Bayesian mixed effect models to account for environmental modulators of acute malnutrition treatment in children

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The present study is a secondary analysis that attempts to characterize which variables have influenced the Middle Upper-Arm Circumference (MUAC) upon admission and the Length of Stay (LOS) for treatment recovery. The sample of children analysed was 852. Initially, data cleaning and a reduction of the dimensionality of dietary diversity were carried out. A selection of the importance of the variables using the Watanabe Akaike Information Criteria (WAIC) was carried out prior to the adjustment of Bayesian mixed effects models, with the variables of travel time to health site and week of admission as random factors, on the MUAC and LOS variables. Clear differences were seen between both contexts. Highlighting significant interactions of travel time in Niger while the seasonal effect stood out in Mali. The MUAC models identified a positive effect of age in both contexts, and in Niger, influences of diet diversity, comorbidities, breastfeeding and vaccination appeared. On the other hand, the LOS models highlighted the severity upon admission, and in Niger also factors related to the treatment protocol and the distance to the water source, while in Mali, the quality of water was more decisive. The present study shows the importance of considering acute child malnutrition from a multidimensional and complex approach, where diverse factors (biological, socioeconomic, ecological, etc.) can influence directly or as modulators of the disease and its treatment. Child wasting undernutrition MUAC travel time Bayesian INLA models Figures Figure 1 Figure 2 Figure 3 Introduction “ Every child has the right to good nutrition. Well-nourished children grow and develop to their full potential. They are better equipped to lead healthy lives, to be free from poverty, to learn and participate, and to continue thriving across the life course, with benefits that continue over generations ”. This is how the latest worldwide report on levels and trends in child malnutrition published by UNICEF, the World Health Organization (WHO) and The World Bank (2023) begins. One of the main messages to take into account in this report is that millions of children under five years do not achieve the aforementioned right of having a good nutrition. Of them, 45 million are affected by wasting, the form of malnutrition that poses the greatest risks to health (Black et al. 2008 ; McDonald et al. 2013 ; Thurstans et al. 2022 ). However, the values provided by recent cross-sectional surveys may not faithfully reflect the actual figures, which could be much higher (cumulative incidence) throughout a year (Isanaka et al. 2021 ; Mertens et al. 2023 ). Furthermore, the anthropometric criteria for diagnosing and treating acute malnutrition have varied over the decades, with each employed indicator showing a different relationship with body composition and clinical indicators (Bhutta et al. 2017 ). First, weight-for-age began to be used (< 60% of a reference value), later the WHO, to avoid including children with growth retardation, established Weight-for-Height as a criterion (Z-score < -2) (Waterlow et al. 1977 ), and afterwards, with the aim of simplifying the protocols, the Middle Upper-Arm Circumference was introduced (WHO, 2007). Currently, the WHO recognizes two well-differentiated states of severity within wasting: Moderate Acute Malnutrition (MAM) and Severe Acute Malnutrition (SAM). The latter is characterized by greater anthropometric severity: WHZ < − 3 and/or MUAC < 115 mm and/or nutritional oedema (WHO, 2023). To prevent and effectively ameliorate levels of child wasting, it is essential to know the causes and main risk factors associated with it. Although poor infant feeding practice is usually pointed out as the main determinant of nutritional status, the complex reality is that there are multiple factors that interrelate with each other and have an important impact on it. These factors include socioeconomic status, level of food insecurity, burden of comorbidities, and access to water and sanitation, among others (Rodríguez et al. 2011 ; Vollmer et al. 2017 ; van Cooten et al. 2019 ). A holistic point of view to understand these underlying causes allows a better approach to the problem to achieve lasting and sustainable solutions in the real world (Agostoni et al. 2023 ). In this sense, there are other external factors that are neither biological, nutritional, nor socioeconomic on their own but that also influence the levels of child malnutrition in a region over time. From an epidemiological point of view, environmental exposures can be broadly categorized into those that are proximate (e.g., directly leading to a health condition) and those that are distal (e.g., indirectly leading to a health condition), such as