Level and Determinant of Child Mortality Rate in Ethiopia

Abstract

Background: One of the objectives of the Sustainable Development Goals (SDG) is to diminish the under-five mortality rate and improvement in maternal health. This study aims to identify factors that affect under-five mortality based on the 2016 EDHS dataset using the multilevel count regression model. Method: The EDHS data have a two-level hierarchical structure, with 14,370 women nested within 11 geographical regions. Multilevel count models were employed to predict the outcomes. Results: The data were found to have excess zeros (53.7%); the variance (1.697) is higher than its mean (0.90). Among families of count models, the HNB model was found to be a better fit for the dataset than the others. The study revealed that a child of multiple births is 1.45 more likely to die as compared with a single birth. Babies delivered in the private sector are a 0.65 lower risk of under-five mortality compared to the babies delivered at home. Conclusion: Vaccination of child, family size, age of mother, antenatal visit, birth interval, birth order, contraceptive used, father education level, mother education level, father occupation, place of delivery, child twin, age first birth and religion were significantly associated with under-five mortality. The Ministry of Health should work properly to raise the awareness of parents for vaccination, family planning services and efforts should be made to improve the parental educational level.

1. Introduction

Seventeen Sustainable Development Goals (SDGs) were agreed upon by global leaders based on millennium development goals. SDG goal 3 target 3.2 is to reduce infant and under-5 mortality by 2030. The target is to drop the “neonatal mortality as low as 12 per 1000 live births and under-five Mortality to as low as 25 per thousand live births” [1]. According to UNICEF, the problem of under-five mortality requires urgent attention from the health sector. If the conditions remain as such, approximately 60 million innocent children will die until 2030 (more than half of the Ethiopian population) [2].

Every year, millions of children under 5 years of age die (WHO, 2016). In 2016, about 15,000 children still die every single day globally. The level of under-five mortality remains high in certain regions of the world. Sub-Saharan African Region continues to be the region with the highest rate of under-five mortality. In 2016, the under five-mortality rate in sub-Saharan African was 79 deaths per 1000 live births, nearly 15 times the average in developed countries [1, 2, 3].

In Ethiopia, the under-five mortality rate stands at 67 per 1000 live births, with large inequalities in her different regions. Every year, more than 257,000 children under the age of five dies [4]. If the situations continue as such, more than 3,084,000 children will die until 2030.

Most of the previous studies were done by using single-level binary logistic and survival analysis including the above studies we mentioned, but under-five mortality varies across different physical, ecological, and political structures within countries. One such contextual determinant is the regional environment [5, 6, 7]. In Ethiopia, there have been regional variations in a number of under-five mortality [8, 9]. In this study, we assume the region affects modeling the determinants of the number of under-five mortality, which may be due to the heterogeneity in regions of the study. As a result, the multilevel model approach is relatively better to determine the covariates related to under-five mortality [10, 11]. Therefore, this study was targeted to investigate the major socio-economic, demographic, health, and environmental proximate factors that might influence under-five mortality in Ethiopia with different multilevel count model approaches.

2. Methodology

The data used for this study was taken from the 2016 EDHS which is a nationally representative survey of women’s age (15–49 years age) groups taken from the CSA, Ethiopia. This survey is the fourth compressive survey designed to provide estimates for the health and demographic variables of interest for the whole urban and rural areas of Ethiopia as a domain. In all of the selected households, measurements were collected from children age 0–59 months, women age 15–49 years, and men age 15–59 years old.

The main outcome variable in this study is the number of under-five death per mother. Thus, this paper attempts to include socioeconomic, demographic, health, and environmental related factors that are assumed as a potential determinant for the barriers in the number of under-five death per mother, adopted from literature reviews and their theoretical justification.

A multilevel count regression model can account for a lack of independence across levels of nested data (in this case, individual mothers nested within regions). Conventional count regression assumes that all experimental units are independent in the sense that any variable which affects the occurrence of under-five mortality has the same effect in all regions, but observations from similar environments might have shown similar behaviors as opposed to observations from a different environment. Multilevel models are used to assess whether the effects of predictors vary from region to region. The main statistical model of multilevel analysis is the HGLM, an extension of the (GLM) that includes nested random coefficients [10, 12].

The multilevel count regression model has a count outcome (number of under-five mortality). Now consider the full model equation for the two-level Poisson regression with $i^{\mathit{th}}$ individual mothers is nested within the $j^{\mathit{th}}$ region. The response variable, i.e., we let $Y_{\mathit{ij}}$ is the $i^{\mathit{th}}$ individual mothers in $j^{\mathit{th}}$ region has under-five mortality. Using a log link function the two-level model is given by:

$$log\left({\mu }_{\mathit{ij}}\right)={\beta }_{\mathit{oj}}+\sum _{l=1}^k{\beta }_{\mathit{lj}}{x}_{\mathit{lij}};l=1,2,.\dots ,k$$E1

Where ${\beta }_{\mathit{oj}}={\beta }_o+U_{\mathit{oj}},{\beta }_{\mathit{lj}}={\beta }_1+U_{1j},\dots .+{\beta }_k+U_{\mathit{kj}}$.

