Varriation In Utilization of Modern Contraceptive Among Married Women In The Seven Woredas of Assosa Zone: A Comparison of Bayesian and Classical Approach. Case Study In Assosa Zone, , Ethiopia

Contraception is a procedure that can be used to avoid pregnancy or childbirth. When women choose to prevent pregnancy or have a longer birth, they frequent Objectives: This study was aimed to identify the predictors of married women’s contraceptive practice using Bayesian and classical approach. In addition, this study has identied the within and between Woredas variation using the hierarchical nature of the data obtained in different woredas. For identifying the better model, researcher has compared the Bayesian and classical multilevel logistic regression models. Methods: This research was conducted in seven Woredas of Assosa zone and was based on a cross-sectional study that primarily focused on married women between the ages of 15 and 49 and the factors that inuenced their contraceptive use. Two stage model comparisons were used to approximate the parameters, with the rst stage having a null, random intercept, and random slope with a Bayesian approach Result and Conclusion: The overall contraceptive prevalence rate among 6866 married women 3121(45.46%). According to the intra Woreda correlation of the appropriate model, the between Woreda variance in married women's contraceptive practice was 15.71%, with the remaining 84.29 percent variation attributed to differences in contraceptive practice between women. Finally, predictors for married women contraceptive practice such as women's age, place of residence, women's educational level, husband's educational level, women's job, husband's occupation, wealth index, religion, and knowledge of family planning. The Bayesian multilevel model was found to be the most suitable model for tting the data after a comparison of classical and Bayesian multilevel models.


Background Of The Study
Contraception can be de ned as the deliberate use of a technique or device to prevent pregnancy. Women who intend to prevent pregnancy and want no more children or wish to postpone a birth are subject to the decision to practice contraception.
The population in the world is substantially increased through time with unprecedented speed. With this regard, it is becoming a global concern for many countries in different parts of the world with which several problems are faced in sustaining the wellbeing of their population (Nations u. , 2016).
Ethiopia is one of the developing countries which have a high level of fertility together with declining mortality that have given rise rapid population growth.
The population size has approximately increased from 83 million in 2007 to 105,350,020 in 2018(CIA, world fact book 2018). The country's total fertility rate substantially increased over three decades, from about six-lifetime births per woman to 7.7 in the 1990s, after which it gradually declined to 4.99(CIA, world factbook 2018).
The urban -rural distribution of the population of Benishangul Gumuz region indicate that the overwhelming majority of the population is living in rural areas.
About 85 per cent of the population reside in the rural area of the region, which is very far from the provision of basic services like education, health and other social services including services of reproductive health and family planning and thereby contraceptives. Therefore, the vast majority of the population were living ill rural areas, engaged in traditional way of life and agricultural practices especially using hand digging tools like spade, stick, pick axe for the production of different agricultural food crops. Apart from traditional way of agriculture crop production, they were also involved in domestic animal husbandry specially keeping small animals like sheep and goats and collecting different forest fruits and roots from their surrounding forest resources, one of the potential forest areas of the country.
Three hundred eleven (78.9%) of rural women in Assosa town had ever used family planning services. The majority of women (288 (92.6%) have ever used injectables, accompanied by pills (146). (46.9 percent). However, 111 (or 84.7 percent) of urban women had used at least one form of contraception. The majority of urban women (93.8%) have ever used injectables, accompanied by pills (22.8%) ( Muluwas Amentie et al,2015).
The aim of this study is to identify socioeconomic and demographic determinant associated with married women's contraceptive practice in the seven woredas. And also, this research article is aiming to determine the within and between woredas variations of married women's modern contraceptive practice in Assosa zone. Finally, this research compared the Bayesian and classical multilevel logistic regression model so as to extract best estimation technique for the data.

1.1.Motivation for Bayesian approach and multilevel model
In statistical modeling and data analysis, Bayesian estimation and inference have a range of advantages. It improves estimation in sparse or small datasets by combining the power of the prior distribution of the parameters with the probability (for example, in strati ed sampling) (Richardson, 2003). Also, unlike maximum likelihood and other classical approaches, nite sample inferences are allowed without recourse to large sample arguments. It can also measure probabilities on both nested and non-nested models (unlike traditional approaches) and, thanks to modern sampling techniques; it can easily t complex random effects models that are more di cult to t using traditional methods (Carlin, 2001). In terms of estimate precision, Bayesian methods can outperform classical estimators. This occurs as a result of specifying the prior, which adds additional information or data based on accumulated knowledge, and the posterior estimation, which is based on the combined sources of information (prior and likelihood), is more precise (Richardson, 2003).