socioeconomic conditions and climate change. Other broad-scale environmental aspects can cause adverse health conditions directly by altering proximate exposures and indirectly through changes in ecosystems and other systems related to human health (Merrill, 2008 ). These concepts have recently been introduced into the conceptual framework of maternal and child nutrition by UNICEF (2020). In this sense, the aforementioned trends report also highlights that nearly 90% of all global child wasting cases are concentrated in the tropical areas of Africa and Asia (UNICEF et al. 2023). These regions experience marked periods of dry seasons and floods, which negatively affect various aspects such as agriculture, economic production, and access to drinking water (Asmall et al. 2021 ). A strong negative association has been documented between child weight and the average monthly variation in temperature across Sub-Saharan region, indicating a mean loss of 0.1 WHZ for every 1 ºC increase (Baker and Anttila-Hughes, 2020 ). To these annual effects, other climatic phenomena with a more stochastic occurrence are added, such as the El Niño Southern Oscillation (ENSO). Studies have highlighted that warmer conditions during ENSO are globally accompanied by an increase in the severity of child malnutrition in the tropics (Anttila-Hughes et al. 2021 ). Additionally, studies have shown significant associations between drought conditions and both wasting and underweight prevalence (Lieber et al. 2022 ). The most recent evidence on the study of child wasting seasonality, considering 15 years of SMART surveys from 19 countries in the northern region of the African continent, points out to the existence of two wasting peaks during the year. The highest peak of prevalence is estimated to begin in April to May, coinciding with the first increase in temperatures. A second peak of wasting is observed from August to October, coinciding with the primary peak of rainfall (Venkat et al. 2023 ). A local study in eastern Chad also identified two annual peaks of wasting and severe wasting at the end of the dry season. The smaller peak corresponds to the start of the harvest period, with the lowest prevalence occurring during the start of the dry season (Marshak et al. 2023 ). This research demonstrates the importance of being cautious regarding the child wasting seasonality in a region, since the existence of a wet and dry season will not necessarily translate into a single hunger season, as has been accepted in previous scenarios (Vaitla et al. 2009 ; Nonterah et al. 2022 ). Environmental geographic variability also directly affects the availability, access, and utilization of basic services, such as health service around the world (Weiss et al. 2018 ). Various studies have focused on mapping the levels of child acute malnutrition in countries such as Ethiopia and South Africa using data from national surveys. These studies demonstrate a non-uniform distribution of its prevalence across the country, highlighting the existence of specific spatial patterns and inequalities between administrative areas that respond to different factors (Sartorius et al. 2020 ; Atalell et al. 2023 ). Moreover, a cross-country study found an association, at the population level, of a higher prevalence of wasting in rural versus urban areas in 13 countries from the East and southern African region, also relating it to socioeconomic inequalities at the household level (Caleyachetty et al. 2023 ). Concerning child wasting, an aspect repeatedly identified as a barrier to accessing correct diagnosis and treatment is the distance to the health site (Puett and Guerrero, 2015 ; Rogers et al. 2015 ). Consequently, some geospatial analyses in various regions have highlighted this problem and its association with the burden of wasting. In Niger, the geographic distribution of community health posts was reported as inefficient. An estimated 58.5% of its population, which is 10.4 million people predominantly living in rural areas, remained beyond a 60-minute catchment of community health posts (Oliphant et al. 2021 ). Additionally, a geospatial coverage analysis conducted in the three largest districts of the Kayes Region in Mali revealed that there exists a high proportion of children living more than 5 km from the nearest health site, estimated at 70.4%. Moreover, a high proportion of children in rural communities were not screened for SAM, estimated at 52.2% (Charle-Cuéllar et al. 2022 ). Traditionally, these analyses and studies have been based on association models typical of classical frequentist statistics. However, the complexity of the contexts being studied, the rapid and abrupt changes that occur in them, as well as the underlying interrelationships between variables require more complete approaches. In this sense, the Bayesian approach is especially interesting and has been widely used in recent