The level-two model (1) can be rewritten as:

$$log\left({\mu }_{\mathit{ij}}\right)={\beta }_o+\sum _{l=1}^k{\beta }_l{x}_{\mathit{lij}}+U_{\mathit{oj}}+\sum _{l=1}^k{U}_{\mathit{lj}}{x}_{\mathit{lij}}$$E2

Where $x_{\mathit{ij}}=\left(x_{1\mathit{ij}},x_{2\mathit{ij}},\dots x_{\mathit{kij}}\right)$ represent the first and the second level covariates, $\beta =\left({\beta }_0,{\beta }_1,.\dots {\beta }_k\right)$ are regression coefficients, $U_{\mathit{oj}},U_{1j},..\dots U_{\mathit{kj}}$ are the random effect of the model parameter at level two (region level). It assumed that the $U_{\mathit{oj}},U_{1j},..\dots U_{\mathit{kj}}$ follow a normal distribution with mean zero and variance ${{\sigma }_u}^2$ [13]. Without $U_{\mathit{oj}},U_{1j},..\dots U_{\mathit{kj}}$, Eq. (2) can be considered as a single-level Poisson regression model.

2.1 Empty model

The empty two-level model for a count outcome variable refers to a population of groups (level-two units) and specifies the probability distribution for group-dependent ${\mu }_{\mathit{ij}}$ in $Y_{\mathit{ij}}={\mu }_{\mathit{ij}}+{\epsilon }_{\mathit{ij}}$ without taking further explanatory variables into account. We focused on the model that specifies the transformed $log\left({\mu }_{\mathit{ij}}\right)$ to have a normal distribution. This is expressed, for a general link function $log\left(\mu \right)$, by the formula.

$$log\left({\mu }_{\mathit{ij}}\right)={\beta }_0+U_{\mathit{oj}}$$E3

Where ${\beta }_o$ is a fixed coefficient and $U_{\mathit{oj}}$ is a random term that is independently and normally distributed with mean 0 and variance ${{\sigma }_u}^2$ (random intercept variance) [14]. This model is also named as empty Poisson regression model (null model). A null model contains only a response variable, and no explanatory variables other than an intercept. Thus, ${{\sigma }_u}^2$ measures regional variations of under-five mortality.

2.2 The random intercept model

A random intercepts model is a model in which intercepts are allowed to vary. The scores on the dependent variable for each individual observation are predicted by the intercept that varies across regions, but the relationship between explanatory and response variables cannot differ between groups. The random intercept model expresses the natural log of ${\mu }_{\mathit{ij}}$, as a sum of a linear function of the explanatory variables. That is,

$$\begin{array}{ll}log\left({\mu }_{\mathit{ij}}\right)& ={\beta }_{0j}+{\beta }_1{x}_{1\mathit{ij}}+{\beta }_2{x}_{2\mathit{ij}}+.\dots +{\beta }_k{x}_{\mathit{kij}}\\ & ={\beta }_{\mathit{oj}}+\sum _{l=1}^k{\beta }_l{x}_{\mathit{lij}}\end{array}$$E4

Where the intercept term ${\beta }_{\mathit{oj}}$ is allowed to vary across the regions and is given by the sum of an average intercept ${\beta }_0$ and regions-dependent deviations $U_{\mathit{oj}}$, that is.

$${\beta }_{\mathit{oj}}={\beta }_o+U_{\mathit{oj}}$$

As a result, we have:

$$log\left({\mu }_{\mathit{ij}}\right)={\beta }_o+\sum _{l=1}^k{\beta }_l{x}_{\mathit{lij}}+U_{\mathit{oj}}$$E5

Note that the above equation ${\beta }_o+{\sum }_{l=1}^k{\beta }_l{x}_{\mathit{lij}}$ is the fixed part of the model. The remaining $U_{\mathit{oj}}$ is called the random part of the model. It is assumed that the random part of $U_{\mathit{oj}}$ are mutually independent and normally distributed with mean zero and variance ${{\sigma }_{\mathit{uo}}}^2$.

2.3 The random coefficients model

A random slopes model is the slopes are different across regions. In other words, the relationship between an explanatory variable and the response is different across all regions. If we fit a model based on the same predictors on the response variable for all regions separately, we may obtain different intercepts and slopes for each region. Now consider a model with group-specific regressions, on a single level one explanatory variable $X$,

$$log\left({\mu }_{\mathit{ij}}\right)={\beta }_{0j}+{\beta }_{1j}{x}_{1\mathit{ij}}$$E6

The intercepts ${\beta }_{\mathit{oj}}$ as well as the regression coefficients or slopes, ${\beta }_{1j}$ are group dependent. These group dependent coefficients can be split into an average coefficient and the group dependent deviation:

$$\begin{array}{ll}{\beta }_{\mathit{oj}}& ={\beta }_o+U_{\mathit{oj}}\\ {\beta }_{1j}& ={\beta }_1+U_{1j}\end{array}$$

Substitution into (6) leads to the model

$$log\left({\mu }_{\mathit{ij}}\right)=\left({\beta }_o+U_{\mathit{oj}}\right)+\left({\beta }_1+U_{1j}\right)x_{1\mathit{ij}}={\beta }_o+{\beta }_1{x}_{1\mathit{ij}}+U_{\mathit{oj}}+U_{1j}{x}_{1\mathit{ij}}$$E7

There are two random group effects, the random intercept $U_{\mathit{oj}}$ and the random slope $U_{1j}$. It is assumed that the level two residuals $U_{\mathit{oj}}$ and $U_{1j}$ have both zero mean given the value of the explanatory variable X. Thus, ${\beta }_1$ is the average regression coefficient like ${\beta }_0$ is the average intercept. The first part of Eq. (7)${\beta }_o+{\beta }_1{x}_{1\mathit{ij}}$ is called the fixed part of the model whereas the second part $U_{\mathit{oj}}+U_{1j}{x}_{1\mathit{ij}}$ is called the random part of the model.

