### Study design and source of data

The dataset used for this study was obtained from 2016 Ethiopian Demographic Health Surveys conducted from January 18 to June 27, 2016, across the country. The survey was a population-based cross-sectional study. For the surveys, the 2016 EDHS sample was stratified and selected in two stages. In the first stage, a total of 645 clusters were randomly selected proportional to the household size from the sampling strata, and in the second stage, 28 households per cluster were selected using systematic random sampling. In this survey, a total of 7230 mothers selected from 645 clusters were included in this study.

### Study variable

#### Dependent variable

Number of perinatal mortality per mother preceding 5 years from the survey.

#### Independent variable

Place of residence, Age of mothers (years), Educational status of mothers, Educational status of husbands, mode of delivery, place of delivery, ANC visit, Parity, Type of birth, and history of abortion.

### Operational definition

*Perinatal mortality* is deaths after 28 competed for gestational weeks (still birth) and the first 7 days of birth (early neonatal death) per mother preceding 5 years from the survey.

*Antenatal care visit* is the number of attending ANC clinic during pregnancy, which categorizes the mother who visited an ANC clinic at least four times (≥ 4), the mother who visited an ANC clinic at most three times (< 4).

*Parity* is the number of life born babies of the mother. The categories are: the mother who had given at least four life birth (≥ 4) and the mother who had given at most three life birth (< 4).

*Mode of delivery* is the mode of giving the last birth preceding 5 years from the survey. Categories are: caesarean section (CS) and normal (vaginal).

*History of abortion* is the history of terminated pregnancy of the mother. Categories: Yes/No.

### Statistical method

In this study, the variable of interest is a count variable. When the dependent variable is a count, it is appropriate to use non-linear models based on non-normal distribution to describe the relationship between the response variable and a set of predictor variables. For count data, the standard framework for explaining the relationship between the outcome variable and a set of explanatory variables includes the Poisson, ZIP, and Poisson hurdle models. The advanced models for this study count data are the Poisson hurdle model.

### Poisson regression model

Poisson regression has been widely used for fitting count data. It is traditionally conceived as the basic count model upon which a variety of other count models are based [10]. The probability mass function for Poisson regression is:

$$\mathrm{P}(\mathrm{Yi}=\mathrm{yi})=\frac{{\mathrm{e}}^{-{\upmu }_{\mathrm{i}}} {{\mu }_{i}}^{{y}_{i}} }{{\mathrm{y}}_{\mathrm{i}!}},\quad{y}_{i}=\mathrm{0,1},\mathrm{2,3},4,\dots$$

\({\upmu }_{\mathrm{i}}\) is the parameter of the Poisson distribution. It can be proved that the Poisson distribution is the mean equal to the variance. Such that the Poisson regression model is:

$$\mathrm{Log }\left({\upmu }_{\mathrm{i}}\right)={\beta }_{0}+{\beta }_{1}{x}_{1}+{\beta }_{2} {x}_{2}+{\beta }_{3} {x}_{3}+\dots +{\beta }_{p}{x}_{p}={X}_{i}^{T}\upbeta .$$

β are the vector coefficients \({X}_{i}^{T}\). Unfortunately, in much of the cases, the number of perinatal mortality data produces variance that is greater than the mean, well known as over-dispersion. The over-dispersion is a result of extra variation in the number of perinatal death means which can be caused by various factors such as model misspecification, omission of important covariates, and excess zero counts [18]. In this case, applying a Poisson regression model for the number of perinatal death data would result in an underestimation of the standard error of the regression parameters. Therefore, the negative binomial model will be introduced.

In some cases, excess zeros in the number of perinatal death data exist and are considered as a result of overdispersion. In this case, the NB model cannot be used to handle the overdispersion which is due to the high amount of zeros. To do this, zero-inflation (ZI) models including Zero Inflated Poisson (ZIP) models can be used. ZIP models assume that all zeros count come from two different processes: the process generating excess zero counts derived from a binary model, and the process generating non-negative counts for the number of perinatal death including zero values. A Poisson regression model with many zero outcomes on the response variable. The zero-inflated Poisson regression model is more effective for many zero outcomes than Poisson regression.

