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Analysis of demographic indicators from Demographic and Health Surveys (DHS) and other household surveys

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demogsurv

The goal of demogsurv is to:

  • Calculate common demographic indicators from household survey data, including child mortality, adult mortality, and fertility.
  • Stratify indicators according to arbitrary age groups, calendar periods, birth cohorts, time before survey, or other survey variables (region, residence, wealth category, education, etc.).
  • Efficiently prepare event / person-year datasets from survey data for other model-based analysis.
  • Provide standard error estimates for all indicators via Taylor linearization or jackknife.
  • Calculate sample covariance for indicators estimated from a single complex survey (e.g. time-series of child mortality estimates).
  • Default parameters are specified for analysis of DHS recode datasets without fuss, but funciton implementation is flexible for use with other survey data.

For analysis of DHS data, the package interacts well with rdhs. See the vignette for an example.

Installation

You can install the development version from GitHub with:

# install.packages("devtools")
devtools::install_github("mrc-ide/demogsurv")

The package will be released on CRAN in due course.

Example

Load the package and example datasets created from DHS Model Datasets.

library(demogsurv)

data(zzbr) # Births recode (child mortality)
data(zzir) # Individuals recode (fertility, adult mortality)

Child mortality

By default, the function calc_nqx calculates U5MR by periods 0-4, 5-9, and 10-14 years before the survey. Before calculating mortality rates, create a binary variable indicator whether a death occurred and a variable giving the date of death, placed 0.5 months in the month the death occurred.

zzbr$death <- zzbr$b5 == "no"      # b5: child is alive ("yes" or "no")
zzbr$dod <- zzbr$b3 + zzbr$b7 + 0.5
u5mr <- calc_nqx(zzbr)
u5mr
#>    tips       est          se      ci_l      ci_u
#> 1 10-14 0.2212304 0.011730185 0.1978969 0.2438851
#> 2   5-9 0.1937855 0.008292561 0.1773675 0.2098759
#> 3   0-4 0.1408711 0.006432798 0.1281701 0.1533871

Note that calc_nqx() does not reproduce child mortality estimates produced in DHS reports. calc_nqx() conducts a standard demographic rate calculation based on observed events and person years within each age group and then converts the cumulative hazard to survival probabilities. The standard DHS indicator uses a rule-based approach to allocate child deaths and person years across age groups and proceeds by calculating direct probabilities of death in each age group (see Rutstein and Rojas 2006). A function calc_dhs_u5mr() will reproduce the DHS calculation, but is not yet fully implemented.

Use the argument by= to specify factor variables by which to stratify the rate calculation.

calc_nqx(zzbr, by=~v102) # by urban/rural residence
#>    v102  tips       est          se      ci_l      ci_u
#> 1 urban 10-14 0.1750790 0.018595935 0.1378145 0.2107329
#> 2 rural 10-14 0.2453074 0.013657991 0.2180578 0.2716074
#> 3 urban   5-9 0.1818306 0.016617688 0.1486035 0.2137609
#> 4 rural   5-9 0.1994068 0.009424996 0.1807194 0.2176679
#> 5 urban   0-4 0.1532941 0.014183345 0.1250339 0.1806416
#> 6 rural   0-4 0.1345284 0.006453178 0.1217876 0.1470845
calc_nqx(zzbr, by=~v190, tips=c(0, 10)) # by wealth quintile, 0-9 years before
#>      v190 tips       est          se      ci_l      ci_u
#> 1 poorest  0-9 0.1768813 0.009976478 0.1570936 0.1962044
#> 2  poorer  0-9 0.1823974 0.009763729 0.1630352 0.2013118
#> 3  middle  0-9 0.1657497 0.010603135 0.1447069 0.1862747
#> 4  richer  0-9 0.1557011 0.012229238 0.1313887 0.1793329
#> 5 richest  0-9 0.1456974 0.015916788 0.1139245 0.1763310
calc_nqx(zzbr, by=~v101+v102, tips=c(0, 10)) # by region and residence
#>       v101  v102 tips       est         se      ci_l      ci_u
#> 1 region 1 urban  0-9 0.1440943 0.01331266 0.1176001 0.1697929
#> 2 region 2 urban  0-9 0.1648417 0.02741923 0.1093342 0.2168898
#> 3 region 3 urban  0-9 0.1618804 0.01696421 0.1279628 0.1944787
#> 4 region 4 urban  0-9 0.1998386 0.03390294 0.1305530 0.2636029
#> 5 region 1 rural  0-9 0.1559257 0.01004546 0.1360056 0.1753866
#> 6 region 2 rural  0-9 0.1755639 0.01088753 0.1539462 0.1966293
#> 7 region 3 rural  0-9 0.2021511 0.03301796 0.1347402 0.2643101
#> 8 region 4 rural  0-9 0.1764668 0.01299817 0.1505927 0.2015527