studies (Sartorius et al. 2020 ; Adhikari et al. 2022 ; Atalell et al. 2023 ), since they provide the advantages of being able to integrate prior knowledge with the observed data and are more flexible when it comes to updating the results as more data is obtained. Additionally, they explicitly incorporate uncertainty by providing posterior probability distributions for the parameters, which facilitates decision-making, allowing risk assessment and optimization of results. The objective of the present study is to determine, in an explanatory manner, which variables, incorporating seasonality and travel time to the treatment provider, are associated with greater severity upon admission and a longer stay in treatment for children diagnosed with acute malnutrition in rural regions of Niger and Mali, considered emergency contexts. Material and methods Study design The present study is a secondary analysis derived from controlled trials, which aimed to test different protocols for the treatment of acute child malnutrition (6–59 months) (Charle-Cuéllar et al. 2023 ; Sánchez-Martínez et al. 2023 ; López-Ejeda et al. 2024 ). The intervention was carried out in the Diffa region, in Niger, during the months of December 2020 to April 2021, including a total of 6 different health sites. Meanwhile, in the Gao region, in Mali, the intervention spanned from June 2020 to June 2021, involving a total of 27 health sites. Further details regarding the spatial distribution of the considered health site can be found in Figure S1 . A three-arm cluster randomized controlled trial was applied in Mali. In the control group, children were treated by specialized health personnel in health sites, using the standard protocol approved by the Ministry of Health of Mali (Community Management of Acute Malnutrition (CMAM) group). The first intervention group applied the same treatment protocol but added Community Health Workers (CHWs) as treatment providers in villages, at a minimum distance of 30 km from the reference health site (Integrated Community Case Management (iCCM) standard group). The second intervention group included, in a decentralized manner, both types of treatment providers (nurses and CHWs) but applied the combined simplified protocol known as the ComPAS protocol (Bailey et al. 2020 ). On the other hand, a non-randomized controlled trial with only two groups was conducted in Niger, both of them including nurses and CHWs. The control group was treated under the country's standard protocol (CMAM protocol), while in the intervention group the combined-simplified ComPAS protocol was applied. In addition to measuring anthropometric variables for diagnosing acute malnutrition (MUAC and WHZ), several information was collected, including sex and age, the presence of comorbidities (fever, vomiting, diarrhoea, malaria, acute respiratory infection), and their vaccination status. Furthermore, the present study was based on a subsample of treated children on which a socioeconomic survey was carried out. Specifically, a total of 676 families in Mali and 771 in Niger were interviewed. The socioeconomic survey was conducted by interviewing the child's caregiver at the treatment facility upon admission, covering 58 variables organized into four dimensions of living conditions: demographics (9), livelihoods (14), food security and diversity (26), and access to healthcare (9). After the completion of each child's treatment, information regarding the treatment outcome was also collected (recovery, default, discharge error, etc) which then enables to select only recovered children. Only cured children were included in the present study. Data cleaning and exploratory analyses Data analysis was carried out using R software v. 4.3.2 (R Core Team, 2023 ). Initially, data cleaning was performed, by considering negative numbers or values beyond four standard deviations away from the mean as transcription errors or extreme outliers, and, hence, being replaced by NA. In addition, for categorical variables, those cases showing less than five observations were either eliminated or combined with another if there was an ordinal relationship. Afterwards, missing values were handled, to reach comparable datasets for the model building step. Firstly, variables with total missing values equal to or greater than 10% (12) were removed from the analysis, remaining a total of 46 (Table S1 ). Subsequently, individuals with any missing values were also removed. This procedure ensures that all participants have information on the same variables without missing values. Finally, after cleaning the data, the total sample set consisted of 413 children from Mali and 439 children from Niger with a mean age of 13.89 ± 7.07 months (Figure S2). The dependent variables modelled were Mid-Upper Arm Circumference (MUAC) at admission and Length of Stay (LOS) for recovery as proxies of severity and treatment effectiveness