The term $U_{\mathit{oj}}+U_{1j}{x}_{1\mathit{ij}}$ can be regarded as a random interaction between group and predictors (X). This model implies that the groups are characterized by two random effects: their intercept and their slope. These two groups’ effects $U_{\mathit{oj}}$ and $U_{1j}$ will not be independent. Further, it is assumed that, for different groups, the pairs of random effects $\left(U_{\mathit{oj}},U_{1j}\right)$ are independent and identically distributed. Thus, the variances and covariance of the level-two random effects $\left(U_{\mathit{oj}},U_{1j}\right)$ are denoted by:

$$\begin{array}{l}\mathit{Var}\left(U_{\mathit{oj}}\right)={\sigma }_{00}={{\sigma }_0}^2\\ \mathit{Var}\left(U_{1j}\right)={\sigma }_{11}={{\sigma }_1}^2\\ \mathit{Cov}\left(U_{\mathit{oj}},U_{1j}\right)={\sigma }_{01}\end{array}$$

The model for a single explanatory variable discussed above can be extended by including more variables that have random effects.

2.4 Multilevel negative binomial regression model

The hierarchical study design or the data collection procedure, over-desperation, and lack of independence may occur simultaneously, which render the standard NB model inadequate. To account for the over-desperation and the inherent correlation of observations, a class of multilevel NB regression models with random effects is presented. The multilevel NB model is then generalized to cope with a more complex correlation structure. The multilevel NB model derives by allowing for between regional random variation of the expected number of under-five mortality ${\mu }_{\mathit{ij}}$.

$$ln{\mu }_{\mathit{ij}}={\eta }_{\mathit{ij}}+e_{\mathit{ij}}$$E8

Where $cov\left(e_{\mathit{ij}},{\eta }_{\mathit{ij}}\right)=0$ and $exp\left(e_{\mathit{ij}}\right)$ follows a gamma probability distribution, $\mathrm{\Gamma }\left(v\right)$, with mean 1 and variance $\alpha =v_{-1}$. Integrating concerning $e_{\mathit{ij}}$ [15] the resulting probability distribution

$$p\left(Y_{\mathit{ij}}=y_{\mathit{ij}}\right)=\frac{exp(-exp\left({\eta }_{\mathit{ij}}+e_{\mathit{ij}}\right)exp{\left({\eta }_{\mathit{ij}}+e_{\mathit{ij}}\right)}^{y_{\mathit{ij}}}}{y_{\mathit{ij}}!}$$E9

One version of the multilevel negative binomial regression model is obtained;

$$p\left(Y_{\mathit{ij}}=y_{\mathit{ij}}\right)=\frac{\mathrm{\Gamma }\left(y_{\mathit{ij}}+v\right)v^v{{{\mu }_{\mathit{ij}}}^{\ast }}^{y_{\mathit{ij}}}}{y_{\mathit{ij}}!\mathrm{\Gamma }\left(v\right){\left(v+{{\mu }_{\mathit{ij}}}^{\ast }\right)}^{v+y_{\mathit{ij}}}}{y}_{\mathit{ij}}=0,1,2..\dots$$E10

With mean and variance given, respectively, as follows:

The multilevel negative binomial regression model gives the expected mean of a number of under-five mortality. $E\left(Y_{\mathit{ij}}\right)={{\mu }_{\mathit{ij}}}^{\ast }=log\left({\eta }_{\mathit{ij}}\right)$. Its variance is given by $var\left({\mathrm{y}}_{\mathrm{ij}}\right)={\mathrm{\mu }}_{\mathrm{ij}}+\mathrm{\alpha }{\mathrm{\mu }}_{\mathrm{ij}}^{2.}$ Where ${\eta }_{\mathit{ij}}={\beta }_{0j}+{\beta }_{1j}{x}_{1\mathit{ij}}+{\beta }_{2j}{x}_{2\mathit{ij}}+.\dots +{\beta }_{\mathit{kj}}{x}_{\mathit{kij}}$

2.5 Multilevel ZIP regression model

ZIP regression is useful for modeling count data with excess zeros, but because of hierarchical study design or the data collection procedure, zero-inflation and correlation may occur simultaneously [16]. Multilevel ZIP regression is used to overcome these problems. Let $Y_{\mathit{ij}}$ be a count say, the number of under-five mortalities the $i^{\mathit{th}}$ mother in the $j^{\mathit{th}}$ region follows a multilevel ZIP distribution:

$$p\left(Y_{\mathit{ij}}=y_j\right)=\left\{\begin{array}{l}{\pi }_{\mathit{ij}}+\left(1-{\pi }_{\mathit{ij}}\right)exp\left(-{\mu }_{\mathit{ij}}\right),\mathit{\text{if}}{y}_{\mathit{ij}}=0\\ \left(1-{\pi }_{\mathit{ij}}\right)\frac{exp\left(-{\mu }_{\mathit{ij}}\right){{{\mu }_i}_j}^{y_{\mathit{ij}}}}{y_{\mathit{ij}}!},\mathit{\text{if}}{y}_{{}_{i}j}=1,2,\dots \dots \end{array}\right.0\le {\pi }_{\mathit{ij}}\le 1$$E11

Recently, the ZIP regression model has been extended to the random effects setting, where by random components $w_j$ and $u_j$ are incorporated within the logistic and Poisson linear predictors to account for the dependence of observations within $j^{\mathit{th}}$ region [16]. These random effects ZIP models are region-specific in the sense that the random effects $w_j$ and $u_j$ so introduced are specific to the $j^{\mathit{th}}$ region. In the following, a multi-level ZIP regression model is developed to handle correlated count data with extra zeros.