### Zero inflated Poisson regression model

In ZIP regression, the counts Y_{i} equal 0 with probability p_{i} and follow a Poisson distribution with mean \({\mu }_{i}\), with probability 1 − p_{i} where i = 0, 1, 2,…, n. ZIP model can thus be seen as a mixture of two-component distributions, a zero part, and no-zero components, given by [10]:

$${\text{P}}\left( {{\text{Y}} = {\text{y}}} \right) = \left\{ {\begin{array}{*{20}l} {p_{i} + \left( {1 - p_{i} } \right)e^{{ - \mu_{i} }},\quad y_{i = 0} } \\ {\left( {1 - p_{i} } \right)\frac{{e^{{ - \mu_{i} }} \mu_{i}^{{y_{i} }} }}{{y_{i !} }} ,\quad y_{i} = 1,2,3, \ldots } \\ \end{array} } \right.$$

Assume that there are **p** predictors for logistic regression function and negative binomial regression function. Hence, the ZIP regression model can be written as follow:

\(\mathrm{Logit }\left({p}_{i}\right)={{x}_{i}}^{T}\beta \, \mathrm{and\,Log}\left({\mu }_{i}\right)={{x}_{i}}^{T}\gamma\) where \({x}_{i}-[1,{x}_{1},{x}_{2}\dots {x}_{p}\)] is (p + 1) \(\times\) 1 dimensional vector, β = [\({\beta }_{0},{\beta }_{1},{\beta }_{2}{,\beta }_{3}\dots {\beta }_{p}\)] and \(\gamma =[{\gamma }_{0},{\gamma }_{1},{\gamma }_{2}, {\gamma }_{3},\dots {\gamma }_{p}\)] is a (p + 1) \(\times\) 1 dimensional vector of regression parameters.

### Poisson hurdle regression model

A hurdle model consists of two components—a point mass at zero and a distribution that generates non-zero counts. The first component is a binary component that generates zeros and ones (here “ones” correspond to non-zero values in data) and the second component generates non-zero values from a zero-truncated distribution. The most widely used hurdle models are those with the hurdle value at zero [4]. All zeros in the hurdle model are assumed to be “structural” zeros, i.e., they are generated from a single process, and are observed since the condition is absent. We explore two zero-truncated count distributions for the hurdle model specification [19]. The hurdle model of count data can be expressed as follows for the Poisson distribution. We consider a Hurdle Poisson Regression Model in which the response variable y has the distribution:

$$\mathrm{P}(\mathrm{Y}=\mathrm{y})=\left\{\begin{array}{l}{p}_{i} , {y}_{i=0}\\ \left(1-{p}_{i}\right)\frac{{e}^{-{\mu }_{i}} {{\mu }_{i}}^{{y}_{i}}}{{y}_{i !}(1-{e}^{-{\mu }_{i}})} ,\quad {y}_{i}=\mathrm{1,2},3,\ldots \end{array}\right.$$

where \({\mu }_{i}\) is the mean of the untruncated Poisson distribution.

Zero and truncated hurdle model:

$${\text{Logit }}(p_{i} ) = x_{i}^{T} \beta \,\,{\text{and Log }}(\mu_{i} ) = x_{i}^{T} \gamma$$

where \({x}_{i}=[1,{x}_{1},{x}_{2}\dots {x}_{p}\)] is (p + 1) \(\times\) 1 dimensional vector, β = [\({\beta }_{0},{\beta }_{1},{\beta }_{2}{,\beta }_{3}\dots {\beta }_{p}]\) and \(\gamma =[{\gamma }_{0},{\gamma }_{1},{\gamma }_{2},{\gamma }_{3},\dots {\gamma }_{p}\)] is a (p + 1) \(\times\) 1 dimensional vector of regression parameters.

The Maximum Likelihood Estimation (MLE) method is used to estimate parameters in the count models. This study was a Poisson logit hurdle to accommodate the excess zeros for the number of perinatal death count data. In this paper, Akaike’s information criteria (AIC) and log‐likelihood values are used for model selection measures. It is also used dispersion parameters to test for overdispersion. The generalized Pearson χ^{2} statistic which is the standard measure of goodness of fit is used to evaluate the sufficiency of the analyzing methods. Akaike’s information criteria (AIC) and log‐likelihood are basic methods of assessing the performance of the models and model selection [10].