Bayesian Multilevel Analysis of Children Vaccination Coverage in Ethiopia

Background: Vaccine preventable diseases (VPDs) account for 17% of the global under-five 27 mortality per annum and more than half of these deaths have occurred in sub-Saharan Africa. 28 Ethiopia is one of the ten countries which account for about 62% of unprotected children and one 29 of the three countries (Ethiopia, Nigeria, and the Democratic Republic of Congo) in which half 30 of the world’s child deaths have occurred are in sub -Saharan Africa. The main objective of this 31 study is to understand the current status of complete immunization coverage and examine its 32 determinant factors among children in Ethiopia. 33 Method: Bayesian multilevel logistic regression models have been utilized to realize the 34 objectives of the research. The dataset used for this study comes from the 2016 Ethiopian 35 Demographic and Health Survey (EDHS). The convergences of parameters are checked by using 36 Markov chain Monte-Carlo (MCMC) using SPSS and MLwiN software. 37 Results: The descriptive result revealed that, out of the 1929 children who are supposed to 38 complete all basic childhood vaccines, 699 (36.2%) children were completely vaccinated, while 39 1230 (63.8%) children were incompletely vaccinated. Moreover, regions Afar, Somali and 40 Gambela have the least proportion of vaccination coverage. Among the multilevel models, 41 Bayesian random coefficient model is found to be a better model to estimate the vaccination 42 coverage of children. Using this model, it has been found that factors like place of residence, 43 maternal educational, mother occupation type, Antenatal Care (ANC) utilization, Postnatal Care 44 (PNC) utilization, type of pregnancy, household wealth index, and field worker visit were found 45 to be the significant factors that influences the vaccination coverage. 46 Conclusion: In general, it has been estimated that the vaccination coverage in the country is 47 relatively low and there was significant variation in the level of vaccination coverage in regions 48 of the country. 49

The sample for the 2016 EDHS was designed to provide estimates of key indicators for the 141 country as a whole, for urban and rural areas separately, and for each of the nine regions and the 142 two administrative cities. The 2016 EDHS sample was stratified and selected in two stages. Each   The child who received all the above doses of each vaccine was categorized as "completely 173 vaccinated". While those who failed to take the recommended doses of vaccine were categorized 174 as "incompletely vaccinated". 175 A random variable represents the i th child response variable with two categories.  When the data was collected in hierarchical or clustered structures the suitable model is 189 multilevel models. Multilevel models are used to account for the correlation of observations 190 within a given group by incorporating group specific random effects. These random effects can 191 be nested (individuals nested in regions, with random effects at the women and region levels) 192 [7].The dependent variable must be examined at the lowest and highest level of analysis.

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This model considers the lack of independence across levels of nested data (i.e., individuals 196 nested within regions). All experimental units are assumed to be independent which means that 197 any variable which affects level of vaccination have the same effect in all regions, but these 198 models are aiming at examining whether the effect of variables vary from region to region. The 199 probability of 'success' or 'failure' is the same for all individuals in the group [7].

200
The random variable has a Bernoulli distribution is one of the standard assumption of the 201 model. Similar to logistic regression the is modeled using the link function logit. The two 202 level models are given by: ) represents the first and the second level of covariates for k 205 variables, = ( 0 , 1 , … … … … . , ) are regression parameter coefficients, and 206 0 , 1 , … … … … are the random cluster effects of model parameter at higher levels with the 207 assumption that follows normal distribution with mean zero and variance 2 . Therefore, 208 conditional on 0 , 1 , … … … , the can be assumed to be independently distributed as 209 Bernoulli random variables [7]. because the level-one error variance of the follows Bernoulli distribution straight from the 221 success probability, as indicated by Var ( ) = (1-) [7].

222
The likelihood function of empty model is Prior distribution 225 The prior distributions are default non-informative uniform distribution for the intercept 0 and 226 gamma for the random part  The full conditional distribution for parameter 0 is given by, The full conditional distribution for parameter 0 2 is given by, Where N is the total number of individual respondents interviewed in all regions of the country 237 that is calculated from ∑ and the scale and shape parameters are α and β respectively which 238 are both fixed constants [7].

Variance Components Model 241
The variance components model has the form; Where the vaccination status of the ℎ women in ℎ region is , the regional level random where 2 is the 'between-region' variance and 2 is the 'between-children' variance .

Bayesian Multilevel Analysis of Random Intercept Models 254
In this model, the intercept is the only random effect that differ with respect to the average value 255 of the response variable, but the relationship between explanatory and response variables cannot 256 differ between groups. It shows the heterogeneity between groups in the overall response [7].

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There is an assumption that there are variables which are potential explanation for observed Where the fixed part is 0 +∑ ℎ ℎ ℎ=1 and the remaining part 0 is the random part of the 264 model [9] and the success probability is 266

Bayesian Multilevel Analysis of Random Coefficients Models 267
In this model, the coefficients of lower-level predictors are modeled. It indicates the unobserved 268 heterogeneity in the effects of explanatory variables on the response variable [7]. 269 We represent the variables that are potential explanations for the observed outcomes variables by In the above model, the part 0 +∑ ℎ ℎ ℎ=1 is the fixed part and 0 +∑ ℎ ℎ ℎ=1 The posterior distribution for the parameters 0 , 1 , 2 , … … … … . , is given by:-

Estimation Techniques for MCMC 293
The software MLwiN, a specialized program for performing multilevel analysis was used to run  Where the predicted value for observation i is .The rule is, the larger deviance, the poorer 302 the fitness of the model [7]. imputations is relatively small, especially when between-imputation variance is not too large.

