between 14 and 50 md <- subset(md, age >= 15 & age < 50) ## create age group into 2-yearly intervals md <- agegroup_as_map(md, age = "age") summary(md$agegroup) table(md$agegroup)
The data gathered by the 1974 Bangladesh Retrospective Survey of Fertility and Mortality
can be used to demonstrate the estimation of child mortality from summary birth histories
using the Trussell version of the BRASS method and the Coale-Demeny model life tables
coale_demeny_ltm
.
data(bangladesh)
data(bangladesh)
A data frame
extracted from Display 6 on page 28 and Display 7 on page 29.
United Nations Population Studies (1990) Step-by-Step Guide to the Estimation of Child Mortality No.107:1-83 (United Nations)
The data of distribution of birthdays for different regions.
data(birthdays_distribution)
data(birthdays_distribution)
A data frame
ASIA
LATC
(Latin America and the Caribbean)
NAME
(North Africa and Middle East)
SASE
(Sub-Saharan Africa, South/East)
SAWC
(Sub-Saharan Africa, West/Central)
Rajaratnam JK, Tran LN, Lopez AD, Murray CJL (2010) Measuring Under-Five Mortality: Validation of New Low-Cost Methods. PLOS Medicine 7(4): e1000253. (doi:10.1371/journal.pmed.100025310.1371/journal.pmed.1000253)
Fake summary data used to demonstrate the application of Cohort-derived and Period-derived methods developed by Rajaratnam et al in 2010.
data(cambodia)
data(cambodia)
A data frame
## codes used to derive the dataset `cambodia` ## install.packages("tidyverse", dependencies = TRUE) ## install.packages("devtools", dependencies = TRUE) ## devtools::install_github("myominnoo/mStats") library(tidyverse) library(mStats) data(microdata) cambodia <- microdata %>% filter(sex == 2) %>% filter(age >= 15 & age < 50) %>% egen(age, seq(15, 45, 5), new_var = "agegroup") %>% generate(n, 1 * wtper) %>% replace(ceb, ceb * wtper) %>% replace(cd, cd * wtper) %>% group_by(iso3, svdate, agegroup) %>% summarise(women = sum(n), child_born = sum(ceb), child_dead = sum(cd)) %>% rename(agegrp = agegroup) %>% data.frame()
Rajaratnam JK, Tran LN, Lopez AD, Murray CJL (2010) Measuring Under-Five Mortality: Validation of New Low-Cost Methods. PLOS Medicine 7(4): e1000253. (doi:10.1371/journal.pmed.100025310.1371/journal.pmed.1000253)
The Coale-Demeny life tables consist of four sets of models, each representing
a distinct mortality pattern. Each model is arranged in terms of 25 mortality
levels, associated with different expectations of life at birth for females in
such a way that e0
of 20 years corresponds to level 1 and e0
of 80 years
corresponds to level 25.
data(coale_demeny_ltm)
data(coale_demeny_ltm)
An object of class "list"
; consist of four data.frame
for
male
, female
and both sexes
.
The four underlying mortality patterns of the Coale-Demeny models are called "North", "South", "East" and "West". They were identified through statistical and graphical analysis of a large number of life tables of acceptable quality, mainly for European countries.
Reference: 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
United Nations Population Studies (1990) Step-by-Step Guide to the Estimation of Child Mortality No.107:1-83 (United Nations)
Coefficients provided by Rajaratnam et al for estimation of under-five child mortality data from the maternal age cohort-derived method (MAC).
data(coef_mac_5q0)
data(coef_mac_5q0)
A data frame
Rajaratnam JK, Tran LN, Lopez AD, Murray CJL (2010) Measuring Under-Five Mortality: Validation of New Low-Cost Methods. PLOS Medicine 7(4): e1000253. (doi:10.1371/journal.pmed.100025310.1371/journal.pmed.1000253)
Random effect coefficients provided by Rajaratnam et al for estimation of under-five child mortality data from the maternal age Cohort-derived method (MAC).