The sample covariance or correlation matrix of the estimates can be obtained via vcov().

vcov(u5mr)  # sample covariance
#>              [,1]         [,2]         [,3]
#> [1,] 1.375972e-04 4.450180e-05 8.842864e-06
#> [2,] 4.450180e-05 6.876656e-05 1.451310e-05
#> [3,] 8.842864e-06 1.451310e-05 4.138089e-05
cov2cor(vcov(u5mr))  # sample correlation
#>           [,1]      [,2]      [,3]
#> [1,] 1.0000000 0.4574926 0.1171894
#> [2,] 0.4574926 1.0000000 0.2720644
#> [3,] 0.1171894 0.2720644 1.0000000

Standard error estimation can be done via Taylor linearisation, unstratified jackknife, or stratified jackknife. Results are very similar.

calc_nqx(zzbr, varmethod = "lin") # default is linearization
#>    tips       est          se      ci_l      ci_u
#> 1 10-14 0.2212304 0.011730185 0.1978969 0.2438851
#> 2   5-9 0.1937855 0.008292561 0.1773675 0.2098759
#> 3   0-4 0.1408711 0.006432798 0.1281701 0.1533871
calc_nqx(zzbr, varmethod = "jkn") # stratified jackknife (varmethod = "jkn")
#>    tips       est          se      ci_l      ci_u
#> 1 10-14 0.2212304 0.011931233 0.1974762 0.2442815
#> 2   5-9 0.1937855 0.008280170 0.1773984 0.2098463
#> 3   0-4 0.1408711 0.006434272 0.1281716 0.1533856

## Compare unstratified standard error estimates for linearization and jackknife
calc_nqx(zzbr, strata=NULL, varmethod = "lin")  # unstratified design
#>    tips       est          se      ci_l      ci_u
#> 1 10-14 0.2212304 0.011976980 0.1973986 0.2443546
#> 2   5-9 0.1937855 0.008367844 0.1772169 0.2100205
#> 3   0-4 0.1408711 0.006507844 0.1280208 0.1535320
calc_nqx(zzbr, strata=NULL, varmethod = "jk1")  # unstratififed jackknife
#>    tips       est          se      ci_l      ci_u
#> 1 10-14 0.2212304 0.012088926 0.1971571 0.2445818
#> 2   5-9 0.1937855 0.008408382 0.1771422 0.2100923
#> 3   0-4 0.1408711 0.006539720 0.1279620 0.1535891

To calculate different child mortality indicators (neonatal, infant, etc.), specify different age groups over which to aggregate.

calc_nqx(zzbr, agegr=c(0, 1)/12)  # neonatal
#>    tips        est          se       ci_l       ci_u
#> 1 10-14 0.04358764 0.004262693 0.03519631 0.05190598
#> 2   5-9 0.04590724 0.003799869 0.03843049 0.05332585
#> 3   0-4 0.03792144 0.003320563 0.03139119 0.04440766
calc_nqx(zzbr, agegr=c(1, 3, 5, 12)/12) # postneonatal
#>    tips        est          se       ci_l       ci_u
#> 1 10-14 0.10613868 0.007294180 0.09172741 0.12032129
#> 2   5-9 0.08366400 0.006097552 0.07163475 0.09553739
#> 3   0-4 0.05107115 0.003999245 0.04320031 0.05887724
calc_nqx(zzbr, agegr=c(0, 1, 3, 5, 12)/12) # infant (1q0)
#>    tips       est          se      ci_l       ci_u
#> 1 10-14 0.1451000 0.008870650 0.1275358 0.16231054
#> 2   5-9 0.1257305 0.006823068 0.1122547 0.13900166
#> 3   0-4 0.0870559 0.005070203 0.0770642 0.09693942
calc_nqx(zzbr, agegr=c(12, 24, 36, 48, 60)/12) # child (4q1)
#>    tips        est          se       ci_l       ci_u
#> 1 10-14 0.08905182 0.007189004 0.07485210 0.10303360
#> 2   5-9 0.07784223 0.005665474 0.06667098 0.08887977
#> 3   0-4 0.05894689 0.004529373 0.05002747 0.06778255
calc_nqx(zzbr, agegr=c(0, 1, 3, 5, 12, 24, 36, 48, 60)/12) # u5mr (5q0)
#>    tips       est          se      ci_l      ci_u
#> 1 10-14 0.2212304 0.011730185 0.1978969 0.2438851
#> 2   5-9 0.1937855 0.008292561 0.1773675 0.2098759
#> 3   0-4 0.1408711 0.006432798 0.1281701 0.1533871