325
As a rule of thumb, if less than 5% of the observation are missing, the missing data can be 326 simply be deleted without any significant ramifications [10]. For this particular study, the 327 percentage of mission observation is less than 5%. However, if more than 5% of the data is 328 missing, deleting the missing data will result in a reduced sample size and an increased standard 329 error of the parameter estimate. In this case it is strongly suggested to use imputation of the 330 mean, mode or median or multiple imputations, to fill in the missing data. The results displayed in Table 1

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On the basis of p-value in the table 1 above, the vaccination coverage of children is associated 343 with region, residence type, educational level of the mother, wealth index, field worker visit, sex 344 of the child, wanted child, mother occupation, antenatal care service follow up, place of delivery, 345 baby postnatal care, husband/partner educational level.

Bayesian Multilevel Logistic Regression Analysis output 347
In the multilevel analysis, a two-level structure is used with regions as the second-level units and      Here also non informative priors were used for the fixed intercept and for the variance. The  Ho: there is no regional variation on vaccination coverage of the children.

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H1: there is a regional variation in the coverage of vaccination.

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By using the p-value from the above table, which is P ≤ 0.001, we reject the null hypothesis and 381 conclude that there is a regional variation (heterogeneity) on vaccination coverage of the 382 children.

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The variances σ 2 ε and σ 2 u in table 3  To identify the effect of explanatory variables, a Bayesian multilevel binary logistic model with 395 random intercept and fixed explanatory variables was estimated and displayed in table 4 below.

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The following table is the output from MLwin 2.36 for the Bayesian multilevel random intercept 397 model.   As depicted in table 5 above, some of the independent variables were found to have significant As provided in table 5 above, the odds of vaccination coverage among children with mothers 436 who need pregnancy later and who wanted no more children were found to be 1.709 times and 437 0.3697 times than those children with mothers who need more children later respectively. Thus, 438 children with mothers who do not need more children later are 63.03% less likely to cover 439 vaccination than children with mothers who want to deliver more children later at 5% level of 440 significance and keeping all the other variables in the model constant.

441
Similarly in table 5, the odds of vaccination coverage among children whose households had 442 been visited by field worker in the last 12 month was found to be 1.337 compared to households 443 who are not the visited by the field worker (ref). Therefore, children whose household are visited 444 by field worker are 33.7 % more likely to cover vaccination than those whose household was not 445 visited by field worker at 5% level of significance and keeping all the other variables in the 446 model constant.

447
As shown in table 5 above, the odds of vaccination coverage among children whose mother had 448 attended postnatal care found 1.9155 indicating that they are 91.55% more likely to cover 449 vaccination compared to children whose mother had not attended postnatal care services (ref) at 450 5% level of significance and keeping all the other variables in the model constant.

451
With regard to the variable ANC service shown in table 5, it has been found that the odds of 452 vaccination coverage among children having mothers who attended antenatal care service was 453 found 8.491 indicating that their odds is 8.491 times than that of children whose mother did not 454 attend the ANC services at 5% level of significance and keeping all the other variables in the 455 model constant. 456 As it has been depicted in table 5, the odds of vaccination coverage among children having 457 mother who had working in agriculture was found 1.534 compared to a women who had not 458 working (ref). This shows that children with mother working in agriculture are 53.4% more 459 likely to cover vaccination than children with mother who did not work in agriculture at 5% level

485
Bayesian multilevel logistic regression random coefficient model was identified to be a better fit 486 for the vaccination dataset. This model was also considered to be the best model to check the 487 antenatal care service utilization in national level [12].

488
The upward trend in immunization coverage in recent years in Ethiopia was due to tremendous 489 efforts of the government to realize the millennium development goal of reducing child mortality 490 from vaccine preventable diseases. A study conducted by [13] in Afar, Somali and Tigray and education about vaccination than women in the rural area as indicated by studies in [13,14].

497
Children with mothers having primary and above education level are associated with an 498 increased in full immunization. In other words, as mothers' level of education increase the 499 probability of having a full immunization of children increased. This has been confirmed with 500 the finding of [14].The importance of maternal education in children's health is universally 501 recognized. Children of more educated mothers are more likely to be fully immunized.

502
Childhood immunization is also influenced by the household wealth index. A child from a family 503 with poor wealth has a higher chance of being incompletely immunized. This might be 504 associated with lack of money that results in poor health seeking behavior. Household income 505 and wealth index influences the likelihood that children receive complete immunization. This 506 result is similar to the results from [14,15]. This might be due to the indirect cost needed for 507 travel to health facilities or time spent away from income generating activity to make it difficult 508 for the poorest households to avail themselves of services that exist in the community [16].

509
The study also found that the type of pregnancy had significant effect on status of vaccine 510 completion. On the basis of this study finding, a child that was born from mothers who wanted 511 pregnancy was more likely to get complete vaccination. This finding matches with the finding 512 from [1] that was conducted in Debre Markos town in Ethiopia.

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The finding from this study also shows that the use of health care service (ANC and PNC) by information to mothers about immunization, including immunization schedules and side effects 528 during their visit. The finding is in conformance with a study done in Indonesia by [15].

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The study also identified some socio-economic indicators of the region as predictors that affect