Without loss of generality, consider the two-level hierarchical situation where $Y_{\mathit{ij}}$ represents the $i^{\mathit{th}}$ observation of under-five mortality the $j^{\mathit{th}}$ individual region $\left(i=1,2,..\dots ,n\right)$ and $\left(j=1,2,..\dots ,m\right)$. Let $m$ be the total number of individuals in each region and ${\sum }_{j=1}^m{\sum }_{i=1}^{\mathit{ni}}\mathit{ni}$ gives the total number of observations. The observations may be taken to be independent between regions, but certain within-household and within-individual correlations are anticipated, which can be modeled explicitly through random effects attached to the linear predictors:

$$log\left({\mu }_{\mathit{ij}}\right)={\beta }_o+\sum _{l=1}^k{\beta }_l{x}_{\mathit{lij}}+U_{\mathit{oj}}+\sum _{l=1}^k{U}_{\mathit{lj}}{x}_{\mathit{lij}}$$E12

$$log\mathit{it}\left({\pi }_{\mathit{ij}}\right)=log\left(\frac{{\pi }_{\mathit{ij}}}{1-{\pi }_{\mathit{ij}}}\right)={\gamma }_o+\sum _{l=1}^k{\gamma }_l{z}_{\mathit{lij}}+W_{\mathit{oj}}+\sum _{l=1}^k{W}_{\mathit{lj}}{z}_{\mathit{lij}}$$E13

Here, the covariates $X_{\mathit{ij}}$ and $Z_{\mathit{ij}}$ appearing in the respective Poisson and logistic components are not necessarily the same, $\beta$ and $\gamma$ are the corresponding vectors of regression coefficients [17, 18]. For simplicity of presentation, the random effect $u$ and $w$ assumed to be independent and normally distributed with mean zero and variance ${{\sigma }_u}^2$ and ${{\sigma }_w}^2$ respectively.

2.6 Multilevel ZINB regression model

Multilevel ZINB regression model is proposed for over-dispersed count data with extra zeros. A multilevel ZINB regression incorporating random effects to account for data dependency and over-dispersion is used [17]. Let $Y_{\mathit{ij}}\left(i=1,2,..\dots ,n;j=1,2,..\dots ,m\right)$ be a count say, the under-five mortality of the $i^{\mathit{th}}$ mother in $j^{\mathit{th}}$ region follows a ZINB distribution:

$$p\left(Y_{\mathit{ij}}=y_{\mathit{ij}}\right)=\left\{\begin{array}{l}{\pi }_{\mathit{ij}}+\frac{\left(1-{\pi }_{\mathit{ij}}\right)}{{\left(1+{\mathit{\alpha \mu }}_{\mathit{ij}}\right)}^{-\frac{1}{\alpha }}},\mathit{\text{if}}{y}_{\mathit{ij}}=0\\ 1-{\pi }_{\mathit{ij}}\frac{\mathrm{\Gamma }\left(y_{\mathit{ij}}+\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$\alpha $}\right.\right)}{y_{\mathit{ij}}!\mathrm{\Gamma }\left(\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$\alpha $}\right.\right)}{\left(1+{\mathit{\alpha \mu }}_{\mathit{ij}}\right)}^{-\frac{1}{\alpha }}{\left(1+\frac{1}{{\mathit{\alpha \mu }}_{\mathit{ij}}}\right)}^{-y_{ij}},\mathit{\text{if}}{y}_{\mathit{ij}}>0\end{array}\right.0\le {\pi }_{\mathit{ij}}\le 1$$

In my study, mothers are nested in regions and the number of under-five mortality is taken to be the response variable. Let $\mathrm{n}$ be the total number of individuals in each region and ${\sum }_{j=1}^m{\sum }_{i=1}^{\mathit{ni}}\mathit{ni}$ gives the total number of observations. Hence the responses of under-five mortality which belong to the different regions are independent, while they are correlated for those who live in the same region. This dependence can be modeled explicitly by considering suitable random effects in the linear predictor.

Negative binomial models for counts permit $\mathrm{\mu }$ to depend on explanatory variables. Then the two-level ZINB regression model can be expressed in vector form as:

$$log\left({\mu }_{\mathit{ij}}\right)={\beta }_o+\sum _{l=1}^k{\beta }_l{x}_{\mathit{lij}}+U_{\mathit{oj}}+\sum _{l=1}^k{U}_{\mathit{lj}}{x}_{\mathit{lij}}$$E14

$$log\mathit{it}\left({\pi }_{\mathit{ij}}\right)=log\left(\frac{{\pi }_{\mathit{ij}}}{1-{\pi }_{\mathit{ij}}}\right)={\gamma }_o+\sum _{l=1}^k{\gamma }_l{z}_{\mathit{lij}}+W_{\mathit{oj}}+\sum _{l=1}^k{W}_{\mathit{lj}}{z}_{\mathit{lij}}$$E15

Here, the covariates $X_{\mathit{ij}}$ and $Z_{\mathit{ij}}$ appearing in the respective negative binomial and logistic components are not necessarily the same, $\beta$ and $\gamma$ are the corresponding vectors of regression coefficients [17, 18]. The vectors $w_j$ and $u_j$ denote the region-specific random effects for simplicity of presentation. The random effect $u$ and $w$ assumed to be independent and normally distributed with mean zero and variance ${{\sigma }_u}^2$ and ${{\sigma }_w}^2$ respectively.

