In mrc-ide/hhsurveydata: Demographic analysis of DHS and other household surveys

knitr::opts_chunk$set(
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This vignette describes the methods implemented by demogsurv for calculating demographic indicators.

Setup

Load the demogsurv package.

## devtools::install_github("mrc-ide/demogsurv")
library(demogsurv)
library(survival)
library(survey)

DHS model datasets are included as example datsets in the package (see ?zzir). Load the example datasets:

data(zzir) # Individual recode
data(zzbr) # Birth's recode

Child mortality (~5~q~0~)

The package implemets a generic function calc_nqx() for calculating the probability of dying between ages $x$ and $x+n$. For calculation of ~5~q~0~, calc_nqx() proceeds by:

1. Calculating the numbers deaths and person-years observed within the age ranges 0, 1-2, 3-5, 6-11, 12-23, 24-35, 36-47, and 48-60 months.
2. Calculating the mortality rate within each age group.
3. Aggregate mortality rates to cumulative mortality hazard over age 0 to 4 years.
4. Convert cumulative hazard to probability of dying.

The calculation uses the same age group stratification as the standard DHS indicators reported for infant and child mortality. But the calculation differs in that it calculates a piecewise constant mortaity hazard within each of these age groups and converts the cumulative hazard to probability of dying, whereas the DHS indicator calculates the probability of dying within each age group as the ratio of the number of deaths divided by the number surviving to the start of the age group. calculates the product overall ages (see Rutstein and Rojas 2006).

Define survival episodes for each child born

The calculation uses the Birth's recode dataset (zzbr), which is formatted as one row per live born child reported in the full birth history. The first step is to define survival episodes for each child.

Define a binary variable indicating whether a death occurred or the episode is censored.

zzbr$death <- zzbr$b5 == "no"  # b5: child still alive (1 = "yes", 2 = "no")

Variable b7 reports the child age at death in completed months. The date of death is calculated as the date of birth plus the age at death plus 0.5 months, such that on average one half month of person-time is contributed in the month of death.

zzbr$dod <- zzbr$b3 + zzbr$b7 + 0.5

Survivor episodes start at the child date of birth (variable b3) and ends at either the child date of death or are right censored at the date of interview (v008).

zzbr$tstop <- ifelse(zzbr$death, zzbr$dod, zzbr$v008)

Aggregate weighted numbers of deaths and person years by age group

The function demog_pyears() is a wrapper for the function survival::pyears() to calculate numbers of events (deaths) and person years stratfied by age group (agegr), calendar period (period), time preceding the survey (tips), or birth cohort (cohort) from survival episode data. We use demog_pyears() to calculate the number of child deaths and person years in the age groups 0, 1-2, 3-5, 6-11, 12-23, 24-35, 36-47, and 48-59 months during the period 0-4 years before the survey.

zzbr$weight <- zzbr$v005 / mean(zzbr$v005) # Normalize weights
aggr <- demog_pyears(~1, zzbr, agegr=c(0, 1, 3, 6, 12, 24, 36, 48, 60)/12, tips=c(0, 5),
                     event="death", tstart="b3", tstop="tstop",
                     dob = "b3", intv = "v008", weights="weight",
                     origin = 1900, scale = 12)

Calculate mortality rate within each age group

The mortality rate $mu_a$ within each age group is estimated as the number of observed deaths divided by the number of person-years.

mx <- aggr$data
mx$agegr <- paste(c(0, "1-2", "3-5", "6-11", "12-23", "24-35", "36-47", "48-59"), "months")
mx$mx <- mx$event / mx$pyears
knitr::kable(mx)

Cumulative hazard and probability of dying

The cumualative hazard is the sum over all age groups of the mortality rate in each age group times the span of the age group.

mx$a_min <- c(0, 1, 3, 6, 12, 24, 36, 48) / 12
mx$a_max <- c(1, 3, 6, 12, 24, 36, 48, 60) / 12

cum_mx <- sum( (mx$a_max - mx$a_min) * mx$mx)
cum_mx

Finally, the probability of dying ~5~q~0~ is one minus the cumulative probability of escaping death:

1 - exp(-cum_mx) # 5q0

Standard error estimation

Via Taylor linearization

To be completed

Via stratified jackknife

To be completed

Adult mortality (~35~q~15~, ~45~q~15~)

To be completed

Total fertility rate

To be completed

mrc-ide/hhsurveydata documentation built on March 31, 2022, 1:05 p.m.