data(coef_mac_re)
data(coef_mac_re)
A data frame
Rajaratnam JK, Tran LN, Lopez AD, Murray CJL (2010) Measuring Under-Five Mortality: Validation of New Low-Cost Methods. PLOS Medicine 7(4): e1000253. (doi:10.1371/journal.pmed.100025310.1371/journal.pmed.1000253)
Coefficients provided by Rajaratnam et al for estimation of under-five child mortality data from the maternal age cohort-derived method (MAC).
data(coef_mac_ti)
data(coef_mac_ti)
A data frame
Rajaratnam JK, Tran LN, Lopez AD, Murray CJL (2010) Measuring Under-Five Mortality: Validation of New Low-Cost Methods. PLOS Medicine 7(4): e1000253. (doi:10.1371/journal.pmed.100025310.1371/journal.pmed.1000253)
Coefficients provided by Rajaratnam et al for estimation of under-five child mortality data from the maternal age period-derived method (MAP).
data(coef_map_5q0)
data(coef_map_5q0)
A data frame
Rajaratnam JK, Tran LN, Lopez AD, Murray CJL (2010) Measuring Under-Five Mortality: Validation of New Low-Cost Methods. PLOS Medicine 7(4): e1000253. (doi:10.1371/journal.pmed.100025310.1371/journal.pmed.1000253)
Random effect coefficients provided by Rajaratnam et al for estimation of under-five child mortality data from the maternal age period-derived method (MAP).
data(coef_map_re)
data(coef_map_re)
A data frame
Rajaratnam JK, Tran LN, Lopez AD, Murray CJL (2010) Measuring Under-Five Mortality: Validation of New Low-Cost Methods. PLOS Medicine 7(4): e1000253. (doi:10.1371/journal.pmed.100025310.1371/journal.pmed.1000253)
This is a dataset of coefficients used to estimate multipliers k(i)
in the TRUSSELL version of
the BRASS method, using Coale-Demeny mortality models.
data(coeff_trussell_ki)
data(coeff_trussell_ki)
A data frame
The basic estimation equation for the Trussell method (equation 4.3) is
extracted from page 26, Table 4.
United Nations Population Studies (1990) Step-by-Step Guide to the Estimation of Child Mortality No.107:1-83 (United Nations)
This is a dataset of coefficients used to derive the time reference t(i)
,
for values of q(x)
in the TRUSSELL version of
the BRASS method, using Coale-Demeny mortality models.
data(coeff_trussell_ti)
data(coeff_trussell_ti)
A data frame
The basic estimation equation for the Trussell method (equation 4.3) is
The names of coefficients were changed from e
, f
, and g
to a
, b
, and c
.
extracted from page 27, Table 5.
United Nations Population Studies (1990) Step-by-Step Guide to the Estimation of Child Mortality No.107:1-83 (United Nations)
The data of distribution of birthdays for different regions.
data(deathdays_distribution)
data(deathdays_distribution)
A data frame
ASIA
LATC
(Latin America and the Caribbean)
NAME
(North Africa and Middle East)
SASE
(Sub-Saharan Africa, South/East)
SAWC
(Sub-Saharan Africa, West/Central)
Rajaratnam JK, Tran LN, Lopez AD, Murray CJL (2010) Measuring Under-Five Mortality: Validation of New Low-Cost Methods. PLOS Medicine 7(4): e1000253. (doi:10.1371/journal.pmed.100025310.1371/journal.pmed.1000253)
Fake data used to demonstrate the application of Cohort-derived and Period-derived methods developed by Rajaratnam et al in 2010.
data(microdata)
data(microdata)
A data frame
iso3
- the iso3 code of the country from which your microdata come
region
- the region that the country belongs in
country
- name of the country
svy_wt
- sample weight given to the respondent. If no sample weights are provided, then
generate this variable with a value of 1 for each respondent
age
- age of the respondent in years: or time since first birth of the respondent in years
sex
- sex of the respondent where 1 indicates male and 2 is female.
ceb
- number of children ever born
cd
- number of children that died
Rajaratnam JK, Tran LN, Lopez AD, Murray CJL (2010) Measuring Under-Five Mortality: Validation of New Low-Cost Methods. PLOS Medicine 7(4): e1000253. (doi:10.1371/journal.pmed.100025310.1371/journal.pmed.1000253)
The data gathered by a survey in Panama between August and October 1976
can be used to demonstrate the estimation of child mortality from summary birth histories
using the Trussell version of the BRASS method and the Coale-Demeny model life tables
coale_demeny_ltm
.
data(panama)
data(panama)
A data frame
extracted from Table49 on page 78.
