Exploratory Data Analysis
Among 645 clusters, 622 were included in this study, 21 clusters were excluded due to zero GPS longitude and latitude coordinate readings for spatial analysis while the rest two of them were not included initially from the EDHS coordinate file. A total weighted 11,023 live births within five years preceding the 2016 EDHS was included in the analysis, and the infant mortality rate (IMR) in Ethiopia was 48 per 1000 live births in 2016. The majority of 9,807(89.0%) in this study participants were from rural dwellers. Among the respondents, 4,851(44.0%) were from the Oromia region and 2,296(20.8%) were from SNNPR. The infant mortality rate (IMR) varies across the regions of the country. The highest IMR was observed in Harari (76.9 per 1000 live birth) and Afar (70.2 per 1000 live birth). The lowest was observed in Tigray (29.3 per 1000 live birth) and Addis Ababa (32.8 per 1000 live birth) (Figure 2).
Figure 3below showsthatthe proportion of infant mortality varies from cluster to cluster. That means the enumeration area is considered as a random effect for this study (Figure 3).
Spatial Analysis of Infant Mortality
The estimated Global Moran’s Index in this study was 0.1546; indicates that the spatial distribution of infant mortality significantly clustered by in Ethiopia. In addition to looking at the Moran’s I to identify whether there is a spatial correlation, the P-value (<0.0185) was found to be less than 0.05, suggesting significant evidence of unexplained spatial autocorrelation in the risk of infant mortality (Figure 4). Similarly, the incremental spatial autocorrelation graph identified the maximum peak distance value (30000 meters), which indicates distances where spatial processes promoting clustering are most pronounced. The color of each point on the graph corresponds to the statistical significance of the z-score values (Figure 5).
Spatial Autocorrelation by Distance
A total 622 clusters were included in this study to analyze the spatial of infant mortality. Each point in the map characterizes one enumeration area with the proportion of infant mortality in each cluster. The green color indicates that the areas with a low proportion of infant mortality whereas the red color indicates enumeration areas with a high proportion of infant mortality. The highest proportions of infant mortality occurred in a majority part of the Harari region, East part of Afar, border of Benishangul Gumuz and Oromia, the central part of Somali, border of Amhara and Benishangul Gumuz, and central part of Oromia. Whereas the low proportion of infant mortality was accumulated in Tigray, Dire Dawa, Gambela, the entire part of Addis Ababa, and the Northeast part of SNNPR (Figure 6).
Cluster and Outlier Analysis of Infant Mortality
Cluster and outlier analysis was conducted to identify the nature of clustering by using Anselin local Moran’s I. The red color (cluster- low) indicates that the low rate of infant mortality is surrounded by a low rate of infant mortality, and the dark green color (cluster-high) indicates a high rate of infant mortality surrounded by the high rate of infant mortality. Whereas the green color (high outlier) indicates a high rate of infant mortality surrounded by the low rate of infant mortality and the yellow color (low outlier) shows a low rate of infant mortality surrounded by the high rate of infant mortality. Significant clusters were found in Afar, Addis Ababa, border of Benishangul Gumuz and Oromia. High outliers were observed on Harari, Dire Dawa, South Tigray, border of Amhara and Oromia, border of Oromia and SNNPR while the low outliers were found in the Somali region (Figure 7).
Hot Spot Analysis of Infant Mortality
The Local Getis-Ord Gi* statistics identified significant hot spot and cold spot areas of infant mortality. The red color indicates that significant hot spot (high-risk) areas for infant mortality and found in Afar and Somali regions. The blue color indicates the cold spot (low risk) areas of infant mortality. These cold spot areas were observed in Addis Ababa, the central part of the Oromia and Amhara regions (Figure 8).
Spatial Interpolation of Infant Mortality
The spatial kriging interpolation analysis was used to predict infant mortality for unsampled areas of the country based on sampled enumeration area measurements. Prediction of the high-risk areas was indicated by red predictions. Afar, Somali, Harari, Southwest SNNPR, East Benishangul Gumuz, South and central part of Oromia were predicted as more risky areas compared to other regions. Whereas, Tigray, Amhara, Addis Ababa, Northwest Oromia, North Somali, Dire Dawa, Northwest Benishangul Gumuz, Northeast SNNPR, border of Gambela and SNNPR, border of Gambela and Oromia were predicted as having less risk for infant mortality (Figure 9).
