Determinants of anemia severity levels among children aged 6–59 months in Ethiopia: Multilevel Bayesian statistical approach

Anemia is a widespread public health problem that affects all stages of life particularly preschool children and pregnant mothers. Anemia among children had significant impact on their growth, development, school performance and mortality. Different strategies like deworming of young children, vitamin A supplementation for children aged 6–59 months, and ferrous sulphate supplementation and provision of insecticide treated bed net for pregnant women were designed to control and prevent anemia. Also, previous studies on anemia factors were conducted but they were not considering the ordered nature of anemia. Therefore, this study aimed to identify the factors of anemia severity levels among children aged 6–59 months in Ethiopia by using ordinal analysis based on Bayesian hierarchical statistical approach. A secondary data analysis was conducted using the 2016 Ethiopian Demographic and Health Survey data. A total of 8483 weighted children were included. Due to the ordered nature of the anemia and nested nature of DHS data, ordinal logistic regression model based on hierarchical Bayesian statistical approach was employed to identify the determinants of anemia severity levels. In this study, moderate anemia level was found to be the commonest type which accounts around 29.4%. Female children, poorer, middle, and richest wealth index, primary maternal education and having ANC visit had lower risk of having higher order of anemia. Moderate maternal anemia and stunted children had higher chance of having higher order of anemia. Children age had significant different effect on mild and moderate anemia. Meanwhile, multiple birth/s and deworming had effect on moderate anemia. In addition, normal birth weight had also significant and different effect on mild and severe anemia and history of feverlike illness on mild anemia. The prevalence of anemia among children aged 6–59 months anemia was found to be a severe public health problem. Children age, sex, maternal education, child stunting, history of fever, multiple birth, birth weight, provision of deworming and maternal anemia was found to be the most important factors for child anemia severity levels. Therefore, intervention efforts to control and prevent anemia in Ethiopia requires targeting of these hindering factors.