United Nations Population Division
United Nations (1983) Manual X: indirect techniques for demographic estimation. Population studies No. 81. New York: United Nations Department of International Economic and Social Affairs (United Nations)
u5mr_cohort()
uses the maternal age cohort-derived methods (MAC) through summary
birth history information and maternal age (or time since first birth) to
calculate the under-five mortality estimates.
u5mr_cohort( data, women = "women", child_born = "child_born", child_dead = "child_dead", agegrp = "agegrp", iso3 = "KHM", svy_year = 2010 )
u5mr_cohort( data, women = "women", child_born = "child_born", child_dead = "child_dead", agegrp = "agegrp", iso3 = "KHM", svy_year = 2010 )
data |
preprocessed data |
women |
total number of women |
child_born |
children ever born |
child_dead |
children dead |
agegrp |
age grouping or time since first birth |
iso3 |
the |
svy_year |
end of the survey |
In this cohort-derived method, under-five mortality and reference time are estimated through summary birth history information from the mothers and her age or time since her first birth.
In case sample weights are available for the mothers, final variables should be multiplied by these weights before summarizing.
Computational Procedure
Two formulas were used to quantify MAC method:
component
logit(5q0ijk) = 0i + Uij +
1i x logit(CDijk /
CEBijk) +
2i x CEBijk +
3i x PR1 +
4i x PR2 +
ijk
where
i = 5-year maternal age group (15-19, 20-24, ... , 45-49)
j = country
k = survey
CDi = total dead children from maternal age group
i
CEBi = total children ever born from maternal age group i
PR1 = ratio of parity among maternal age group 15-19 and parity among maternal age
group 20-24
PR2 = ratio of parity among maternal age group 20-24 and parity among maternal age
group 25-29
Uij = country-specific random effects
All coefficients vary by maternal age group, as indicated by i
and the random
effects also vary by country, as indicated by j
.
Reference time component
reftimeijk = 0i +
1i x (CDijk /
CEBijk) +
2i x CEBijk +
3i x PR1 +
4i x PR2 +
ijk
data.frame
iso3
- total number of women
svy_year
- total number of children ever born
agegrp
- five-year age groups
ref_time
- time between survey year and interpolated year
year
- reference year
q5
- under-five mortality
Rajaratnam JK, Tran LN, Lopez AD, Murray CJL (2010) Measuring Under-Five Mortality: Validation of New Low-Cost Methods. PLOS Medicine 7(4): e1000253. (doi:10.1371/journal.pmed.100025310.1371/journal.pmed.1000253)
## Example using fake survey data from Cambodia data(cambodia) camb <- u5mr_cohort(cambodia, women = "women", child_born = "child_born", child_dead = "child_dead", agegrp = "agegrp", iso3 = "KHM", svy_year = 1234) with(camb, plot(year, q5 * 1000, type = "b", pch = 19, col = "black", xlab = "Year", ylab = "U5MR per 1000 live births", main = paste0("Under-five mortality, q(5) in Bangladesh, estimated\n", "using the maternal age cohort-derived method")))
## Example using fake survey data from Cambodia data(cambodia) camb <- u5mr_cohort(cambodia, women = "women", child_born = "child_born", child_dead = "child_dead", agegrp = "agegrp", iso3 = "KHM", svy_year = 1234) with(camb, plot(year, q5 * 1000, type = "b", pch = 19, col = "black", xlab = "Year", ylab = "U5MR per 1000 live births", main = paste0("Under-five mortality, q(5) in Bangladesh, estimated\n", "using the maternal age cohort-derived method")))
u5mr_period()
uses the maternal age period-derived method (MAP) through summary
birth history information and maternal age (or time since first birth) to
calculate the under-five mortality estimates.