Spatial distribution of the spatial autocorrelation term: autocovariate variable
Figure 10 shows the spatial distribution of the autocovariate variable in equation , which represents the spatial autocorrelation term in the GLMM. The autocovariate variable has the same unit as the dependent variable, which also represents the incidence of death occurrence, but it is just a macro spatial trend. Figure 10 show that the spatial distribution of incidence of death occurrence has a strong spatial tendency and heterogeneity, which presents a transitional and gradual change throughout the country. The incidence is very high in the Northern and central part of Afar, the entire part of Harari, the central part of Somali, Southern and Western SNNPR, Eastern Oromia, and Western Benishangul Gumuz regions that is consistent with what we observed in Figure 6 that these areas were characterized by a high proportion of infant mortality.
Spatial Covariance Structures
Figure 4 show that the spatial distribution of infant mortality exhibit spatial correlations and this study investigate various possible spatial covariance structures. Based on statistical software SAS offers several possible spatial covariance structures: Exponential, Gaussian, Linear, Spherical, etc. each represents a particular pattern of changes in spatial covariance among residuals as observations grow in distance from one another. Below We utilized the DIC and AIC fit statistics to examine Spherical and Gaussian spatial covariance structures. Our first observation is that the fit statistics drop in value, indicating a better fit to the data(Table 1).
Results of this study indicated that the Spherical and Gaussian spatial covariance structures were fit to the residuals from the GLMM. Focusing on the AIC fit statistics, we observe a drop from 4146.12 to 4039.27 in Gaussian covariance structure compared to a model with an unstructured covariance structure. This is an improvement, but as part of our model building process, we consider the two spatial covariance structures. When comparing the Gaussian and Spherical models, the fit statistics do now show a meaningful drop, suggesting that perhaps a Gaussian covariance structure is not appropriate. As a result, the Spherical spatial covariance structure better fits the data. We used this covariance structure for modeling in this study, since it has smaller DIC and AIC fit statistics as compared to the other(Table 1).
Table 1 Goodness of fit statistics for different covariance structures
|
DIC |
AIC |
BIC |
Without spatial correlation (unstructured) |
4137.08 |
4146.12 |
4156.35 |
Gaussian |
4031.19 |
4039.27 |
4051.46 |
Spherical |
4028.52 |
4034.75 |
4047.82 |
The intercept-only model without explanatory variable was constructed to measure the effect of community variation on infant mortality.
The variance of random effects at the cluster is ( =3.6413, p-value<0.0001) which was statistically significant and reflects there is statistically significant variation in the infant mortality among infants across the community (see Table 2).
The estimated intra-class correlation computed(ICC)was 52.5%. This indicates about 52.5% of the total variation for infant mortality was due to the difference between communities, leaving 47.5% of the variability to be accounted for the infants or other unknown factors.
The covariance parameter estimates in Table 2 indicates that the estimated higher-level error variance goes down from 3.6413 to 2.7646. The proportion of explained variance at infant-level computed as\(\text{P}\text{C}\text{V}={R}_{1}^{2}=\frac{{\sigma }_{e|b}^{2}-{\sigma }_{e|m}^{2}}{{\sigma }_{e|b}^{2}}\)
=\(\frac{3.6413-2.7646}{3.6413}\) =0.241=24.1%
This indicates that the proportion of explained variation at the individual level for infant mortality with level-1 predictor is about 24.1%. Similarly, the Wald test value 9.17 with a p-value<.0001 was statistically significant and suggested that there is statistically significant variation in the infant mortality among infants across the community ( Table 2).
The cluster or community level residual goes down to 1.7692 from 2.7646, so the community level \({R}_{2}^{2}\) becomes \({R}_{2}^{2}=\frac{2.7646-1.7692}{2.7646}\) = 0.360=36%.The proportion of explained variance at the community level for infant mortality is about 36%. This indicates that 36% of variability at the community level for infant mortality was explained by individual-level and community-level predictors. The Wald value (Z=6.45, and p-value<.0001) indicates that the random effects were statistically significant (Table 2).