Study Area and Period
Assosa zone is one of the three zones found in Benishangul Gumuz Regional State, located 667 km west of Addis Ababa. Administratively, the zone is structured into seven districts that are (Bambasi, Shirkole, Homosha, Kurumuk, Oda bildigilu, Menge and Assosa). According to the Ethiopian Central Statistical Agency's 2007 Census, this Zone has a total population of 310,822, with 158,932 men and 151,890 women. Urban residents account for 39,957 people, or 12.86 percent of the population. The Berta (59.95%), Amhara (23.86%), Oromo (10.31%), and Tigrayans (1.5%) were the four largest ethnic groups identi ed in the Assosa zone; accounting for 1.48 percent of the population was from Sudan.

Study design.
Here the researchers have been employed cross-sectional study design.

Source population
It included all women between the ages of 15 and 49.

Sampling Methods
In this study, the researchers have used probability sampling technique for which systematic random sampling was important to take lists of households in their respective Districts and Kebele.

Instrument
The data were collected using structured questionnaires, interview and focus group discussion. The questionnaires contain socio-demographic characteristics of married women aged from 15 to 49 and factors associated with utilization of modern contraceptive. In this study, the primary outcome is utilization of modern contraceptive which could be binary variable code as 0 for non-user and 1 for users of modern contraceptive. The factors that are included in the study were socio-demographic characteristics (women age, residence, religion) and other factors such as occupation of husband, occupation women, number of living children, knowledge of family planning, women's Educational status, husband's education level, wealth index, mass media exposure, desire for more children.

Data Quality Control
Measures were taken to ensure that the data obtained are of high quality. Before the actual analysis, the checklist was pretested, and any required adjustments were made to increase the data's reliability. Similarly, the study's con dentiality and anonymity were preserved. Finally, the principal investigator double-checked the data for accuracy.

Data Analysis
The researchers used statistical package for social science version 26 for data entry and imported to R software version 3.5.4 for deep analysis of the Bayesian and the classical multilevel logistic regression. The MCMCglmm package was used for Bayesian inference in this case. This is the most important package for Bayesian multilevel models built in the R programming language, which allows for fast Bayesian inference. Similarly, the classical multilevel model was computed using the R package glmmPQL, which is capable of computing using the penalized quasi likelihood estimation process. The selection of a prior is one of the pre-conditions in every Bayesian analysis. Non-informative priors, which express complete ignorance of the parameter values, were used in this analysis. For xed parameters, the researchers used a normal distribution with a mean of 0 and a variance of 10000 (large variance). In addition, for single variance (random intercept), a gamma distribution with parameter α=0.001 and β=0.001 has been used. Finally, the prior for random effects in the random coe cient model was the inverse-wishart distribution. However, the scalar values for variance and covariance were taken from a similar example in the MCMCglmm package (Had eld, J,et al 2019). Considering various methods for detecting poorly sampled Markov Chains would be useful for examining the convergence of MCMC. Among several ways of test of convergence, the most popular and straight forward convergence assessment methods such as trace plot and density plot were used.

Result And Discussion
This research used cross-sectional data from the seven districts of the Assosa zone to classify determinants of married women's modern contraceptive to examining demographic and economic variables that had previously been considered in similar studies. The aim of this study was to examine both descriptive and inferential analysis in order to identify the determinants of married women's contraceptive practice status. As a result, 6866 married women were used in the report, and the ndings are divided into two parts. The bivariate analysis (cross tabulation) is the rst part of the result, which looked into the relationship between each explanatory variable and married woman's contraceptive practices. As a result, most explanatory variables such as District, place of residence, women's age, husband education level, desire for child, husband occupation, women occupation, wealth index, women education level, religion, and knowledge of family planning, mass media exposure, number of living have a signi cant association with married women contraceptive practice at 5% level of signi cant(see table1). Similarly, the result in the table below also indicated that out of 6866 married women considered in the analysis 3121(45.46%) were practicing some form of contraceptive at the time of data collection. Utilization of modern contraceptive of married women has also varied signi cantly across Assosa zone districts. 3.1.Test of heterogeneity proportions of modern contraceptive use.
The two-level structure is used with the district (Woreda) as the second-level unit and the married women as level one unit. This is based on the idea that there may be differences in married women's contraceptive use between district that are not captured by the explanatory variables and hence may be regarded as unexplained variability within the set of all district (Snijders, 1999). Therefore, the Pearson chi-square for the proportion of utilization of modern contraceptive across the seven districts has been investigated in the table below Therefore; the Pearson chi-square for the proportion of utilization of modern contraceptive across the seven districts has been investigated in the table below. Consequently, the Pearson Chi-square, P-value =0.000 which is less than 0.05 level of signi cance, implying strong evidence of heterogeneity for married women contraceptive practice across districts(see Table 2).

