Bayesian analysis of the joint risk of malaria and anemia among under-age ﬁve children in Nigeria

- Background A life-threatening malaria parasites are known to have a substantial causative eﬀect with the occur-rences of frequent episodes of other diseases causing rapid progression to death. The parasites feed on iron molecules present in the red blood cells, therefore, resulting in low functional hemoglobin concentration causing anemia in children, and preventing rapid recovery. This study quantiﬁes the impact of malaria on under-age ﬁve anemic children in Nigeria. - Method The joint risk and disease speciﬁc risks factors of malaria and anemia were estimated using a generalized linear mixed model in a Bayesian framework and a Besag-York-Molli´e spatial prior model to account for spatial heterogeneity. Data were sourced from the Demographic and Health Survey conducted by the National Population Commission. - Results - Conclusion


Introduction
Malaria has been known to be the most frequent and severe public health problems contributing to the severity of other diseases such as diarrhea and anemia (White, 2018). It is a life-threatening mosquito-borne disease in humans and animals caused by the plasmodium parasite, spread to humans through infected mosquito bites, usually Anopheles mosquitoes. Falciparum malaria is the most severe type of malaria disease and can possibly lead to death within few days of disease onset. However, anemia in the presence of malaria is a health risk for under-age five children.
Anemia was identified as the main cause of morbidity and mortality among under age five children in most developing countries, especially in Africa (Muhammad et al., 2017;Gayawan et al., 2014; U. S. Embassy, 2015). It is believed to be the most common low nutrition illness among preschool children. Anemia in children threatens the quality of life, causing symptoms such as increased heart rate, poor wound and tissue healing, and slow or delayed growth and development (Oladeinde et al., 2012), which eventually lead to a poor cognitive performance of children and possibly death.
It is usually a result of low concentration of functional hemoglobin (Hb) level in the body, a condition in which the amount of red blood cells decreases below normal. Iron deficiency is the most common causes of anemia (Gayawan et al., 2014), it occurs when there is insufficient amount of iron in the red blood cells. 70% of iron in the bloodstream is found in the red blood cells, which carry oxygen through the entire body. Malaria parasites attack these red blood cells by feeding on iron in blood cells for development during the liver stage and causes a shortage in Hb concentration level resulting in frequent episodes of anemia (Spottiswoode et al., 2014). Moreover, life-threatening malaria-anemia disease is a severe health problem in developing countries that is further compromised in the presence of infections in the body. Malaria parasites play a major causative role in anemia, especially on children less than 59 months, placed at higher risk due to the amount of iron needed for development (Clark, 2008;Sadrzadeh and Saffari, 2004).
In 2017, an estimate of 219 million cases of malaria occurred worldwide, of which 92% of the case were in African Region. Fifteen countries in sub-Sahara Africa and India carried about 80% of the global malaria burden, and Nigeria accounted for about 25% of malaria cases worldwide (Adigun et al., 2018;WHO, 2018). Reports from World Health Organization (WHO) shows that among under-age five children in the high-burden countries in Africa, the prevalence of anemia was 61%; of children who tested positive for malaria, the prevalence of anemia is 79%. An under-age five children are said to have anemia if the mean blood Hb concentration is less than 110g/l (11/dl) (Gayawan et al., 2014). The estimate of Hb concentration of an average preschool child in Nigeria is 100d/l (97,104 CI) such that the level of public health significance was classified as severe (WHO, 2015).
The distribution of the key risk factors of malaria and anemia, such as mother's education, family wealth index, access to health care delivery, place of settlement, among preschool children in Nigeria have only being reported nationally, and a concrete study of the relationship between both diseases have not been adequately considered. Moreover, studies have focused on spatial modeling of single illness in a univariate framework or multivariate approaches for two or more diseases. A multivariate model was used to identify the risk factors of malaria and anemia for pregnant women in Mali (Dicko et al., 2003). Kateera et al. (2015) utilized bivariate and multivariate models to measure the prevalence of malaria, anemia, and under-nutrition among under age five children in rural Rwanda. Ehrhardt et al. (2006) employed a multivariate approach to investigate the interactions between malaria, anemia, and malnutrition among African children. However, most diseases share common risk factors such as environmental in cases of anemia and malaria. Possible identification of geographical patterns in a joint analysis of disease will provide proof of underlying risk surface on subsets within a population than when a single or multivariate disease analysis are considered (Leonhard and Nicola, 2000).
This analysis aims to quantify the risk relationship shared between malaria and anemia among under age-five children in Nigeria. A generalized linear mixed model was utilized , within a Bayesian framework to account for the different risk factors considered. The Baseg-York-Mollié (BYM) spatial prior model (Besag et al., 1991) was used to account for the spatial heterogeneity.

