Determinants of Under-Five Mortality in Tach-Armachiho District, North Gondar, Ethiopia

Background : Under-five mortality rate, often known by its acronym U5MR, indicates the probability of dying between birth and five years of age, expressed per 1,000 live births. Globally, 16,000 children under-five still die every day. Especially in Sub-Saharan Africa every 1 child in 12, dying before his or her fifth birthday. This study aims to identify the determinants of under-five mortality among women in child bearing age group of Tach-Armachiho district using count regression models. Methods: For achieving the objective, a two stage random sampling technique (simple random sampling and systematic random sampling techniques in the first and second stages respectively) was used to select women respondents. The sample survey conducted in Tach-Armachiho district considered a total of 3815 households of women aged 15 to 49 years out of which the information was collected from 446 selected women through interviewer administrated questionnaire. Results: The descriptive statistics result showed that in the district 16.6% of mothers have faced the problem of at least one under-five death. In this study, Poisson regression, negative binomial, zero-inflated Poisson and zero-inflated negative binomial regression models were applied for data analysis. Each of these count models were compared by different statistical tests. So that, zero-inflated poisson regression model was found to be the best fit for the collected data. Results of the zero-inflated Poisson regression model showed that education of husband, source of water, mother occupation, kebele of mother, prenatal care, place of delivery, place of residence, wealth of house hold, average birth interval Conclusions: In this study, it was found that the factors like average birth interval and average breast feeding were found to be statistically significant factors in both groups (not always zero category and always zero category) with under-five child death whereas education of husband, source of water, place of delivery, mother occupation and wealth index of the household have significant effect on under-five mortality under not always zero group. Place of residence, kebele of mother and prenatal care have a significant effect on under-five mortality in Tach-Armachiho district on inflated group.

five mortality rate above 100 deaths per 1000 live births are in Sub-Sahara Africa [6]. According to the "Level and trends in child mortality Report 2013" Ethiopia is one of the seven high-mortality countries (together with Bangladesh, Malawi, Nepal, Liberia, Tanzania and Timor) with the greatest declines by two thirds or more in lowering child mortality between 1990 and 2012 [7]. Infant mortality rate in Ethiopia was 59 deaths per 1000 live births, while underfive mortality rate was 88 per 1000 live births [8].
The Ethiopian Demographic and Health Survey reported 123 and 88 deaths per 1000 live births in its 2005 and 2011 reports, respectively. The recent UNICEF report puts Ethiopia's child mortality rate at 68 per 1000 live births. These figures imply that the child mortality rate in the base year 1990 was as high as 206. The reduction from 206 to 68 deaths in 1000 live births clearly shows that Ethiopia has designed sound health policies and backed them up with the necessary resources to ensure great success in implementation [9,4]. According to UN Interagency Group for Child Mortality report, in 2015 the under-five mortality rate of Ethiopia was 59 per 1000 live births [10].

Study Area, Study population and Data Collection Method
Tach Armachiho is one of the districts in North Gondar Zone Amhara Regional State of Ethiopia. The district is located 814 km Northwest of Addis Ababa and 65 km North West of Gondar town with the altitude of 600-2000 meters above sea level (masl) with the temperature of 25-42°C and with annual rainfall of 800-1800 mm [12]. According to the district administrative data the district have 24 kebeles. Total population of the district is 106085 among this 54358 are males and 51727 are females with 21217 total number of households [13]. All women who are currently living at least for six months in Tach Armachiho district are the study population. The target population comprises of those women residing in Tach Armachiho district with the age of women from 15-49 that were selected from the total population. In this study, the researcher used primary data. Primary data were conducted using interviewer administrated questionnaire and the questionnaire was collected and pre-tested by selected respondents under the supervision and monitoring of the researcher. In the preliminary, the questionnaire was prepared by English language and then it was translated to Amharic language. Enumerators engaged with the close supervision of the researcher and they trained on the methods of administering, on the contents of the questionnaires and on the objective of why the data is collected.