u5mr_period( data, child_born = "child_born", child_dead = "child_dead", agegrp = "agegrp", svy_wt = "svy_wt", iso3 = "KHM", svy_region = "ASIA", svy_year = 1234 )
u5mr_period( data, child_born = "child_born", child_dead = "child_dead", agegrp = "agegrp", svy_wt = "svy_wt", iso3 = "KHM", svy_region = "ASIA", svy_year = 1234 )
data |
preprocessed data |
child_born |
children ever born |
child_dead |
children dead |
agegrp |
age grouping or time since first birth |
svy_wt |
sample weights: if not available, use 1. |
iso3 |
the |
svy_region |
region of the country from which the survey data come
|
svy_year |
end of the survey |
In this period-derived method, under-five mortality and reference time are estimated through distributions of child birthdays and death days for different categories of mothers, stratified by maternal information such as region, age, and number of child ever born or dead. These distributions are used to find the expected number of children ever born and dead in every year prior to the survey (up to 25 years) for a mother in each particular strata.
By applying these distributions to each mother in each strata, and summing across all strata, expected numbers of children ever born (CEB) and child dead (CD) are generated for each year prior to the survey. The ratio of CD and CEB for each year can then be calculated.
Computational Procedure
The formulas used to quantify MAP method is as follows:
logit(5q0tjk) = 0t +
Utj +
1t x
logit(CDtjk / CEBtjk) +
tjk
where
t = index of calendar time (0, 24)
j = country
k = survey
CDi = total dead children in time bin
t
CEBi = total children ever born in time bin t
data.frame
ref_time
- time between survey year and interpolated year
year
- reference year
q5
- under-five mortality
Rajaratnam JK, Tran LN, Lopez AD, Murray CJL (2010) Measuring Under-Five Mortality: Validation of New Low-Cost Methods. PLOS Medicine 7(4): e1000253. (doi:10.1371/journal.pmed.100025310.1371/journal.pmed.1000253)
data("microdata") ## get only female md <- subset(microdata, sex == 2) ## get those aged between 14 and 50 md <- subset(md, age >= 15 & age < 50) ## create age group into 2-yearly intervals md <- agegroup_as_map(md, age = "age") u5mr_period(md, child_born = "ceb", child_dead = "cd", agegrp = "agegroup", svy_wt = "svy_wt", iso3 = "KHM", svy_region = "ASIA", svy_year = 1234)
data("microdata") ## get only female md <- subset(microdata, sex == 2) ## get those aged between 14 and 50 md <- subset(md, age >= 15 & age < 50) ## create age group into 2-yearly intervals md <- agegroup_as_map(md, age = "age") u5mr_period(md, child_born = "ceb", child_dead = "cd", agegrp = "agegroup", svy_wt = "svy_wt", iso3 = "KHM", svy_region = "ASIA", svy_year = 1234)
u5mr_trussell()
uses the Trussell version of the BRASS method
and calculates under-five mortality estimates.
u5mr_trussell( data, women = "women", child_born = "child_born", child_dead = "child_dead", agegrp = "agegrp", model = "west", svy_year = 1976.5, sex )
u5mr_trussell( data, women = "women", child_born = "child_born", child_dead = "child_dead", agegrp = "agegrp", model = "west", svy_year = 1976.5, sex )
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:
|
svy_year |
end of the survey |
sex |
indicates sex-specific estimates: |
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)
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)
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)
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.
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)
.
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 .
where and
are the model values of
q(x)
for
levels j
and j+1
, and is the estimated value.
The desired common index , or
q5
is given by
where h is the interpolation factor calculated in the following way:
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.
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
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
United Nations (1983) "Manual X indirect techniques for demographic estimation" https://www.un.org/en/development/desa/population/publications/pdf/mortality/stepguide_childmort.pdf
## 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)
## 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)