2.7 Multilevel hurdle regression model

The hurdle model [19] has mostly been adopted to conduct an economic analysis of healthcare utilization. The hierarchical study design or the data collection procedure, zero-inflation, and lack of independence may occur simultaneously, which the standard Hurdle Poisson regression model is inadequate. To account for the preponderance of zero counts and the inherent correlation of observations, a class of multilevel Hurdle Poisson regression models with random effects is presented. In this study, suppose that $Y_{\mathit{ij}}$ is the number of under-five mortality in $i^{\mathit{th}}$ mother in the $j^{\mathit{th}}$ region. Then multilevel Poisson Hurdle model can be written as follows

$$p\left(Y_{\mathit{ij}}=y_{\mathit{ij}}\right)=\left\{\begin{array}{l}{\pi }_{\mathit{ij}}\mathit{\text{if}}{y}_{\mathit{ij}}=0\\ \left(1-{\pi }_{\mathit{ij}}\right)\frac{exp\left(-{\mu }_{\mathit{ij}}\right){{\mu }_{\mathit{ij}}}^{y_{\mathit{ij}}}}{(1-exp\left(-{\mu }_{\mathit{ij}}\right)y_{\mathit{ij}}!}\mathit{\text{if}}{y}_{\mathit{ij}}=1,2,..\dots \end{array}\right.0\le {\pi }_{\mathit{ij}}\le 1$$E16

In the regression setting, both the mean ${\mu }_{\mathit{ij}}$ and zero proportion ${\pi }_{\mathit{ij}}$ parameters are related to the covariate vectors $x_{\mathit{ij}}$ and $z_{\mathit{ij}}$ respectively. Moreover, responses within the same region are likely to be correlated. To accommodate the inherent correlation, random effects $u_j$ and $w_j$ are incorporated in the linear predictors ${\eta }_{\mathit{ij}}$ for the Poisson part and ${\xi }_{\mathit{ij}}$ for the zero part. The

Hurdle Poisson mixed regression model is

$${\eta }_{\mathit{ij}}=log\left({\mu }_{\mathit{ij}}\right)={x_{\mathit{ij}}}^T\beta +u_j$$E17

$${\xi }_{\mathit{ij}}=log\left(\frac{{\pi }_{\mathit{ij}}}{1-{\pi }_{\mathit{ij}}}\right)={z_{\mathit{ij}}}^T\gamma +w_j$$E18

Where $\beta$ and $\gamma$ are the corresponding $\left(p+1\right)\times 1$ and $\left(q+1\right)\times 1$ vector of regression coefficients. The random effects $u_j$ and $w_j$ are assumed to be independent and normally distributed with mean 0 and variance ${{\sigma }_u}^2$ and ${{\sigma }_w}^2$, respectively [12].

3. Result and discussion

3.1 Result

A total of 14,370 women from all the 11 regions of the country were included and 7720 (53.3%) of the mothers have not faced any under-five death and only 78 (0.5%) of them lost 7 of their under-five children. Since there is a large number of zero outcomes. Additional screening of the number of under-five death calculated showed that the variance (1.697) is greater than the mean (0.9) indicating over-dispersion. This is an indication that the data could be fitted better by count data models which takes into account excess zeroes (Table 1).

Number of death	Frequency	Percent
0	7720	53.7
1	3314	23.1
2	1773	12.3
3	798	5.6
4	413	2.9
5	198	1.4
6	76	0.5
7	78	0.5
Total	14,370	100
Mean	0.90
Variance	1.67

Table 1.

Frequency distribution of the number of under-5 deaths per mother.

The mean numbers under-five death for uneducated fathers (1.1063) are higher than fathers with secondary and above education (0.353) and the mean number of under-five death that children who are delivered at home (1.0995) have highest than those delivered in health institutions (0.2507). Moreover, the highest and lowest mean number of child death are observed for a child of birth order of four and above and first birth order (1.1189 and 0.6167) respectively.

The result also showed that the breastfeeding mothers have a lower mean number of under-five deaths (0.6254) and the highest mean number of under-five death is occurred children born less than or equal to 24 months (1.0568) (Table 2)

Variables	Categories	Mean	Std. D	Women
Region	Tigray	0.7333	1.1375	1376
	Afar	1.1227	1.4106	1475
	Amhara	1.0535	1.3547	1478
	Oromia	0.8052	1.2342	2059
	Somali	0.9174	1.3566	1937
	Benishan	1.2054	1.5991	1251
	SNNPR	0.9580	1.2749	1809
	Gambela	0.6487	0.8761	928
	Harari	0.6169	0.9381	744
	Addis Abeba	0.2424	0.5738	524
	Dire Dawa	1.0292	1.4637	789
Residence	Urban	0.5816	1.0940	2512
	Rural	0.9645	1.3251	11,858
Education level of father	No education	1.1063	1.4265	8250
	Primary	0.7457	1.1365	4101
	Sec. and above	0.3531	0.7016	2019
Education level of mother	No education	1.1093	1.4111	9932
	Primary	0.4861	0.8710	3197
	Sec. and above	0.2627	0.5973	1241
Father’s occupation	Not working	1.0675	1.4414	2579
	Had working	0.8604	1.2587	11,791
Marital status	Married	0.8745	1.2812	13,086
	Others	1.1324	1.4152	1284
Age of first birth	<=16	1.1596	1.4613	6065
	>16	0.7062	1.1222	8305
Type of birth	Single	0.8556	1.2596	13,813
	Multiple	1.9390	1.6889	557
Place of delivery	Home	1.0995	1.3804	10,884
	Public sector	0.2691	0.6788	3107
	Private sector	0.2507	0.5846	379
Breastfeeding	No	1.2331	1.4524	6436
	Yes	0.6254	1.0793	7934
Birth order	first birth	0.6167	1.0082	3206
	2–3	0.7851	1.2032	4705
	4 and above	1.1189	1.4421	6459
Contraceptive used	No	0.9965	1.3607	10,976
	Yes	0.5775	0.9940	3394
Vaccination of child	No	1.0140	1.3573	11,881
	Yes	0.3419	0.7256	2489
Antenatal visit	No visit	1.1856	1.4147	9658
	1–3	0.3599	0.7550	2092
	4 and above	0.2649	0.6638	2620
Previous birth interval	0–24 months	1.0568	1.4120	7129
	25–36 months	0.9061	1.2517	3407
	>36 months	0.5939	1.0272	3834

Table 2.