This study was conducted in Ethiopia which is an East African country with an estimated population of 115.5 million that makes it second most populous country in Africa27. It has a high central plateau that varies from 1290 to 3000 m (4232–9843 ft) above sea level, with the highest mountain reaching 4533 m (14,872 ft)28. In Ethiopia, 75% of the land are malaria’s areas and more than 54 million people are vulnerable for malaria infection29. Moreover, the prevalence of intestinal parasite infections was high in Ethiopia which affects 48% in preschool and school-age children30. Administratively, Ethiopia is federally decentralized in to 9 regions and two city administrations and regions are divided into zones, and zones, into administrative units called districts. Each district is further subdivided into the lowest administrative unit, called kebele. Regarding to the health care system in Ethiopia, the fourth health sector development plan introduced a three-tier health-service delivery system. This system was arranged by including Primary health care unities (i.e., health posts and health centers) and primary hospitals at primary level, general hospitals at secondary level, and specialized hospitals at tertiary level31. This study was based on the EDHS 2016 data which was a nationally representative sample conducted from January 18 to June 27, 2016. Regarding the sampling technique, two stage stratified cluster sampling technique were employed to select study participants. Stratification was conducted by separating each region into urban and rural areas. In the first stage, 645 enumeration areas (202 from urban area) were selected with probability proportional to the enumeration area size and with independent selection in each sampling stratum. In the second stage, 24–32 households from each cluster were selected with an equal probability systematic selection from the household listing. For this study, the data was accessed from the Measure demographic and health survey (DHS) website (http://www.measuredhs.com). The study population were children aged from 6 to 59 months who had born 5 years prior to 2016 DHS study in Ethiopia and in the selected enumeration areas. In EDHS anaemia testing was conducted for all children from aged 6 to 59 months for whom consent was obtained from their parents or other adults responsible for them. Blood sample was drawn from a drop of blood taken from a finger prick (or a heel prick in children aged from 6 to 11 months) and collected in a microcuvette. Haemoglobin analysis was carried out on-site using a battery-operated portable HemoCue analyser. The response variable for this study was anemia level among children aged from 6 to 59 months which has four levels31: In this study, both individual and community-level explanatory variables were considered. The individual-level variables included were sex, age of child, age of mother, wealth index, mass media exposure, educational status, marital status, maternal anemia, parity, ANC visit, place of delivery, birth spacing, multiple birth, birth weight, recent history of diarrhea and fever, stunting, Vit.A supplementation, drugs for intestinal parasites, immunization. The Place of residence and CDI were considered as community-level factors. The community-level variable, CDI, was measured based on the availability of three basic services in the community: improved water supply, electricity city, and improved sanitation services. It is classified as: After accessing the data from measure DHS, the variables of the study were extracted from Birth recorded data set of EDHS data using STATA version 14. The data was weighted using sampling weight during any statistical analysis to adjust for unequal probability of selection due to the sampling design used in EDHS data. Hence, the representativeness of the survey results was ensured. A two-level multivariable ordinal logistic regression analysis was used to estimate the effect of explanatory variables on anemia severity. The data has two levels with a group of J EAs and within-group j (j = 1, 2…, J), a random sample nj of level-one units (individual children). The response variable is denoted by Yij=0if theith children are in thejth EAs had not anemia in the test result So, appropriate inferences and conclusions from this data does require advanced modeling techniques like multilevel modeling, which contain variables measured at different levels of the hierarchy, to account the nested effect33. Four models were fitted for the data. The first model was an empty model without any explanatory variables, to calculate the extent of cluster variation on anemia level. Variation between cluster (EAs) were assessed by computing Intra-class Correlation Coefficient (ICC), Proportional Change in Variance (PCV) and Median Odds Ratio (MOR). The ICC is the proportion of variance explained by the grouping structure in the population. It was computed as: ICC = σμ2σμ2+π2/3; where: the standard logit distribution has variance of π2/3, σμ2 indicates the cluster variance. Whereas PCV measures the total variation attributed by individual level and community level factors in the multilevel model as compared to the null model. It was computed as: varianceofnullmodel-varianceoffullmodelvarianceofnullmodel34. MOR is defined as the median value of the odds ratio between the cluster at high risk and cluster at lower risk of higher anemia level when randomly picking out two clusters (EAs). It was computed as :MOR = exp (2∗σμ2∗0.6745) ∼ MOR = exp (0.95∗σμ)35. The second model was adjusted with individual level variables; the third model was adjusted for community level variables while the fourth was fitted with both individual and community level variables. The analysis was conducted based on Bayesian statistical approach which assumes parameters are unknown and random that follows a certain probability distribution. This approach had three components which are the likelihood function, prior distribution, and posterior distribution36. It is the key component of Bayesian statistical approach that reflects information about the parameters contained in the data. But the data used for this analysis had ordered response with two hierarchies which requires to employ multilevel ordinal analysis. For ordered data, there are different types of ordinal models. This study first considers the common and most applicable model for ordinal response variable which is cumulative logit model. It is an extension of binary logistic regression model and estimate the odds of being beyond a particular level of the response37. It is formulated as where k = 1, 2, K − 1; ak is cut point of response variable; Bp are fixed coefficients of the corresponding predictor variables and γ0j random intercept coefficient. A positive logit coefficient indicates that an individual is more likely to be in a higher category as opposed to a lower category of the outcome variable33. But this model has constrained Proportional Odds Assumption (POA) or parallel lines assumption. That is, for each cumulative logit the parameters of the models are the same, except for the intercept38. This assumption was tested by using brant test of parallel lines and it becomes significant for overall model as well as some variable (i.e., POA assumption was not satisfied). Then Continuation ratio and Adjacent-categories logistic regression model with category specific effect were fitted to relax the POA. It also called sequential model which compares the probability of a response higher level equal (yij>k) to a given category (Y = k)39. The model is given as where k = 1, 2, K − 1; ak is cut point of response variable; Bp are fixed coefficients of the corresponding predictor variables and γ0j random intercept coefficient. It is the modeling of pairs of adjacent categories of the ordinal response variable. This model compares the probability of being in the higher category relative to the lower category. The model can be expressed as where k = 1, 2, K − 1; ak is cut point of response variable; Bp are fixed coefficients of the corresponding predictor variables and γ0j random intercept coefficient38. It is the probability distribution that represents the prior information associated with the parameters of interest. In Bayesian two common types of priors were used (Informative and Non-informative priors). An informative prior is a prior distribution that is used when information about the parameter of interest is available before the data is collected. It can obtain from previous studies, expert knowledge (experience) and a combination of both. Due to lack of these sources, non-informative (flat) prior distributions, which gives less value to the data collected before while giving high attention to the data or likelihood, were used for this study. Normal flat prior distribution for the population level parameters, and uniform prior distribution for the group level parameters were used. It represents the total knowledge about the parameters after the data have been observed. It is obtained by multiplying the prior distribution over all parameters by the likelihood function (i.e., fθ|y∝fy|θ∗f(θ)). Where f(θ) is the prior distribution; fy|θ is the likelihood of the data and fθ|y is posterior distribution40. Simulation technique was applied by using Bayesian regression model using stan (BRMS) package in R41 with two chains that have 8000 with 3000 warm up iterations. The parameters were allowed to be initiated randomly in the simulation procedure. The samples were drawn by using one variant of Markov chain Monte Carlo (MCMC) algorithm called No-U Turn Sampler (NUTS) which improves the limitations of Hamiltonian monte Carlo’s (HMC) by introducing the slice variable that sampled uniform distribution in the sampling procedure. Like HMC, NUTS sampler surpasses the random walk behavior of Gibbs and Metropolis- Hasting sampler by including the clever auxiliary variable. This property of HMC and NUTS sampler make more efficient than other MCMC sampling techniques with small iteration42. The results from a given distribution are not deemed reliable until the chain has reached its stationary assumption. But the inference becomes appropriate when target distributions is well converged. Therefore, monitoring its convergence is essential for producing reliable results from the posterior distribution. The convergence of the targeted distribution was assessed by trace plot, density plot, effective sample size and R hat statistics. Unlike classical approach, Akaike Information Criterion (AIC), Bayesian Information Criterion (BIC) and Deviance information criterion (DIC) are not appropriate model section criteria for Bayesian statistical approach. To overcome this, this study computes Leave-One-Out cross-validation (LOO) and the Watanabe Akaike Information Criterion (WAIC). Models were selected using LOO because WAIC, which is computed as log predictive density for each data point minus estimated effective number of parameters, becomes unreliable if any of estimated effective number parameter exceeds 0.443. But in this case, it becomes in tens. Based on LOO results, which Estimates out-of-sample pointwise predictive accuracy using posterior simulations, the model with smaller LOOIC was selected as the best fitted model. Adjusted odds ratio (AOR) with 95% Credible Interval (CrI) from best fitted model was used to select variables which have significant association with anemia level among children aged 6–59 months. This study is a secondary data analysis from the EDHS data, so it does not require ethical approval. For conducting this study, online registration and request for measure DHS were conducted. The dataset was downloaded from DHS on-line archive after getting approval to access the data. In this study, patients and the public were not involved in the study design or planning of the study. Furthermore, since we used secondary analysis DHS data patients were not consulted to interpret the results and were not invited to contribute to the writing or editing of this document for readability or accuracy.

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