Relationship between changing malaria burden and low birth weight in sub-Saharan Africa: A difference-in-differences study via a pair-of-pairs approach

  1. Siyu Heng
  2. Wendy P O'Meara
  3. Ryan A Simmons
  4. Dylan S Small  Is a corresponding author
  1. Graduate Group in Applied Mathematics and Computational Science, School of Arts and Sciences, University of Pennsylvania, United States
  2. Department of Statistics, The Wharton School, University of Pennsylvania, United States
  3. Global Health Institute, School of Medicine, Duke University, United States
  4. Department of Biostatistics and Bioinformatics, School of Medicine, Duke University, United States
3 figures, 11 tables and 2 additional files


Work flow diagram of the study.
Formed quadruples (pairs of pairs) of matched high-low and high-high pairs of clusters.

In Step 1, pairs of clusters from the early and late time periods are matched on geographic proximity and categorized as ‘high-high’ (comparison, or control) or ‘high-low’ (treated). In Step 2, pairs of high-high clusters are matched with pairs of high-low clusters based on cluster-level sociodemographic characteristics. The difference-in-differences estimate of the coefficient of changing malaria burden on the low birth weight rate is based on comparing (D–C) to (B–A).

The estimated low birth weight rate of each cluster within the 219 high-high pairs and the 219 high-low pairs.

The estimated low birth weight rate for each cluster are obtained from averaging over all the 500 imputed data sets of the 18,112 individual records. We draw a line to connect two paired clusters (one early year cluster and one late year cluster). Box plots for the low birth weight rates are also shown. Two of the four outliers of the late year clusters among the high-low pairs (i.e. the top four late year clusters in terms of low birth weight rate among the high-low pairs) may result from their extremely small within-cluster sample sizes (no more than three individual records for both two clusters).


Table 1
The 19 selected sub-Saharan African countries along with their chosen early/late years of malaria prevalence (i.e. estimated parasite rate 𝑃𝑓PR2-10) and IPUMS-DHS early/late years.

Note that some DHS span over two successive years.

CountryMalaria prevalenceIPUMS-DHS
Early yearLate yearEarly yearLate year
Burkina Faso2003201020032010
Congo Democratic Republic2007201320072013–14
Cote d’Ivoire200020121998–992011–12
Table 2
Summary of the Bayesian logistic regression model fitted over records with observed birth weight which is used to predict missing low birth weight indicators.
PredictorPosterior meanPosterior stdz-scorep-value
Mother’s age (linear term)−0.2070.045−4.562<0.001***
Mother’s age (quadratic term)0.0030.0013.987<0.001***
Wealth index0.0600.0371.5910.112
Child’s birth order (linear term)−0.9890.338−2.9250.003**
Child’s birth order (quadratic term)0.2110.0862.4470.014*
0 - rural; 1 - urban0.1260.1031.2140.225
Mother’s education level−0.2260.062−3.633<0.001***
Child is boy−0.0680.083−0.8150.415
Mother is married or living together−0.1730.117−1.4820.138
Indicator of antenatal care−0.0460.093−0.4930.622
Indicator of low birth size2.4100.09026.776<0.001***
Indicator of large birth size−1.3870.129−10.786<0.001***
Table 3
An interpretation of the coefficients of the intercept term and the three indicators defined in model (1) (i.e. the k0,k1,k2,k3) within each matched quadruple.

The coefficient of the low malaria prevalence indicator (i.e. the k1) incorporates the information of the magnitude of the effect of changing malaria burden (from high to low) on the low birth weight rate.

Table 4
The mean Haversine distance of the early year clusters and late year clusters is 24.1 km among the 219 high-low pairs of clusters, and 28.7 km among the 219 high-high pairs of clusters.

The within-pair longitudes’ and latitudes’ correlations between the paired early year and late year clusters among the high-low and high-high pairs all nearly equal one. The mean values of the longitudes, the latitudes, the annual malaria prevalence (i.e. 𝑃𝑓PR2-10) measured at the early year, denoted as 𝑃𝑓PR2-10 (early), and at the late year, denoted as 𝑃𝑓PR2-10 (late), of the paired early year clusters (clusters sampled at the early year) and late year clusters (clusters sampled at the late year) among the 219 high-low and 219 high-high pairs of clusters used for the statistical inference respectively. Note that an early year cluster has a late year 𝑃𝑓PR2-10 and a late year cluster has an early year 𝑃𝑓PR2-10 since the MAP data contain 𝑃𝑓PR2-10 for each location and for each year between 2000 and 2015.