Sample Size Determination and Sampling Techniques
.The sample size for collecting data for this study determined by using formula of simple random sampling [14]. The formula to estimate sample size is given as follows: study. According to [15] suggest that 30 representative participants from the population of interest is a reasonable minimum recommendation for a pilot study where the purpose is preliminary survey.
d= desired degree of precision. Most of the time 5% is desirable to increase the sample size and the precision of the study [16].
Z α 2 ⁄ = Z Value for the 95% level of confidence is (1.96) N= total number of population size in the study area (in this case total number of households).
n= desired number of sample size.
Based on the above formula , the desired sample size for the study is as follows: However, in estimating the sample size of two stage random sampling especially if the first and the second sampling techniques are different, it is often convenient to use the design effect. This has two primary uses, in sample size estimation and in appraising the efficiency of more complex plans [14]. The design effect is kept as low as possible in order for the results to be usably reliable. Unless previous surveys have been conducted or similar ones in other countries so that proxy estimates of design effect can be utilized, a default value of 1.5 to 2.0 for design effect is typically used by the sampling practitioner in the formula for calculating the sample size. To keep the design effect as low as possible, select a systematic sample of households at the last stage, geographically dispersed, rather than a segment of geographically contiguous households [17]. By minimizing or controlling the design effect as much as possible the researcher takes 1.5 for design effect.
Finally: n f = n*1.5=297*1.5= 446 Lastly the estimated sample size has to be distributed to the four selected kebeles using proportional allocation method since all kebeles have no the same total number of households.

Study Variables
The response variable for this study was the number of under-five death experienced by individual mother. Children who were born alive and later die before reaching their fifth birthday was considered.

Methods of Data Analysis Poisson and Negative binomial regression model
The Poisson regression model is often considered as a benchmark model for modeling count data. This model dominates the count data modeling activities as it suits the statistical properties of count data and is flexible to be reparameterised into other form of distributional functions [18,19]. Though practically it is inadequate for its restrictive assumptions, still the Poisson regression model is the simplest model and lends a good starting point to model count data. In this model, the response variable is assumed to be independent and follows a Poisson distribution.
Poisson regression assumes a Poisson distribution, characterized by a substantial positive skewness with variance equals mean. It tends to fit such data better than the linear regression model. However, if the variance is larger than the mean, it induces deflated standard errors and inflated standardized normal (i.e. Z-normal) values, resulting in increased Type I errors that make Poisson regression less adequate. Some researchers suggest that, when there is an overdispersion which does not arise from an excess of zeros, it is better to use other models, such as negative binomial which can take care of the over dispersion problem [20,21].
Poisson regression model is used when the dispersion parameter becomes zero (α=0) otherwise negative binomial regression model is better. The negative binomial distribution is one of the most widely used distributions when modeling count data that exhibit variation that Poisson distribution cannot explain. When the Poisson model assumption fails, this model may fit better, and addresses the issue of overdispersion by introducing a dispersion parameter to accommodate for unobserved heterogeneity in count data. However, this is true only if it is not attributed to excess zeros [22,23]. The negative binomial regression model may not be well flexible to handle excess zeros. This motivates the development of zero-inflated count model to model excess zeros in addition to overdispersion. This technique was first introduced by [24]. In such cases, one can use the zero-inflated Poisson or zero-inflated negative binomial model to fit the data.