Calculate annual 5q0 by calendar year (rather than years preceding survey).

calc_nqx(zzbr, period=2005:2015, tips=NULL)
#>    period       est         se       ci_l      ci_u
#> 1    2005 0.1937695 0.01611970 0.16154821 0.2247525
#> 2    2006 0.1890020 0.01485224 0.15936341 0.2175956
#> 3    2007 0.1983320 0.01469757 0.16900148 0.2266273
#> 4    2008 0.1906183 0.01306713 0.16459769 0.2158285
#> 5    2009 0.1979731 0.01559065 0.16682639 0.2279554
#> 6    2010 0.1874172 0.01366295 0.16019216 0.2137596
#> 7    2011 0.1768661 0.01378438 0.14940096 0.2034444
#> 8    2012 0.1390004 0.01488779 0.10932074 0.1676910
#> 9    2013 0.1224668 0.01183607 0.09895918 0.1453611
#> 10   2014 0.1225079 0.01208800 0.09849310 0.1458829

Adult mortality

The function calc_nqx() can also used to calculate adult mortality indicators such as 35q15. First, the convenience function reshape_sib_data() transforms respondent-level data to a dataset with one row for each sibling reported. Then define a binary variable for whether the sibling is alive or dead.

zzsib <- reshape_sib_data(zzir)
zzsib$death <- factor(zzsib$mm2, c("dead", "alive")) == "dead"

Calculate 35q15 for the seven year period before the survey.

calc_nqx(zzsib, agegr=seq(15, 50, 5), tips=c(0, 7), dob="mm4", dod="mm8")
#>   tips       est          se      ci_l      ci_u
#> 1  0-6 0.1778199 0.009395366 0.1591976 0.1960298

Calculate 35q15 by sex, replicating Table MM2.2.

zzsib$sex <- factor(zzsib$mm1, c("female", "male"))  # drop mm2 = 3: "missing"
calc_nqx(zzsib, by=~sex, agegr=seq(15, 50, 5), tips=c(0, 7), dob="mm4", dod="mm8")
#>      sex tips       est         se      ci_l      ci_u
#> 1 female  0-6 0.1790557 0.01296694 0.1532435 0.2040811
#> 2   male  0-6 0.1766238 0.01332997 0.1500787 0.2023399

This calculation exactly reproduces the 35q15 estiamtes produced for Table MM2 for DHS reports. Additional functionality will be added in future for producing ASMRs (Table MM1), MMR, and PM (Table MM3) will be added in future.

Fertility

The functions calc_asfr() and calc_tfr() calculate age-specific fertility rates and total fertility rate, respectively. The default calculation is by five-year age groups for three years before the survey, exactly reproducing the estimates produced in DHS reports.

## Replicate DHS Table 5.1.
## Total ASFR and TFR in 3 years preceding survey
calc_asfr(zzir, tips=c(0, 3))
#>   agegr tips       asfr     se_asfr
#> 1 15-19  0-2 0.11901592 0.008154144
#> 2 20-24  0-2 0.20736603 0.012782416
#> 3 25-29  0-2 0.21553394 0.008245023
#> 4 30-34  0-2 0.18803561 0.010426419
#> 5 35-39  0-2 0.12494212 0.008135705
#> 6 40-44  0-2 0.06044451 0.007502008
#> 7 45-49  0-2 0.02828233 0.006066635
calc_tfr(zzir)
#>   tips      tfr    se_tfr
#> 1  0-2 4.718102 0.1949224