High-low pairsHigh-high pairs
Mean within-pair haversine distance24.1 km28.7 km
Within-pair correlation of longitude0.99990.9996
Within-pair correlation of latitude0.99980.9997
LongitudeLatitude𝑃𝑓PR2-10 (early)𝑃𝑓PR2-10 (late)
Early clusters among high-low pairs16.92−1.150.520.17
Late clusters among high-low pairs16.88−1.150.480.12
Early clusters among high-high pairs19.150.430.510.47
Late clusters among high-high pairs19.130.460.530.49
Table 5
Balance of each covariate before matching (BM) and after matching (AM).

We report the mean of each covariate (including early and late years) for high-low and high-high pairs of clusters, before and after matching. We also report each absolute standardized difference (Std.dif) before and after matching.

Before matchingAfter matchingStd.dif
(410 pairs)(540 pairs)(219 pairs)(219 pairs)
Urban/rural (early)0.440.
Urban/rural (late)0.600.210.370.320.850.09
Toilet facility (early)0.880.600.820.790.860.10
Toilet facility (late)0.940.690.900.880.900.10
Floor material (early)1.901.681.601.670.310.10
Floor material (late)2.221.791.921.870.590.07
Electricity (early)0.360.
Electricity (late)0.540.180.330.300.990.10
Mother’s education (early)1.000.360.690.641.360.10
Mother’s education (late)1.230.420.870.831.780.10
Contraception indicator (early)
Contraception indicator (late)
Table 6
Inference with multiple imputation and mixed-effects linear probability model (1).

The unit of estimates and CIs is a percentage point.

RegressorEstimate95% CIp-value
0 - high prevalence; 1 - low prevalence−1.48[−3.70, 0.74]0.191
0 - early year; 1 - late year−0.06[−1.82, 1.69]0.943
0 - high-high pairs; 1 - high-low pairs0.21[−1.40, 1.82]0.797
Mother’s age (linear term)−1.86[−2.48, −1.23]<0.001***
Mother’s age (quadratic term)0.03[0.02, 0.04]<0.001***
Child’s birth order (linear term)−13.91[−18.49, −9.32]<0.001***
Child’s birth order (quadratic term)2.91[1.82, 4.00]<0.001***
Wealth index0.09[−0.38, 0.56]0.709
0 - rural; 1 - urban0.82[−0.63, 2.27]0.269
Mother’s education level−2.02[−2.82, −1.22]<0.001***
Child is boy−1.75[−2.75, −0.74]<0.001***
Mother is married or living together−1.43[−3.04, 0.19]0.083
Antenatal care indicator−0.96[−2.06, 0.13]0.085
Appendix 1—table 1
The early and late years coded in the IPUMS-DHS and GPS data sets.
GPS dataMalaria prevalenceIPUMS-DHS
Burkina Faso (BF)200320102003201020032010
Cameron (CM)200420112004201120042011
Congo Democratic Republic (CD)200720132007201320072013
Cote d’Ivoire (CI)199820122000201219982011
Ethiopia (ET)200020102000201020002011
Ghana (GH)200320142003201420032014
Guinea (GN)200520122005201220052012
Kenya (KE)200320142003201420032014
Malawi (MW)200020102000201020002010
Mali (ML)200120122001201220012012
Namibia (NM)200020132000201320002013
Nigeria (NG)200320132003201320032013
Rwanda (RW)200520142005201420052014
Senegal (SN)200520102005201020052010
Tanzania (TZ)199920152000201519992015
Uganda (UG)200020112000201120012011
Zambia (ZM)200720132007201320072013
Zimbabwe (ZW)200520152005201520052015
Appendix 1—table 2
The numbers of the high-high pairs of clusters and high-low pairs of clusters contributed by each of the 19 selected sub-Saharan African countries after the matching in Step 1 and Step 2.

We also summarize the total number of pairs of clusters after Step 1 matching in the first column.