Method
Nigeria has 36 states, and the Federal Capital Territory (FCT), grouped into Six geopolitical zones ( Figure 1). Efforts have been put in place to eradicate malaria and anemia in Nigeria, however, malaria and anemia remain endemic in Nigeria and remain a major health burden, threatening children development less than 59 months old. In combination with the Democratic Republic of Congo, Nigeria contributes up to 40% of the global malaria burden (NMIS, 2016). It also accounts for 11% maternal mortality, 25% infant mortality, and 30% under-five mortality (NMIS, 2016).
The disease overburdens the health system of the country. Nigeria implemented strategic plans to eradicate malaria and control anemia, moreover, beginning from the year 2014, Nigeria embarked on the implementation of National Malaria Strategic Plans (NMSP), ended in the year 2020 to achieve pre-elimination status. This study made use of data collected before and after NMSP was initiated. including FCT was conducted. In the second stage of the selection process, an average number of 26 households in NMIS2010 and 25 households in NMIS2015 were selected from each cluster by equal probability systematic sampling. Women in the selected households were administered a Women's questionnaire. Moreover, all children age 6-59 months present on survey day including visitors were eligible. Due to the strong association of malaria and anemia, tests for anemia in children aged 6-59 months were included in the survey. Finger-or-heel-prock blood samples from children were tested for malaria and anemia immediately. The data collection survey incorporated three biomarkers for testing malaria, anemia using RDT, and thick blood smear and thin blood film sample preparation on microscope slides. The NPC enumerators used a global positioning system (GPS) receiver to record coordinates where data were collected (NMIS, 2016). The extraction of variables of interest leads to a total of 3,393 households, with 73% and 27% samples from NMIS 2010 and NMIS 2015 respectively.

Statistical Analysis
A generalized linear mixed model, within a Bayesian approach, was adopted to account for the risk of a child having both malaria and anemia accounting for the socio-economic, demographic, and spatial risk factors on the prevalence of anemia and malaria among under age-five children.
Four response variables were considered in this study; first, presence of anemia in children, coded as binary, second, presence of malaria with binary outcomes, third, is the Hemoglobin (Hb) level with continuous outcomes, and four, quantify the relationship of anemia and malaria with binary outcomes. For the binary outcomes, 1 indicates the presence of disease, and 0 indicates otherwise.
The response variable indicating the relationship between malaria and anemia was coded as 1 if a child has both diseases and 0 otherwise.
Let y ijk , k = 1, 2, 3, where k = 1 indicates presence of malaria, k = 2 indicates presence of anaemia, and k = 3 indicates presence of both diseases. The index j = 1, 2, ..., n i , where n i is the number of children in county i ∈ {1, 2, ..., 37}. In the binanary cases, Bernoulli distribution was assumed. That is, for each child, independently with success probability π = exp(η) 1+exp(η) , where η is a linear predictor given as; In addition, hemoglobin concentration assumed a Gaussian distribution with constant variance σ 2 , where b 0 is the global risk of a child having disease k, β is a vector of linear effects such as mother's level of education, family wealth index etc, modeled independently with a flat prior given as p(β) ∝ 1. z is a random effect of a child's age modeled as a temporal structure using a random work with order two, given as; where t = 2, 3, ..., 59. A BYM is specified on the u and v. That is, v is the spatial unstructured effects modeled as exchangeable structure given as v ∼ N ormal 0, σ 2 v I), where I is an identity matrix, and u is the spatial structure effects jointly modeled using intrinsic conditional autoregressive (ICAR) model (Besag et al., 1991). The model was estimated using the Integrated Laplace approximation (INLA). The main advantage of approximating the joint posterior distribution with INLA over the popular Markov Chain Monte Carlo method is its computational advantage and does not suffer convergence problems. The hyper-parameters were assigned such that the priors lead to non-informative priors. R software (R Core Team, 2019) was used for the data analysis.
Detail of the analytical procedures used is in Blangiardo et al. (2013).   proportion of children living with malaria and anemia were from the rural region. The average