In this model, the individual-level variables, community-level variables, and spatial autocovariate variables were introduced. The proportion of explained variance at community-level computed as: \({R}_{3}^{2}=\frac{1.7692-0.7579}{1.7692}\)= 0.572=57.2. It indicates that about 57.2% of the variability at the community level for infant mortality was explained by the individual-level, community-level, and spatial autocovariate variables. The random effects were statistically significant with a Wald value of 5.04 and p-value<.0001 (Table 2). In this study the random coefficients model does not converge; as a result, we exclude the random coefficients model.
Table 2
Covariance parameter estimate for models in the study
Cov Parm
|
Subject
|
Estimate
|
Standard
Error
|
Z Value
|
Pr > Z
|
Model I
|
Variance
|
PSU
|
3.6413
|
0.5126
|
7.10
|
<.0001
|
Model II
|
Variance
|
PSU
|
2.7646
|
0.3015
|
9.17
|
<.0001
|
Model III
|
Variance
|
PSU
|
1.7692
|
0.2741
|
6.45
|
<.0001
|
Model IV
|
Variance
|
PSU
|
0.7579
|
0.1505
|
5.04
|
<.0001
|
|
SP(SPH)
|
PSU
|
92.0000
|
0
|
.
|
.
|
Factors Of Infant Mortality
The result of the selected model Table 3 shows that individual-level factors such as birth size, birth type, sex of a child, breastfeeding status, birth order, birth interval, ANC usage, and wealth index were found to be significantly associated with the odds of infant mortality. On the other hand, community-level factors such as place of residence and region had significant effects (P-value<0.05) on the log-odds of the ith infant in the jth cluster experiences death. In addition to the individual and community level factors, the spatial autocovariate variable (Si) was also significantly associated with infant mortality ( Table 3).
Table 3
Parameter estimate for models in the study using individual-level, community-level, and spatial autocovarite variable
Variables
|
Category
|
Estimate
|
SE
|
(95%CI)
|
Intercept
|
|
-4.9958*
|
0.46
|
(-5..89,-4.09)
|
ANC usage
|
No
|
0.3739**
|
0.13
|
(0.16,0.58)
|
Yes
|
0
|
|
|
Birth interval
|
<=24 month
|
0.8324**
|
0.15
|
(0.58,1.07)
|
25-36
|
0.1497**
|
0.13
|
(-0.11,0.40)
|
>36
|
0
|
|
|
Birth order
|
2-3
|
0.3262
|
0.17
|
(0.01,0.64)
|
4-5
|
0.1880
|
0.22
|
(-0.20,0.57)
|
6 and more
|
1.1331**
|
0.22
|
(0.73,1.53)
|
First
|
0
|
|
|
Breastfeeding status
|
No
|
1.3701**
|
0.14
|
(1.16,1.57)
|
Yes
|
0
|
|
|
Family size
|
4-6
|
-1.1150
|
0.17
|
(-1.42,-0.80)
|
7 and more
|
-2.0979
|
0.23
|
(-2.50,-1.69)
|
1-3
|
0
|
|
|
Marital status
|
Married
|
-0.3946
|
0.25
|
(-0.84,0.05)
|
Unmarried
|
0
|
|
|
Mothers education
|
No education
|
0.3491
|
0.28
|
(-0.16,0.85)
|
Primary
|
0.1653
|
0.25
|
(-0.33,0.66)
|
Secondary & higher
|
0
|
|
|
Sex of child
|
Male
|
0.4668**
|
0.13
|
(0.26,0.67)
|
Female
|
0
|
|
|
Sex of household head
|
Male
|
0.7174
|
0.18
|
(0.37,1.07)
|
Female
|
0
|
|
|
Birth size
|
Average
|
-0.2798
|
0.12
|
(-0.51,-0.04)
|
Small
|
0.2417**
|
0.13
|
(-0.23,0.47)
|
Large
|
0
|
|
|
Type of birth
|
Multiple
|
1.9205**
|
0.21
|
(1.56,2.38)
|
Single
|
0
|
|
|
Wealth index
|
Medium
|
-0.2736
|
0.16
|
(-0.58,0.03)
|
Poor
|
0.3074*
|
0.14
|
(0.04,0.57)
|
Rich
|
0
|
|
|
Region
|
Addis Abeba
|
0.2438
|
0.25
|
(-0.24,0.73)
|
Afar
|
0.4322*
|
0.22
|
( 0.01,0.86)
|
Amhara
|
0.4276
|
0.32
|
(-0.20,1.06)
|
Benishangul
|
0.7658
|
0.24
|
( 0.29,1.24)
|
Dire Dawa
|
0.6528
|
0.30
|
( 0.06,1.24)
|
Gambela
|
0.3823
|
0.28
|
(-0.17,0.93)
|
Harari
|
0.4454*
|
0.25
|
(-0.04,0.94)
|
Oromia
|
0.4293
|
0.31
|
(-0.18,1.04)
|
SNNPR
|
0.3189
|
0.32
|
(-0.31,0.94)
|
Somali
|
0.4160*
|
0.23
|
(-0.03,0.87)
|
Tigray
|
0
|
|
|
Residence
|
Rural
|
0.4867**
|
0.29
|
(-0.05,1.02)
|
Urban
|
0
|
|
|
Si (P-value=0.0028)
|
|
-0.5778*
|
0.19
|
(-0.95,-0.20)
|
ANC usage: Ifants of mothers who did not received ANC during the last pregnancy were 45% higher likely to die in their first year of life compared with infants whose mothers did receive ANC, AOR = 1.45 ,95% CI: 1.17, 1.78). This indicated the mothers who did not use ANC1.45 times more likely as compared to those who did during their pregnancy.