CountryStep 1 matchingStep 2 matching
Total pairsHigh-highHigh-lowHigh-highHigh-low
Burkina Faso4001500190
Congo Democratic Republic30011551124
Cote d’Ivoire14019272
Appendix 1—table 3
Summary of the low malaria prevalence indicators, the time indicators, the group indicators, the covariates, and the birth weight records among the 18,112 study individual records.
VariablesPercentages of some categories
Low malaria prevalence indicatorHigh prevalence (70.6%)
Low prevalence (29.4%)
Time indicatorEarly year (50.3%)
Late year (49.7%)
Group indicatorHigh-high pairs (40.9%)
High-low pairs (59.1%)
Mother’s age in years≤19 (7.1%)
20–29 (52.5%)
30–39 (31.4%)
≥40 (8.9%)
Wealth indexPoorest (20.2%)
Poorer (23.3%)
Middle (22.8%)
Richer (20.4%)
Richest (13.3%)
Child’s birth order1 (21.5%)
2–4 (46.0%)
4+ (32.6%)
Urban or ruralRural (77.1%)
Urban (22.9%)
Mother’s education levelNo education (36.6%)
Primary (47.2%)
Secondary or higher (16.2%)
Child’s sexFemale (49.3%)
Male (50.7%)
Mother’s marital statusNever married or formerly in union (11.6%)
Married or living together (88.4%)
Indicator of antenatal careYes (61.9%)
No or missing (38.1%)
Self-reported birth sizeVery small or smaller than average (13.0%)
Average (45.5%)
Larger than average or very large (41.5%)
Low birth weight indicatorYes (4.6%)
No (48.5%) or Missing (47.0%)
Appendix 2—table 1
Diagnostics for multiple imputation with the mixed-effects linear probability model.

We report the between-imputation variance (`Between var’), the within-imputation variance (‘Within var’), and the variance ratio: (between-imputation variance)/(within-imputation variance), denoted as `Var ratio’.

RegressorBetween varWithin varVar ratio
0 - high prevalence; 1 - low prevalence3.21 × 10−59.62 × 10−50.334
0 - early year; 1 - late year2.20 × 10−55.81 × 10−50.379
0 - high-high pairs; 1 - high-low pairs1.92 × 10−54.83 × 10−50.398
Mother’s age (linear term)3.32 × 10−66.85 × 10−60.486
Mother’s age (quadratic term)8.28 × 10−101.68 × 10−90.493
Child’s birth order (linear term)1.60 × 10−43.87 × 10−40.413
Child’s birth order (quadratic term)8.55 × 10−62.24 × 10−50.382
Wealth index1.74 × 10−64.05 × 10−60.430
0 -rural; 1 - urban1.27 × 10−54.21 × 10−50.303
Mother’s education level4.56 × 10−61.20 × 10−50.380
Child is boy7.12 × 10−61.91 × 10−50.373
Mother is married or living together1.83 × 10−54.96 × 10−50.370
Antenatal care indicator9.63 × 10−62.16 × 10−50.447
Appendix 3—table 1
The results of the sensitivity analyses for the coefficient of the low malaria prevalence indicator under various sensitivity parameters (p1,p2) divided into the four cases: Case 1: p1>0,p2>0; Case 2: p1>0,p2<0; Case 3: p1<0,p2>0; Case 4: p1<0,p2<0.

The unit of estimates and CIs is a percentage point.

Case 1p2=5.0p2=10.0
Estimate95% CIp-valueEstimate95% CIp-value
Case 2p2=-5.0p2=-10.0
Estimate95% CIp-valueEstimate95% CIp-value
Case 3p2=5.0p2=10.0
Estimate95% CIp-valueEstimate95% CIp-value
Case 4p2=-5.0p2=-10.0
Estimate95% CIp-valueEstimate95% CIp-value

Additional files

Source code 1

The source code for producing the results in Figure 1, the results in Figure 3, the results in Tables 2, 3, 5 and 6, the results in Table 4, the results in Appendix 1—table 2, the results in Appendix 1 Table 3, and the results in Appendix 3—table 1 can be found respectively in 'Code for Figure 1.R', 'Code for Figure 3.R', 'Code for primary analysis.R', 'Code for Table 4.R', 'Code for Appendix 1 Table 2.R', 'Code for Appendix 1 Table 3.R', and 'Code for Sensitivity Analyses.R' in the source code files.

The source code are also posted on GitHub (, 2021a).
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  1. Siyu Heng
  2. Wendy P O'Meara
  3. Ryan A Simmons
  4. Dylan S Small
Relationship between changing malaria burden and low birth weight in sub-Saharan Africa: A difference-in-differences study via a pair-of-pairs approach
eLife 10:e65133.