respectively. As a temporal variable, the day of the child's admission to treatment was included, which was later grouped into a new variable indicating the week (starting from the day of the beginning of the study of Mali in June) on which each child was admitted to treatment. Regarding the spatial variable, information is available on the travel time from the child's home to the health site where treatment was provided, grouped into 7 categories progressively increasing travel time (1: Less than 15 min, 2: 15–30 min, 3: 30–90 min, 4: 90–120 min, 5: 120–150 min, 6: 150–180 min, 7: more than 3 hour). This temporal data is considered the most suitable proxy for operationalizing accessibility (Weiss et al., 2018 ). Initially, an exploratory analysis was conducted to examine the relationships between this set of variables in both contexts. An initial descriptive graph was created using a locally estimated scatterplot smoothing (LOESS) function to model the relationship between the MUAC and LOS variables over time (weeks) and travel time to the health site. In this sense, Pearson correlation coefficients were calculated, stratified by key variables, to better understand the underlying interrelations and modulation effects. Following this, with the objective of reducing the dimensionality of the data, a Principal Component Analysis was conducted on the frequency values of the dietary diversity survey. The calculation was performed by a singular value decomposition of the centered and scaled data, retaining the first four Principal Components, which became new variables in the dataset. To interpret the relationships in the diet data, it was represented a correlation matrix along with its dendrogram, generated through a Hierarchical Cluster Analysis (HCA) using Euclidean distances as metrics. Variables selection Prior to modelling, the covariates were ordered based on their importance in analyzing each dependent variable. For this purpose, several univariate models were built, one for each covariate and country independently. The Watanabe Akaike Information Criteria (WAIC) was then calculated for model comparison. The models with the lowest WAIC values were chosen to establish the order of importance among the covariates. Moreover, the WAIC value is considered a measure of model accuracy (Watanabe and Opper, 2010 ). All univariate models were performed using the subsample of individuals without missing values, incorporating the temporal variable of week and the spatial variable of travel time to the health site as random effects. This ensured homogeneity in the information available for each model, enabling their WAIC values to be comparable. Defining Bayesian model Bayesian inference is a valuable method for data modelling that allows to estimate posterior distributions of model parameters β by updating prior distributions with information from recorded observations y using Bayes’ Theorem: \(\:\pi\:\left(\beta\:|y\right)=\:\frac{\pi\:\left(y|\beta\:\right)\:\pi\:\left(\beta\:\right)}{\pi\:\left(y\right)}\:\propto\:\:\pi\:\left(y|\beta\:\right)\:\pi\:\left(\beta\:\right),\) (Moraga et al. 2021 ) The models implemented in the present study were performed using the Integrated Nested Laplace Approximation (INLA) approach through the open-source R-INLA package (Rue et al., 2009 ). INLA avoids sampling by accurately approximating posterior marginal distributions, making it an efficient alternative to Markov Chain Monte Carlo (MCMC) methods (Lindgren and Rue, 2015 ). Mixed-effects models were specifically chosen for their ability to model and incorporate complex relationships between variables, as they allow the inclusion of both linear fixed effects and random effects of different natures (Gómez-Rubio, 2020 ). Regarding the Bayesian parameters of the model, the prior distribution for fixed effects (regression coefficients and global intercept) was specified as Gaussian, centered on 0, and with a large variance (minimally informative). For health site variables, travel time to the health site and week of admission, we assumed nonlinear relationships with the response variable by including them in the model as random effects. To evaluate what type of random effect to implement for the temporal and travel time variables in each model, the WAIC of the possible combinations was calculated (Table S2). The possibilities considered included random walks of orders 1 and 2 (rw1 and rw2), while for the health site, it was established as independent (iid). These random walk processes are very suitable for modelling biological and natural processes, allowing a certain degree of randomness and dependence on previous values (Codling et al. 2008 ). Finally, the prior distribution for random effects was specified as a Half-Cauchy distribution, as it yielded a better WAIC than using the default multivariate Gaussian distribution with zero mean and precision matrix