3.2.Model comparison of Bayesian and classical approach
Considering the standard errors of the calculated coe cients for comparison of both approaches (Bayesian and classical) is an effective process, and the model with the smaller standard error is the model that ts the data best. The result in the table below displays the approximate coe cients and standard errors for both approaches. Hence, the result indicated that all estimated coe cients' standard errors in Bayesian random intercept model are smaller than the classical random intercept model (see table 3). Therefore, the Bayesian approach is better in tting for this data than the classical approach. As compared to women in urban areas, women in rural areas have a 42.9 percent lower probability of using contraception (odd ratio: 0.571, 95 percent credible interval (-0.763361 -0.367230). This may be due to the fact that family planning services are not distributed or accessible in rural areas as much as they are in urban areas. For women aged 20-24, the likelihood of using contraception is 43.5 percent (odd ratio: 1.435:95 percent) credible interval (0.0733, 0.6307) times higher than the reference age group of 15-49 years. It's also been discovered that women in the 25-29 age group are 55 percent more likely than women in the 15-19 age group to use contraception. When compared to orthodox women, married Muslim women had a 46.5 percent lower chance of using contraception.
Married women with husbands with a primary education level are 0.386 (odd ratio: 1.38597 credible interval (0.176190, 0.479801) times more likely to use contraception than women with husbands with no education level (see Table 4).

Intra class correlation
The intra woreda correlation coe cient for this study was estimated Where 3.29 is the logistic distribution variance. This indicated that about 15.71% of the total variability in married women contraceptive practice is due to the fact that differences across regions and the remaining unexplained 84.29% accounts the between married women differences.

Checking Convergence
This is the graph that shows the number of iterations versus the generated values. If all of the values in this graph are found within an area with no strong periodicities, convergence can be achieved (up and down periods). As a consequence, none of the trace plots below have any up and down times. Furthermore, density plots are almost identical to normal plots. This means that all posterior gures have been converged (see gure 2).

3.5.Discussions of the results
On the basis of their respective standard errors, the models chosen in the Bayesian framework were compared to the classical model. As a result, the Bayesian model was found to be superior to the classical model since the standard errors of predictors in this model were lower. The Bayesian random intercept model has shown that the random intercept is signi cantly different from zero in this model, suggesting that contraceptive practice among married women differs by woreda. This analysis appears to be in agreement with previous research (Hailu, 2015).
The location of a woman's residence has a direct impact on her contraceptive use. As a result, women who live in rural areas are less likely to use contraception than women who live in urban areas. This nding is consistent with previous studies (Balew,2015;Worku, 2015). Similarly, the study found that women of Muslim and other religions have a detrimental effect on contraceptive use, which seems to agree with the ndings of a study conducted in Ethiopia (Hailu, 2015;Tiruneh, 2015).
According to the ndings, a woman's occupation is a major determinant of her contraceptive use status. As a result, working women were more likely than non-employed women to use contraception. This logic may have arisen as a result of the fact that working women are more likely to have access to contraception than their counterparts due to improved economic conditions. This nding appears to be consistent with a previous analysis of a similar scenario (Endriyas, 2017).
With the MCMCglmm packages in R program, the posterior inference was implemented with the Metropolis-Hasting algorithm with 60000 iterations, 10,000 samples as burn in, and 50 thinning interval to render the sequence sampling independent or low autocorrelation.

Con icts of Interest
The authors declare that they have no conflicts of interest in this work.

Authors' Contributions
Eshetu Mebrate conceptualized the study, searched literature, and trained the research assistants for data collection. Mekdes Derbie also contributed to the design of the study and advised on methods and data interpretation. She also critically revised and edited the manuscript.

Data Availability
The manuscript contains all of the data produced or analyzed during this analysis.

Funding
Not applicable

Figure 2
Trace and density plot for convergence check.

Supplementary Files
This is a list of supplementary les associated with this preprint. Click to download. TableA.docx