Zero-inflated Poisson and Zero-inflated negative binomial regression model
Zero-inflated Poisson (ZIP) model has been first considered by [24] as a mixture of a zero point mass and a Poisson. This model assumes two latent groups, one is capable of having positive counts and the other will always have zero count. [25) Similarly considers the negative binomial model case. When there are excess zeros and high variability in the non-zero outcomes, ZIP models are less adequate than ZINB models The probability mass function for zero-inflated Poisson regression model is given as: If Yi are independent random variables having a zero-inflated Poisson distribution, the zeros are assumed to arise in two ways corresponding to distinct underlying states. The first state occurs with probability i and produces only zeros, while the other state occurs with probability (1i) and leads to a standard Poisson count with mean λi. In general, the zeros from the first state are called structural zeros and those from the Poisson distribution are called sampling zeros. This two-state process gives a simple two-component mixture distribution with probability mass function: This is denoted by Yi~ZIP (λi, i) such that 0≤ϕi<1, where λi is the mean of the non-zero outcomes that can be modeled with the associated explanatory covariates using a natural logarithmic link function as: where Xi=(1,xi1, xi2, …, xik) Ꞌ is a (k+1)x1 vector of explanatory variable of the i th subject and β is (k+1)x1 vector of regression coefficient parameters. i (0< i<1) is the probability of an excess zero (being in the zero mortality state) determined by a logit model [24,26]. To predict membership in the "Always Zero" group, use the same variables or use a smaller subset of the variables or even different variables altogether and extended it by specifying a logit model form in order to capture the influence of covariates on the probability of extra zeros: that is: Note that when i is equal to zero, then the mean of a ZIP model is the same as that of a Poisson model, and the ZIP model is essentially the same as a Poisson model. It can be further verified by the variance to mean ratio that a ZIP model is suitable to capture over-dispersed data in view of the fact that its variance is generally greater than its mean value. The ratio ϕ 1-ϕ plays a similar role as the dispersion factor α in a NB model and it is employed to capture the overdispersion characteristics of the analyzed data.
An alternative formulation for the ZIP which is found to be more useful for interpretation is: is the probability of observing at least one child death count. For observations y1, y2,…,yn the likelihood function for ZIP model is given by [27].
Taking log on both sides the log-likelihood function is given by: where I(·) is an indicator function that is one if the response (yi) equals zero, and zero otherwise.
The first and second derivatives of ln (L) with respect to β and γ are: where p and q are the number of covariates for non-zero group and for zero group respectively.
To apply the zero-inflated Poisson model in practical modeling situations, the parameters λi and i can be obtained through the following link functions [24]: Where X (n x (k+1)) and Z (n x (q+1)) are covariate matrixes, and β and γ are, respectively, unknown parameter vectors with (k+1)x1 and (q+1)x1 dimension [27]. Maximum likelihood estimates for β and γ can be obtained using standard approaches for mixture model.
The use of the logit link function for ϕ constrains i to lie between 0 and 1 and will problematic when ϕ = 0, a case of interest as this corresponds to the standard Poisson regression model.

Model Comparisons for Under-Five Mortality
The response variable in this study was the number of under-five deaths per mother in her life time. Such type of data is well fitted using count data regression models rather than other regression models. In this study different possible count data models were considered. To identify the most appropriate and well fitted count regression model for the collected data, loglikelihood ratio test, Akaike information criteria and Bayesian information criteria were used.

Descriptive Statistics.
The data was analyzed from women of child bearing age in the study area. Based on table 2, Out of the total number of women considered in the sample 83.4% of the mothers have not faced any U5D in their lifetime. From the sampled women, the proportion of experiencing under-five mortality was about 16.6 percent. Table 2 and Figure 1 showed the number and percentage of U5D that the mothers in the sample have encountered in their lifetime. Large numbers of under-five mortality per mother were less frequently observed, which seems highly skewed to the right with excess zeroes. This perhaps an indication that count data models with excess zeroes may be take into account. Table 3 presents summary statistics of the explanatory variables that directly influence the risk of under-five mortality. The variables which are included in the study are education of mother, place of residence, age at first birth, education of husband, source of water, availability of toilet facility, place of delivery, child vaccination adaptation, distance of health center, kebele of mother, occupation of mother, occupation of husband, wealth index, health status of mother, prenatal care, average birth interval and average breast feeding.
The Another maternal variable that possibly has a strong bearing on the survival prospects of a child is the mother's age at the time of first birth. Regarding mother's age at first birth, the mean number of under-five mortality was 0.28 for mothers who started their first birth below the age of 20 and the death showed a high variability with a standard deviation of 0.643. However, on the average 0.13 number of under-five deaths existed for the mother's who delivered their first children on the age of 20 and above. It also showed less variation of child deaths than for the mothers who delivered their first child before the age of 20. Besides mothers who delivered their children at home faced more under-five mortality than mothers who delivered their children at health center. The mean numbers of under-five mortality for mothers who delivered their children at home and at health center were 0.27 and 0.14 respectively.
Concerning kebeles, Kokora and Sanja had the highest mean number of under-five deaths per mother were 0.31 and 0.25 respectively, while Kembew and Masero-demb kebeles had the third and fourth smallest mean number of under-five deaths per mother which were 0.20 and 0.17 respectively. As far as the distance of health facilities was concerned, mean number of under-five death per mother increased with an increase in the distance of health facilities from mothers home. Specifically, the mean under-five death was 0.22 for women's home distance from health center was below 8 kilometer, 0.28 mean number of under-five death was occurred for those mothers whose home distance from health center was eight and above kilometer. Whereas, the variation of under-five mortality was higher for the mothers home had long distance from health centers than the homes which had smallest distance.
When child vaccination adaptation of mother was assessed, the mean number of under-five mortality per mother was 0.60 for mothers who did not adapted vaccinating their children with