τΣ. Therefore, in the present study the INLA models were fit for each variable of interest as follows: $$\:{{\eta\:}}_{i}=\alpha\:+\sum\:_{j=1}^{{n}_{\beta\:}}{\beta\:}_{j}·\:{x}_{ij}+\:\sum\:_{k=1}^{{n}_{f}}{f}^{\left(k\right)}\left({u}_{ki}\right);\:i=1,\dots\:n$$ where η i is the linear predictor, α is the intercept, β j x ij are the covariate parameters and covariates, f (k) are the random effects terms on some covariates \(\:{\left\{{u}_{k}\right\}}_{k=1}^{{n}_{f}}\) , and i = 1, …, n are the variables of interest. The selection of the final model was carried out in a stepwise manner to optimize prediction error. Therefore, variables were introduced one by one according to the order of the lowest WAIC established previously by the univariate models. When introducing a new variable into the model, if the WAIC of this expanded model decreased by more than three units compared to the previous one, the variable remained in the model. Otherwise, the variable was removed from the model, and the next one was tested. This procedure was repeated until two of these stepwise phases were completed to reach the final model. Results Preliminary exploratory analysis suggests that MUAC values and LOS for recovery differ across the categories of the variables of time from the health site and week of child’s treatment admission. Likewise, a difference is also noticeable in the behaviour of the data in both contexts, as shown in Fig. 1. This variation between the data from Mali and Niger appears to be particularly pronounced in the LOS values, both along the travel time and for the week variable categories, with higher values recorded in individuals from Mali. MUAC: Mid-Upper Arm Circumference; LOS: Length of Stay. Figure 1. Scatter plots showing the relationship between MUAC upon admission and LOS with the Week and Travel time category variables for Mali and Niger. Locally estimated scatterplot smoothing (LOESS) was applied to each country data. Next, for quantifying the observed relationship, the sample set was to key factors that may impact the variables of interest. Table S3 shows the results of these correlations, and despite the limitation that only linear relationships have been evaluated, some relevant results that are worth highlighting were observed when comparing both countries and the categories of the stratification variables. In general, we observe that all the values obtained show weak linear relationships (< 0.4), and in many cases, they are not significant. However, we found interesting differences between the categories of some key variables. Firstly, in Niger, we observed an initial effect of severity on the relationship established between MUAC and LOS with Week, such that MAM children present significant correlations while SAM do not. There is also a quite notable effect of the presence of comorbidities, with significant effects observed in individuals who presented any. On the other hand, Mali stands out compared to Niger for presenting a large number of significant correlations between the MUAC and Week variables. Therefore, it seems to exhibit a fairly evident temporal effect in its evolution. Likewise, we found differential relationships between groups of categories in the treatment protocol, in the degree of severity, in the presence of comorbidities, and in the fact of being vaccinated or not. However, the sex and the age of the individual did not appear to have any effect, as the relationships were significant in both groups. Figure 2 shows the interrelations established in Mali and Niger between the variables of food consumption frequency and each of the first four Principal Components (PC) computed with Principal Component Analysis. The correlations between all these pairs of variables were placed in a correlation matrix, and then a dendrogram was constructed, which showed relevant groups according to the dietary pattern in the population: PC: Principal Component. Figure 2. Relationships between the Principal Components and the frequency variables of consumption of food groups. The side legend shows the numerical correspondence of the correlation value with a colour gradient. In Mali, a clear pattern in the consumption of certain foods is associated with PC2, indicating a relationship in the consumption of fish and seafood, cereals, dairy products, fats, condiments, and sugar products. On the other hand, PC3 and PC4 are associated with a greater consumption of animal organs such as kidney or liver and fruits rich in vitamin A. Another interesting association is found with the consumption of meat, eggs, other fruits, roots and tubers, and other vegetables. Finally, it should be noted that PC1 presents negative correlations, pointing that an increase in its values ​​would result a general reduction in the frequency of food consumption. If we pay attention to the relationships of food consumption in Niger, we find slightly different