Result of Analysis
Hb level of female children was 11.8g/dl, whereas, for male children, the average Hb was 11.4g/dl.   It means that parents from the richest category of wealth index would have enough resources to provide an adequate diet for their children. Other categories of wealth index are not significantly different from the poorest category. Children who the mother have a secondary level of education are significantly less likely to have anemia compared to children who the mother had no formal education. Other levels of education were not significant from the base category. The presence of fever in the last two weeks is not significantly different from the absence of fever. Children with malaria are 97.7% significantly more likely to be anemic compared to children without anemia.

Estimates of linear risk factors
The result revealed that subsequent episodes of malaria significantly contribute to children having anemia. It proves the significant coexistence between malaria and anemia. Children whose parents had a radio system and use mosquito net are significantly less likely to be anemic compared to those without a radio system and mosquito net. The risk of anemia is significantly higher for all regions than the base category, except for children in the Northeast region. The result shows that there are improvements in the anemic status of children between the years 2010 and 2015, in the sense that children surveyed in 2015 are 29.7% less likely to be anemic. The reduction might be as a result of sensitization programs centered on regions with severe anemia. In the second panel, the expected risk of children having malaria in the rural area is 91% significantly more likely to have malaria compared to children leaving in the urban settlement, which supports Wilson et al. (2015) claim. Malaria affects children irrespective of their gender since there is no significant difference between the risk of malaria between male and female children.
Sources of water and toilet system do not significantly contribute to whether a child has malaria or not. Though the poorer category of wealth index is not significantly different from the poorest category, which is the base, it can be concluded that the risk of children having malaria declines with an increase in the wealth index. Children with a Higher level of mothers education are significantly less likely to have malaria compared to the reference category, which is no education, whereas other education levels are not significantly different. Children's risk of fever in the last two weeks before the survey and children whose parents have radio systems are not significantly different from the base category. Children who sleep under treated mosquito nets are less likely to have malaria compared to those sleeping without a treated mosquito net. It can be concluded that the region where a child resides does not significantly contribute to a child having malaria. The result implies that the impact of malaria is similar in these regions. In 2015, children are more likely to have malaria compared to the base category 2010.
In the third panel, place of residence, sources of water, and the toilet system does not significantly contribute to the Hb level of a child when compared to respective base categories. In other words, residence, water source, and toilet system do not explain more information on the variation that exists in the hemoglobin level of children. Gender does not significantly contribute to the Hb level, which confirms the result obtained in Dang et al. (2003). Though the poorest category does not significantly contribute to the Hb level of children, the higher the wealth index, the lower the effect on the mean Hb level. Regarding the mother's level of education, the primary and higher category do not significantly contribute to the mean Hb level, whereas the secondary category contributes significantly higher to the mean Hb level compared to the base category. The risk of children with fever in the last two weeks before the survey does not significantly contribute to the Hb level of children. The effect of listening to radio contributes higher to the mean Hb level of children, whereas having a mosquito net does not, compared to the base category. The result shows that the risk in the Northeast, Northwest, Southeast, Southsouth, and Southwest regions on mean Hb is lower compared to the base category, which is Northcentral. The effect of 2015 on the mean Hb is significantly lower compared to the base category.
In the fourth panel, children leaving in the rural region are 41% significantly more likely that the anemic status of children is due to subsequent episodes of malaria. In other words, children living in the rural area are more likely to suffer from both malaria and anemia. Gender and source of water are not significant compared to the base categories. However, children whose parents used improved toilet systems are less likely to have a shared risk of malaria and anemia compared to the base category. Children of a richer and richest category of family wealth index have a significantly lower risk than the base category. However, as the level of wealth index increases, the risk of a child having a shared effect of malaria and anemia declines. The education level on the shared risk is not significantly different from the base category, which is no formal education. Moreover, the risk of a child having malaria and anemia declines as the level of education increases. Fever in the last two weeks before the surveys does not significantly contribute to the risk of a child having malaria and anemia. Children who sleep under a mosquito net and whose parents listen to the radio are 17.6% and 11.3% less likely to have a shared component of malaria and fever than the base category. Regarding region, children from Northwest, Southeast, Southsouth, and Southwest are significantly more likely to have malaria and anemia than the base category, whereas Northeast is not significant. In 2015, children are 30.9% more likely to have malaria and anemia than the year 2010 survey, which is the base category. Kogi are the areas with the highest Hb compared to the whole country. In Figure 3, the regions Ebonyi, Kebbi, Kwara, Nasarawa, Ondo, Osun, Nasarawa, and Zamfara are the regions at high risk of both anemia and malaria.  Figure 4 showed a nonlinear relationship between children's age and the associated risk factors.