Model Comparisons for Under-Five Mortality
The starting point of count regression models are fitting Poisson regression model. The fitted Poisson regression model is then tested for overdispersion. If so, the negative binomial model is an immediate solution to accommodate this overdispersion. However, the overdispersion might be occurred due to excess zeroes. This brings the zero-inflated models into the picture. Thus, in order to select an appropriate model which fits the data well, the standard Poisson, negative binomial, zero-inflated Poisson and zero-inflated negative binomial regression models were considered.

Model selection
In order to select the best fit count regression model, different statistical tests were used. Among this likelihood ratio test, Vuong test, mean absolute difference, Pearson sum of predicted and actual probability and residual plots for estimated models were considered.
The BIC's and AIC's in the above When the log-likelihoods of ZIP and ZINB models were observed in Table 9 there was virtually no difference in their log-likelihoods indicated that the ZINB model did not improve the fit over the ZIP model. Moreover, the likelihood ratio test was used to compare the fit of the ZIP with ZINB regression models. Table 9 showed that the likelihood ratio test at one degree of freedom is found to be non-significant (X 2 =0.000 and p-value= 0.500), which indicates that ZIP   Lastly, ZIP regression model is found to be the most appropriate model for our under-five mortality data. This fits the data better than the other possible candidate count regression models.
Next in the discussion part, the results of ZIP regression model were discussed. Table 6 and 7 provide estimates of the effect of some selected variables on the mortality of children. A distinction has to be made between the parameters in the non-zero model predicting the mean response and the parameters for estimating the probability of zero-inflation model. The interpretation of the coefficients in the non-zero group was the same as that of standard Poisson regression model. The factors such as education of husband, source of water, place of delivery, mother occupation, wealth index, average birth interval and average breast feeding time were found to have statistically significant effect with predictors of this count outcome. But the rest of the predictors were found to be statistically not-significant with underfive child death.