associations. First of all, PC1 is associated with the consumption of fruits rich in vitamin A, vegetables especially rich in vitamin A, roots and tubers, and legumes. Another interesting association is found with PC2 and the consumption of fats, dairy products, sugar products, and condiments. Finally, PC3 and PC4 are associated with cereal consumption and negatively associated with the rest. A final interesting pattern indicates a group of children who have increased their protein consumption, with a higher frequency of eggs, meat, fish, seafood, animal organs, and other fruits and vegetables in their diets Final models for MUAC The parameters of the final models on the MUAC upon admission for Mali and Niger are presented in Table 1 . The number of variables introduced in the final model for Niger was five, and this model reached a WAIC of 2617.18. On the other hand, in the case of Mali, the final model was simpler, containing two variables, with a corresponding WAIC of 2691.22. Although one variable is shared in both models, our results seem to indicate two different situations to understand the severity (MUAC) of children upon admission to treatment depending on the context. Table 1 Final model of MUAC upon admission in Niger and Mali: INLA posterior mean estimates (including standard deviations) and its credible interval are presented. Country Parameter Mean SD CI Niger Intercept 109.713 1.788 (106.188; 113.240) Comorbidities Yes -2.529 0.575 (-3.657; -1.402) Food Diversity PC1 -0.508 0.131 (-0.765; -0.252) Age Admission (months) 0.145 0.047 (0.052; 0.237) Receiving breastfeed now Yes 3.329 1.099 (1.173; 5.485) Vaccination Yes 1.365 0.471 (0.442; 2.290) Food Diversity PC2 0.544 0.164 (0.222; 0.867) Mali Intercept 107.739 1.773 (104.265; 111.219) Age mother pregnant (years) 0.139 0.051 (0.040; 0.238) Age Admission (months) 0.160 0.038 (0.086; 0.235) PC: Principal Component; SD: Standard Deviation; CI: Credible Interval. If we pay attention to the Niger model, we find variables of different natures involved in determining the MUAC upon admission. A first group seems to be related to the health status of the individual. Presenting any comorbidity negatively affects the MUAC, modifying its values ​​by -2.529 mm (CI: -3.657; -1.402). Likewise, the vaccination has a positive effect on the MUAC value, increasing it on average by 1.365 mm (CI: 0.442; 2.290). A second group of variables are associated with the child's diet. Firstly, breastfeeding is a quite positive factor according to the model on the MUAC value, if it is present in the child's diet, it causes the MUAC to increase on average by 3.329 mm. (CI: 1.173; 5.485). Furthermore, dietary diversity also seems to have an interesting effect. Since PC1 (vegetables and fruits) and PC2 (fats and dairy products) are present in the model, the first one seems to have a negative effect on the MUAC, since for each unit that increases its value, the MUAC is reduced in the individual by 0.508 mm (CI: -0.765; -0.252). On the other hand, the effect of the PC2 is positive on the MUAC value, so that for each unit that increases its value, the MUAC increases by 0.544 mm (CI: 0.222; 0.867). Another variable present in the model in the case of Niger is the age of the individual, which has a positive effect on the MUAC, observing an average increase of 0.145 mm (CI: 0.052; 0.237) for each month. Regarding the final model of MUAC upon admission in Mali, which stands out for being much simpler than the one of Niger, we can highlight the shared presence of the variable age upon admission, which acquires a very similar effect, so that for each month that the child turns, his MUAC upon admission increases by 0.160 mm (CI: 0.086; 0.235). Another variable that participates in the model is the age at which the mother began her pregnancy with the treated child, which also appears as a positive factor on the MUAC value. For each year that the mother's age increases, the child's MUAC upon admission increases on average by 0.139 mm (CI: 0.040; 0.238). Final models for LOS Table 2 show the parameters of the final models of LOS for recovery in Niger and Mali. Once again, the Niger model presents a greater number of variables. It reaches a WAIC of 3269.66 with these five variables. On the other hand, the model in Mali with three variables shows a WAIC of 2952.29. In the case of the LOS for recovery variable, both the Niger and Mali models seem to identify very similar factors related to the study variable in both contexts. Table 2 Final model of LOS for recovery in Niger and Mali: INLA posterior mean estimates (including standard deviations) and its credible interval are presented. Country Parameter Mean SD CI Niger Intercept 166.883 12.208 (142.934; 190.835) MUAC Admission (mm) -1.061 0.107 (-1.270; -0.853) Protocol Simplified -10.849 1.463 (-13.719; -7.980) Food Diversity PC4 1.801 0.560 (0.703; 2.899) Distance to collect water 