Summary statistics of predictor variables related to under-five death in Ethiopia.

3.2 Multilevel count analysis of the data

3.2.1 Test of heterogeneity

Comparisons of multilevel models with their single-level count model, with LRT statistic given in Table 3. The values of LRT’s for each model are larger than the critical value ${\mathrm{X}}_{\mathrm{\alpha }}^2\left(2\right)=5.99$ with p-value <0.05. Thus, there is evidence of heterogeneity of under-five death across regions. It also observed that multilevel count regression model is best fit over the single level count regression models (Table 3).

Test	Multilevel Models
	Poisson	NB	ZIP	ZINB	HP	HNB
LRT	111.34	107.8	111.2	105.2	133.86	130.48

Table 3.

Likelihood ratio test value for multilevel and ordinary count model.

3.2.2 The goodness of fit and model selection criteria

The multilevel HNB regression model has a smaller value in deviance, AIC, and BIC than the other model. Consequently, we conclude that in this study multilevel HNB regression model is better than the other model (Table 4).

Criteria		Multilevel Models
		Poisson	NB	ZIP	ZINB	HP	HNB
Deviance		30200.4	30177.7	29661.7	29659.8	29331.1	29312.3
AIC		30246.4	30225.7	29745.7	29741.8	29415.1	29398.3
BIC		30420.6	30407.4	30063.8	30052.2	29733.2	29723.9

Table 4.

Model selection criteria for the multilevel count regression models.

3.2.3 Model comparisons in multilevel HNB model

The smallest deviance, AIC, and BIC is the better to fit. The result indicated that the random coefficient model is a better fit as compared to the empty model with random intercept and the random intercept and fixed-effect model (Table 5).

Model selection	Intercept-only	Random intercept	Random coefficient
Deviance	37,263	29,312	29042.9
AIC	37,273	29,398	29186.9
BIC	37,311	29,724	29,705

Table 5.

Summary results of multilevel HNB model selection criteria.

3.2.4 Results of random coefficient HNB model

From Table 6 in the random effect for truncated count part, estimates for intercepts and the slopes vary significantly at 5% significance level, which implies that there is a considerable variation in the effects of family size, age of mother and mother’s education these variables differ significantly across the regions. The value of 0.45, 0.175, 0.100, and 0.102 are the estimated variance of intercept (region), family size, age of mother, and mother’s education respectively.

Estimation of Fixed effect count part
	Estimate	S.E	Z value	P-value	IRR	95% CI for RR
						Lower	Upper
Intercept	−1.5889	0.2300	−6.908	0.0001	0.204	0.130	0.320
Vaccination child (No) (Ref)
Yes	−0.3219	0.0635	−5.071	0.0001	0.725	0.640	0.821
Family size	−0.0384	0.0184	−2.088	0.03681	0.962	0.928	0.998
Age of mother	0.0535	0.0044	12.229	0.0001	1.055	1.046	1.064
Antenatal visit (No)
1–3	−0.2352	0.0662	−3.552	0.0003	0.790	0.694	0.900
4 and above	−0.2406	0.0740	−3.249	0.0011	0.786	0.680	0.909
PB interval (≤24 months)
25–36 months	−0.2429	0.0298	−8.165	0.0001	0.784	0.740	0.831
37 and above	−0.3700	0.0361	−10.245	0.0001	0.691	0.643	0.741
Birth order (First)
2–3	0.3828	0.0419	9.141	0.0001	1.466	1.351	1.592
4 and above	0.4611	0.0398	11.575	0.0001	1.586	1.467	1.715
Religion (Orthodox)
Muslim	0.1909	0.0429	4.452	0.0001	1.210	1.113	1.316
Others	0.1535	0.0526	2.916	0.00354	1.166	1.052	1.293
Contraceptive use (No)
Yes	−0.1742	0.0382	−4.558	0.0001	0.840	0.779	0.905
Father’s education (No education)
Primary	−0.0393	0.0318	−1.235	0.21688	0.962	0.903	1.023
Secondary or above	−0.3334	0.0749	−4.449	0.0001	0.716	0.619	0.830
Mother’s education (No education)
Primary	−0.3224	0.1085	−2.973	0.0001	0.724	0.586	0.896
Secondary or above	−0.2525	0.2301	−1.098	0.27240	0.777	0.495	1.220
Father occupation (No)
Had working	0.0920	0.0304	3.023	0.00250	1.096	1.033	1.164
P delivery (home)
Public sector	−0.0451	0.0676	−0.667	0.50487	0.956	0.837	1.091
private sector	−0.4296	0.2063	−2.083	0.03724	0.651	0.434	0.975
Child Twin (single)
Multiple	0.3746	0.0390	9.607	0.0001	1.454	1.347	1.570
AMF birth (≤16)
17 and above	−0.3486	0.0244	−14.270	0.0001	0.706	0.673	0.740
Log(theta)	6.69	0.8435	7.93	0.0001
Estimation of Random effect truncated count part
Intercept $({\widehat{\mathrm{\sigma }}}_{\mathrm{u}0}^2$)	0.450	0.201	2.24	0.0250	0.1347	1.4527
Family size $({\widehat{\mathrm{\sigma }}}_{\mathrm{u}2}^2$)	0.175	0.086	2.035	0.0418	0.0736	0.4130
Age of mother $({\widehat{\mathrm{\sigma }}}_{\mathrm{u}3}^2$)	0.100	0.042	2.38	0.0173	0.0365	0.2354
Mother’s education $({\widehat{\mathrm{\sigma }}}_{\mathrm{u}8}^2$)	0.102	0.037	2.76	0.0052	0.0382	0.2701