Breastfeeding: The reference group here was mothers who breastfed their children. Infants, who were not breastfed died at a rate which was about 3.93 times more likely as compared than infants who were breastfed. The estimated odds of infant death were 3.93 with 95%.( CI:3.19,4.80).
wealth index:Among mothers who belong to the poor wealth index, the estimated odds of infant death were 1.36 (OR=1.36, 95% CI:1.04,1.77) times more likely as compared to their counterpart rich wealth index in the same clusters.
Sex of infant: The ods ratio for male infants was 1.59 found to be (95% CI:1.29,1.95) meaning that the risk of males dying was about 59% higer than that for female infants. The confidence interval indicated that the risk of death for female infants could be as low as 29% and as high as 95%.
Birth order: The reference group, in this case, was taken as a single birth. Infants belonging to the 6 and more birth order category were about 13% more likely to die relative to the reference group (OR= 1.1331 95%,CI:0.73,1.53).
Birth size :The estimated odds of infant death among infants born with birth size perceived by their mothers as small was 1.27 (OR=1.27, 95% CI:0.79,1.60) times more likely than infants born with birth size perceived by their mothers as large.
Preceding Birth:The estimated odds of death among infants born with a preceding birth interval of less than or equal to 24 months were 2.29 (OR=2.29, 95% CI:1.78,2.91) times more likely to die as compared to infants born with a birth interval of more than 36 months in the same clusters keeping other covariates constant. Whereas the estimated odds of dying among infants born with a preceding birth interval of between 25-36 months was 1.16 (OR=1.16, 95% CI:0.89,1.49) times more likely to die as compared to infants born with a birth interval of more than 36 months in the same clusters keeping other covariates constant.
Type of birth:: The predictable value of odds of infant mortality among multiple births was 6.82 with, 95% CI:4.75,10.80. This showed that infant mortality among multiple 6.82 times more likely than singletons of the same.
In addition to the individual-level characteristics, community-level characteristics (such as the ways of life in the regions, and residence in Ethiopia) were significantly associated with infant mortality.
Residenc: The estimated odds of infant mortality among rural residents were 62%, higher as compared to their counterpart urban residents keeping other covariates constant.
Regions: Infants living in pastoralist regions (Afar, Somali, and Harari ) were significant to compare tigray region. The odds ratio of afar 1.54 times more likely to die in their first year compared with infants living in Tigray regions with, AOR=1.54, (95% CI:0.67,5.20). In addition this,, Somali, and Harari regions were 1.51 (OR=1.51, 95% CI:0.77,3.63), and 1.56 (OR=1.56, 95% CI:0.31,4.31) times more likely as compared to infants from the Tigray region. Respectively(see Table 3).Furthermore, the spatial autocorrelation between clusters. In Table 3 the P=0.0028 also proves that it was true, in a sense that there was a spatial correlation of infant mortality between clusters. The spatial variable correlation with infant death was a negative value, -0.5778, which indicates that clusters with a low incidence of infant mortality were usually surrounded by clusters with a high incidence of infant mortality. Bear in mind that during the interpretation of one variable so far it is assuming that the other variables are held constant (Table 3).