Results in
The findings of the study showed that education of husband was found to be a significant factor on under-five child mortality. Those children that were born from a father who have secondary and above education level, 71.8% less likely to risk of under-five deaths as compared to being born to non-educated father by keeping the other predictors constant. Similar results were obtained by [28,29]. This may be due to the fact that educated husbands give better care for their children, fulfill quality food, supporting their wives before and after delivery time and immunizing their children at the right time.
Source of drinking water was also found to have a significant effect on under-five mortality. The findings of this study showed that mothers who used water from unprotected sources were at a higher risk of experiencing under-five death than those who used pipe/tube water. The risk of under-five mortality for those children whose mothers used unprotected source of water was 66.6% higher than those who used piped/tube water supply. Similar findings were obtained by [30,31].
Place of delivery was also investigated as a significant effect factor for under-five child deaths, such that children born in health centers had decreased the risk to death compared to those children born at home. That is children who were born at health center were less likely to die before age five than those who were born at home. The risk of under-five deaths of those mothers who delivered at health center showed that a 75.4% decrement than mothers who delivered their children at home. This was similar with the study of [32,30].
Mother's occupation was also found to have a significant effect with under-five mortality, such that children born from mothers who have other type of work were 89% times more likely to die before age five as compared to those mothers who are house wives. This finding was consistent with [29].
In addition, economic status of the household was also one of the socio-economic factors that are included in this study. Results in Table 6 indicated that under-five child mortality risk was 52.9% less likely from children of rich mothers as compared to children of poor mothers. This is quite expected; under-five mortality for the poor family is higher than that of the rich family [29,33].
It is believed that wealthier families can provide better nutrition, shelter and health services to their children, which intern can enhance young children's survival. Table 6 revealed that average birth interval was found to be statistically significant effect on under-five mortality. Women with a short birth interval between two pregnancies have insufficient time to restore their nutritional reserves, which might affect foetal growth. The findings of this study showed that mothers who have average birth interval time greater than or equal to two years were at a lower risk of experiencing under-five deaths than those who have average birth interval time of less than two years. The risk of under-five mortality for those children whose mothers average birth interval time is greater than or equal to two were 78.4% less as compared to those who have average birth interval time less than two years. Similar findings were obtained by [34,35,30]. Table 6 showed that children of mothers whose average breast feeding time is two and higher have a significantly lower under-five deaths than children of mothers whose average breast feeding time is lower than two. Hence, the risk of under-five mortality for those children who are fed with their mothers breast for two years and above were 74% less likely than mothers whose average breast feeding time is less than two years by keeping all other factors constant. Similar findings were obtained by [36]. It is recognized that mother's milk provides protection against gastro intestinal and respiratory diseases, it also meets children's nutritional requirements.
The second set of coefficients on Table 7 predicts the dichotomous outcome of group membership. Only residence, kebele of mother, prenatal care, average birth interval and average breast feeding were found to be statistically significant predictors of these dichotomous outcomes.
Place of residence was found to be a significant factor for under-five child mortality. The odds of experiencing under-five mortality for those women residing in urban area were 91% less likely of those women residing in rural areas. This result is similar with [37].
The results of always zero group revealed that the odds of under-five mortality in Masero-demb, Kokora and Kembew were 13.36, 5.45 and 3.34 times more likely than among under-five deaths in Sanja respectively.
As an indicator of health care service utilization during pregnancy, prenatal care service factors demonstrated a significant effect with under-five child mortality. Children born from mothers attending prenatal care have 83.7 percent lower risk of mortality than children born from mothers attending no prenatal care. Similar findings were obtained by [34]. Giving prenatal care increase the chance of under-five survival. Appropriate prenatal care can play a role by educating women and their families to recognize delivery complications that require referral to health care services to achieve a better health outcome for both mothers and children. Average birth interval was also found significant effect with under-five mortality under the category of "always zero" group. The odds of under-five mortality of average birth interval greater than and equal to two was 85 percent less likely as compared to average birth interval less than two. Lastly, average breast feeding time was also another covariate for under-five mortality and which was found to be statistically significant. Children of mother's who feed their children for two and above two years were 92 percent less likely for under-five mortality than of mother's who feed their children for less than two years.

Conclusion
The study has empirically examined and distinguished the factors that have significant effect on under-five mortality in Tach-Armachiho district. In this study, it was found that ZIP and ZINB regression models were better fitted the data than Poisson and negative binomial regression models. Moreover, the zero-inflated Poisson model was better fitting to the data, which is characterized by excess zeros and low variability in the non-zero outcomes. The source of overdispersion for this data was originated from the inflation of zeros and there exists low heterogeneity of not always zero-group values.
Fitting zero-inflated Poisson regression model, it was found that the factors like average birth interval and average breast feeding were found to be statistically significant factors in both groups (not always zero category and always zero category) with under-five child death whereas education of husband, source of water, place of delivery, mother occupation and wealth index of the household have significant effect on under-five mortality under not always zero group. Place of residence, kebele of mother and prenatal care have a significant effect on under-five mortality in Tach-Armachiho district on inflated group.

Limitations of the Study
The data used in this study was primary data of woman aged from 15-49 years. Only surviving women were interviewed; therefore, no data were available for children if their mother had died.
Although many factors affect under-five mortality as indicated by different studies in different countries. This study was undertaken to explore some covariates only this is because of crosssectional nature of our analysis and most variables were time varying covariates.

Consent for publication
Not applicable.

Availability of data and materials
The datasets used and/or analyzed during the current study are available from the corresponding author on reasonable request.