Estimation of Fixed effect for zero-inflated part
	Estimate	S.E	z value	P-value	OR	95% CI for RR
						Lower	Upper
Intercept	3.1270	0.2914	10.730	0.0001	22.81	12.882	40.373
Vaccination child (No)
Yes	0.5298	0.1276	4.153	0.0001	1.699	1.323	2.181
Family size	0.2215	0.0246	9.018	0.0001	1.248	1.189	1.309
Age of mother	−0.1836	0.0072	−25.503	0.0001	0.832	0.821	0.844
Antenatal visit (No)
1–3	0.6961	0.0660	10.539	0.0001	2.006	1.762	2.283
4 and above	0.8253	0.0714	11.560	0.0001	2.283	1.985	2.626
PB interval (≤24 months)
25–36 months	0.5637	0.0544	10.361	0.0001	1.757	1.579	1.955
37 and above	1.2763	0.0575	22.211	0.0001	3.583	3.202	4.011
Contraceptive use (No)
Yes	0.2636	0.0571	4.616	0.0001	1.302	1.164	1.456
Father’s education (No education)
Primary	−0.0760	0.0533	−1.425	0.154	0.927	0.835	1.029
Secondary or above	0.1388	0.0845	1.644	0.100	1.149	0.974	1.356
Mother’s education (No education)
Primary	0.1262	0.0595	2.121	0.033	1.135	1.010	1.275
Secondary or above	0.2165	0.1131	1.915	0.055	1.242	0.995	1.550
Father occupation (No)
Had working	−0.3287	0.0620	−5.302	0.0001	0.720	0.638	0.813
P delivery (home) (ref.)
Public sector	0.7722	0.1884	4.099	0.0001	2.164	1.496	3.131
Private sector	0.4454	0.3847	1.158	0.0001	1.561	0.735	3.318
Child Twin (single)
Multiple	−1.4608	0.2398	−6.093	0.0001	0.232	0.145	0.371
AMF birth (≤16)
17 and above	1.0501	0.0469	22.404	0.0001	2.858	2.607	3.133
Estimation of random effect for zero-inflated part
Intercept $({\widehat{\mathrm{\sigma }}}_{\mathrm{w}0}^2$)	0.668	0.234	2.855	0.0043		0.1681	2.6562
Vaccination child $\left({\widehat{\mathrm{\sigma }}}_{\mathrm{w}1}^2\right)$	0.161	0.058	2.776	0.0055		0.0185	0.5704
Family size $({\widehat{\mathrm{\sigma }}}_{\mathrm{w}2}^2$)	0.146	0.070	2.086	0.0369		0.0566	0.3733
Age of mother $({\widehat{\mathrm{\sigma }}}_{\mathrm{w}3}^2$)	0.042	0.015	2.8	0.0051		0.0083	0.2096
Place of delivery $({\widehat{\mathrm{\sigma }}}_{\mathrm{w}8}^2$)	0.333	0.161	2.068	0.0385		0.1234	0.8987
Child Twin $({\widehat{\mathrm{\sigma }}}_{\mathrm{w}9}^2$)	0.463	0.212	2.184	0.0284		0.0707	1.8771

Table 6.

The results of random coefficients HNB model.

The fixed part of Table 6 shows vaccination of children has a significant impact on the number of non-zero under-five death per mother. The expected number of non-zero under-five death for vaccinated children are decreased by a factor of 0.73 as compared with non-vaccinated children.

Unexpectedly, the findings of this study also showed that family size is a significant determinant of under-death. The risk of under-five death increases as family size decreases. For a unit increased family size, then the expected number of non-zero under-five death per mother is decreased by 0.04%. And also, mother’s current age is a significant positive association with under-five mortality. Particularly, with each yearly increase in the age of mother, the expected number of non-zero under-five death is increased by 0.06%.

The result also revealed that the expected number of non-zero under-five death whose mothers visited at least 4 times during pregnancy is 0.79 times lower compared to child whose mothers who have not received any antenatal check during pregnancy.

This study found that preceding birth interval has a significant negative association with under-five mortality. The expected number of non-zero under-five death with children born more than 36 months after the previous birth decreased by 31 percent relative to children born less than 2 years after the previous birth. In addition to this as birth order increases the under-five mortality shown an increase. The expected number of non-zero under-five deaths with children’s birth order 4 and above is increased by 59% as compared to the first order.

The finding of this study also revealed that mother’s and father’s levels of education have a significant factor in the number of under-five death. The expected number of non-zero under-five death for mothers with primary education is 0.724 times lower as compared to those with non-educated. Likewise, the expected number of non-zero under-five death for fathers with secondary and above education is 0.716 times lower as compared to those with non-educated (Table 6).

The random effect for the logit part also shows that estimates for intercepts and slopes vary significantly, which suggests that there is considerable variation in the effects of vaccination of child, family size, age of mother, place of delivery, and child twins, these variables differ significantly across the regions. The value of 0.688, 0.161, 0.146, 0.042, 0.333, and 0.463 are the estimated variance of intercept (region), vaccination of child, family size, age of mother, place of delivery, and child twins respectively (Table 6).

The fixed part of zero-inflated HNB model indicted that the estimated odds that the number of under-five death becomes zero with vaccinated children is 1.70 times as compared to non-vaccinated children. An increase in family size by 1 result, the estimated odds that the number of under-five death becomes zero is increased by 1.25. Similarly, the age of mother increase in by a year, the estimated odds that the number of under-five death becomes zero is decreased by 17%.