Estimates of non-linear risk factors
The middle-black line represents the point estimates, and the red lines represent the 95% upper and lower confidence interval estimates for each age. As the age increases, the risk of a child having anemia reduces at a constant rate until age 35 months, where it had a slight distortion ( Figure 4a). The result agrees with the findings that younger children suffer more from the disease (Mulenga et al., 2005). In Figure 4b, a child's risk of malaria increases with age. It confirms the result obtained by Adebayo et al. (2016) that children are more exposed to mosquito bites as they gradually rely less on the parents to meet all their immediate needs. Additionally, this may be due to a strong immune system associated with breastfeeding, which favors the younger children.
Negligence on the parents' part to prevent their children from infected mosquito bites, as they grow older, worsen malaria cases, which make the children more vulnerable to malaria. In Figure   4c, as the age increases, the hemoglobin level of children increases until age 40 months and became slightly constant till age 59 months. In Figure 4d, as the age increases, there is a gradual decrease in the shared risk factor of malaria and anemia until age 32 months where it appreciates slightly. That is, the risk of malaria and anemia in rural settlements is higher than in urban settlements.
It agrees with the recent findings that a higher percentage of diseases in the urban areas were transported from the rural, tagging rural settlements a high transmission and endemic regions. It could be associated with a high ratio of less-informed parents and their negative attitude towards the control measures and programs to mitigate these diseases, thus, causing high incidence and low child recovery rates. Moreover, the lack of vital education on frequent environmental sanitization against mosquito, and cases where children consume inappropriate diets weakens the immune system and causes frequent episodes of the diseases and slow recovery. Thus, sustainable strategic intervention programs, formal and informal education should be targeted and maintained in rural areas. Female children are less likely to have anemia, which confirms the result obtained in Gayawan et al. (2014), while (Koukounari et al., 2008) concluded otherwise for children between 10-21 months in Kenya. In other words, rapid progression to death is frequently found for male children. It could be associated with higher Hb concentration found among female children. As expected, use of an improved toilet system lowers the risk of anemia and shared risk of having both diseases compared with unimproved systems. The rate of children having both diseases is higher for families with a low wealth index. Hence, programs to mitigate the impact on children should be targeted at lowincome earners. Parents' education plays an essential role in children's development and health.
Highly educated parents are more informed and would promote programs to mitigate the impact of diseases in children, such as the distribution and use of mosquito nets and environment sanitization.
The use of mosquito nets prevents malaria and reduces the anemic nature in children since children will be free of malaria parasites, thus, the irons within the red blood cells are unaltered. The risk The datasets analysed during the current study are available in the DHS website repository upon registration.

-Competing interests
The authors declared that they have no competing interests -Funding

No funding received -Authors' contributions
Osafu Augustine Egbon contributed to the data analysis, manuscript writing, and final manuscript revision. -Acknowledgements The author would like to acknowledge Ezra Gayawan for his research ideas and guide.