## ASFR and TFR by urban/rural residence
reshape2::dcast(calc_asfr(zzir, ~v025, tips=c(0, 3)), agegr ~ v025, value.var = "asfr")
#>   agegr      urban      rural
#> 1 15-19 0.07718083 0.16269262
#> 2 20-24 0.15883881 0.25754199
#> 3 25-29 0.16862119 0.24797353
#> 4 30-34 0.14294124 0.21875542
#> 5 35-39 0.08182797 0.15262614
#> 6 40-44 0.04817726 0.07005696
#> 7 45-49 0.02404944 0.03087701
calc_tfr(zzir, by=~v025)
#>    v025 tips      tfr    se_tfr
#> 1 urban  0-2 3.508184 0.2813637
#> 2 rural  0-2 5.702618 0.1425967
calc_tfr(zzir, by=~v025, varmethod="jkn")
#>    v025 tips      tfr    se_tfr
#> 1 urban  0-2 3.508184 0.3004737
#> 2 rural  0-2 5.702618 0.1427030

Replicate fertility estimates stratified by various sociodemographic characteristics.

## Replicate DHS Table 5.2
calc_tfr(zzir, ~v102)  # residence
#>    v102 tips      tfr    se_tfr
#> 1 urban  0-2 3.508184 0.2813637
#> 2 rural  0-2 5.702618 0.1425967
calc_tfr(zzir, ~v101)  # region
#>       v101 tips      tfr    se_tfr
#> 1 region 1  0-2 5.334781 0.1781935
#> 2 region 2  0-2 5.255445 0.2842471
#> 3 region 3  0-2 3.079052 0.3674651
#> 4 region 4  0-2 5.500077 0.2452335
calc_tfr(zzir, ~v106)  # education
#>           v106 tips      tfr    se_tfr
#> 1 no education  0-2 5.585398 0.1406657
#> 2      primary  0-2 5.041455 0.3599601
#> 3    secondary  0-2 3.245211 0.2956154
#> 4       higher  0-2 1.388428 0.3198573
calc_tfr(zzir, ~v190)  # wealth quintile
#>      v190 tips      tfr    se_tfr
#> 1 poorest  0-2 5.951668 0.2183868
#> 2  poorer  0-2 5.693275 0.1867203
#> 3  middle  0-2 5.270892 0.2283221
#> 4  richer  0-2 4.406202 0.2813975
#> 5 richest  0-2 2.907027 0.2738504
calc_tfr(zzir)  # total
#>   tips      tfr    se_tfr
#> 1  0-2 4.718102 0.1949224

Generate estimates stratified by both calendar period and time preceding survey.

calc_tfr(zzir, period = c(2010, 2013, 2015), tips=0:5)
#>      period tips      tfr    se_tfr
#> 1 2010-2012    4 5.260048 0.3166023
#> 2 2010-2012    3 5.207062 0.2697222
#> 3 2010-2012    2 4.084194 0.3176187
#> 4 2013-2014    2 5.020537 0.2999262
#> 5 2013-2014    1 4.555710 0.2448427
#> 6 2013-2014    0 4.720417 0.3525991

Calculate ASFR by birth cohort.

asfr_coh <- calc_asfr(zzir, cohort=c(1980, 1985, 1990, 1995), tips=NULL)
reshape2::dcast(asfr_coh, agegr ~ cohort, value.var = "asfr")
#>   agegr 1980-1984 1985-1989 1990-1994
#> 1 15-19 0.1636472 0.1641461 0.1470502
#> 2 20-24 0.2610719 0.2402068 0.2140443
#> 3 25-29 0.2519899 0.2321897 0.2957371
#> 4 30-34 0.2012103 0.1674921        NA
#> 5 35-39 0.1473996        NA        NA

To Do

  • Refactor for single calc_rate() function used by mortality and fertility calculations.

  • Add indirect indicators

  • Implement DHS child mortality calculation (Rutstein and Rojas 2006).

  • Handle married women only datasets.

  • Calculate multiple aggregations of nqx and sample correlation of these (e.g. NN, PN, 1q0, 4q1, 5q0).

  • Document everything…

  • Develop, test, and create examples for non-DHS household surveys, e.g. MICS, WFS.

  • Extend interface to allow specification of formula, variable name, or vectors.

  • Add some basic data checking before rate calculation, good warnings, potentially automatic handling. [ ] Variable names all exist. [ ] No missing data in date variables. [ ] Episode start date is before episode end date. [ ] All birth history ids appear in respondent dataset.

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