The result also revealed that the estimated odds that the number of under-five death becomes zero with mothers visit 4 and above is 2.28 times higher as compared to mothers who have not received any antenatal visit during pregnancy. In addition to, the estimated odds that the number of under-five death becomes zero for those children born with preceding birth intervals of more than 36 months is 3.58 times children born with preceding birth intervals of fewer than 24 months. The study also found that the employment status of a father is found to have an association with under-five mortality. The odds of the number of under-five death becomes zero with children born from fathers who have to work is 0.72 times fathers without work. Moreover, estimated odds that the number of under-five death among mothers who are used contraceptives is 1.30 times more than as compared to mothers who were not used contraceptive (Table 6).

3.3 Discussion of the results

In this study, we have examined the influence of particular social, economic, and demographic characteristics of mothers on under-five mortality in Ethiopia. Results showed that several factors are implicated in under-five mortality.

The level of parental education emerged as a strong predictor of under-five mortality, that is, the mortality rate decreases with an increase in parental education level. This result is in line with the previous study that, the higher the level of maternal and father education, the lower child mortality [20, 21, 22, 23]. The risk of under-five death associated with multiple births is very high relative to single births and this study is similar to the previous studies that birth type to be linked with under-five child death as multiple births are associated with a higher risk of child mortality [9, 21, 23, 24]. The result also showed that under-five mortality is decreased as the length of preceding birth interval increased. This finding is similar to Gebretsadik and Gabreyohannes [21], Bereka and Habtewold [24], and Getachew and Bekele [25].

The finding of the study revealed that the death of under-five children from mothers using contraceptive is significantly less than children from non-contraceptive methods using mothers. The result is in accordance with Getachew and Bekele [25] and Bedada [26]. Those vaccinated children are lower risk of mortality than that of non-vaccinated children. Similar result was observed in another study done by Berhie and Yirtaw [9].

Mother’s age at first birth is negatively correlated with under-five mortality that decreased the risk of under-five mortality as increase mother’s age at first birth. The estimated result also shows that mothers age at first birth increases reduced the risk of under-five mortality and mothers born their first child at a younger age face high under-five mortality risk which is similar to the previous studies conducted by different scholars [22, 23, 24, 25, 26]. In addition to this, the study reported that for every unit increase in the ages of mother, the risk of under-five mortality increases, and this is similar to the findings of Yaya et al. [22] and Alam et al. [23]. Further, the result of this study indicated that the religion of respondents has significantly associated with under-five death with those who practice Islamic and those who practice other religions having higher chances of experiencing under-five death compared to those who practice Orthodox Christianity religions. This is consistent with the study of Yaya et al. [22].

The study showed that children born from working fathers have a higher risk of mortality than non-working fathers. This finding is consistent with Getachew and Bekele [25] additionally, increase the number of antenatal visits during pregnancy is reduce the risk of under-five mortality and this finding is confirmed by the previous researches [25]. Children born in the public and private sectors are at lower risk than those born at home. This might be due to the proper health care and attention they received during and after delivery. This has been confirmed by different studies [24, 25, 27].

The study also revealed that household size is an important variable that affects the number of under-five mortality. Amazingly, as household size increases the risk of under-five mortality significantly decreased. This result is consistent with Berhie and Yirtaw [9], Alam et al. [23], Bedada [26], and Ahmed et al. [28]. Birth order increases the under-five mortality also increases and this result is consistent with the literature reviewed and contribution from different studies on birth order [9, 24, 28].

4. Conclusions and recommendations

The purpose of this study was to identify, socioeconomic demographic, health, and environmental related determinants and to assess regional variation of a number of under-five mortality per mother in Ethiopia. The descriptive results showed that 53.7% of mothers have not experienced under-five death and only 0.5% of them lost 7 of their under-five children.

In multilevel count regression analysis, individual mothers are considered as nested within the various regions in Ethiopia. As a first step in the multilevel approach, the likelihood ratio test is applied to see if there are differences in the number of under-five death among the regions. The test suggested that, the number of under-five death varies among regions and multilevel count model fit better than the single level count model. Among the six multilevel count regression model, multilevel HNB model is the best to account for the heterogeneity of the number of under-five mortalities per mother among regions of Ethiopia.

From the three multilevel HNB regressions models, the random coefficients model provided the best fit for a number of under-five death per mother. In fixed part of random coefficients HNB model the variables like mother’s age, education level of father, father’s occupation, family size, age of mother at first birth, religion, vaccination of child, contraceptive use, birth order, preceding birth interval, child twin, place of delivery and antenatal visit have statistically significant effect on under-five mortality. The random part of multilevel HNB model also revealed that under-five deaths per mother differ among regions of the country in terms of mother’s education, family size, ages of mother, place of delivery, vaccination of child, and type of birth. As a result, this study proposes that all regions need to have separate estimates of HNB regressions for all 11 geographical regions.

Based on the findings of the study, we forward the following possible recommendations:

1. Policies and programs aimed at addressing regional variations in under-five mortality must be formulated and their implementation must be vigorously pursued. To achieve this, while under-five mortality reduction measures which have worked to some extent in the Affar, Amhara, Benshangul-Gumuz, SNNP and DireDawa must be strengthened to achieve more results in the region, these measures could be extrapolated and applied in the remaining regions of the country. Such measures include having hospital delivery, attending prenatal care, vaccination of child, etc.

2. Efforts are needed to extend educational programmers aimed at educating mothers on the benefits of the antenatal check, age of first birth, spacing birth interval, vaccination of child, and place of delivery to reduce under-five mortality.

3. The concerned body should work closely with both the private sector and civil society to teach households to have sufficient knowledge and awareness on under-five mortality and mechanisms of reduction and to make children very well.

4. Further studies should be conducted by taking three or four-level count regression into account to assess the variation of under-five mortality across enumeration areas and regional levels.