100–300m 3.756 1.495 (0.824; 6.690) Distance to collect water 300–500m 5.372 1.764 (1.911; 8.835) Distance to collect water more than 500m 1.839 2.101 (-2.282; 5.961) Travel Health site one day Yes -3.726 1.707 (-7.075; -0.377) Mali Intercept 83.646 19.634 (45.084; 122.141) MUAC Admission (mm) -0.407 0.167 (-0.734; -0.078) Food Diversity PC4 2.402 1.060 (0.321; 4.480) Water supply other 7.584 11.00 (-14.009; 29.163) Water supply water tanker 1.822 16.917 (-31.372; 35.004) Water supply rain water 21.651 9.907 (2.207; 41.085) Water supply surface water -4.922 4.366 (-13.494; 3.640) Water supply unprotected well 11.762 3.830 (4.241; 19.273) Water supply protected well 8.545 3.278 (2.109; 14.974) Water supply community tap 6.180 3.807 (-1.293; 13.647) MUAC: Mid-Upper Arm Circumference; mm: millimetres; PC: Principal Component; SD: Standard Deviation; CI: Credible Interval. In Niger (see Table 2 ), the protocol variable stands out with the highest value of posterior mean estimate. So, when the child is treated with the simplified protocol, its LOS is reduced by 10.849 days (CI: -13.719; -7.980) compared with the national Standard protocol. Another relevant variable is that referring to the travel health site, which seems to indicate that being able to travel on the same day would have a positive effect on the shortening of the time in treatment, modifying the LOS on average by -3.726 days (CI: -7.075; -0.377). On the other hand, we found the MUAC upon admission, which reflects the severity with which the child began treatment. This last variable indicates in the model that a greater MUAC participates favourably in shortening the time in treatment, since for each millimetre that it increases, the LOS for recovery decreases by 1.061 days (CI: -1.270; -0.853). We also see how the PC4 of diet diversity (fruits) intervenes to lengthen the LOS for recovery in Niger; according to the model, for each unit that increases this variable, it results in an increase in the LOS of 1.801 days (CI: 0.703; 2.899). Finally, the distance to the drinking water source also has an important influence. Being 100–300 m or 300–500 m compared to the reference category, which is less than 100 m, causes an increase in LOS of 3.756 days (CI: 0.824; 6.690) and 5.372 days (CI: 1.911; 8.835) respectively. However, for the longest distance category, the impact was not significant, possibly because of a small sample size. The final LOS for recovery model in Mali includes very similar variables to those selected in the case of Niger. Firstly, MUAC upon admission also has a positive effect in reducing LOS for recovery, so that for each millimetre of increase, the reduction is 0.429 days (CI: -0.756; -0.101). A second variable shared in both models is the fourth Principal Component of dietary diversity, which in the case of Mali, an increase also has a negative effect on the LOS, since for each unit of increase, the LOS increases by 2.457 days. (CI: 0.369; 4.545). Finally, the third variable considered in the model is related to drinking water, in this case, its source. We observe how the categories of rain water, unprotected well, and protected well have an appreciable effect, compared to the reference category which is home tap, they increase the LOS for recovery, with the first of them being the most harmful since they represent an average increase of 21.091 days (CI: 1.663; 40.485), followed by unprotected well that increases LOS by 11.482 days (CI: 3.929; 19.023), and protected well by 8.403 days (CI: 1.919; 14.877), respectively. Model prediction In the specific case of the final model of LOS for recovery in Niger (Table 2 ), we found quite a difference in the effects of each variable and their respective weights in the model. Figure S3, which shows the posterior distributions of all these parameters, shows us the estimated probability (y axes) that each coefficient has of taking on a specific value (x axes), providing a better comparison for understanding the distribution of effects that contribute to the predictions made by the model. For the sample of boys and girls treated in Niger, a paradigmatic case of prediction can be proposed: the maximum LOS value predicted by our model was 65.39 days (58.53; 72.27). This prediction corresponds to an 8-month-old girl whose MUAC was 90 mm. She could not make the travel to the health site in a single day, was treated with the simplified protocol, the source of water consumption was located 100–300 m away, and her value in the PC4 of dietary diversity was: 0.84. The opposite extreme case is found in a 17-month-old boy, for whom the model predicts the lowest LOS for recovery: 17.09 days (12.64; 21.53). This individual had a MUAC of 120 mm, he could make the travel to the health site in a single day, was treated with the simplified protocol, the source of water consumption was located less than 100 m, and his value in the PC4 of diet diversity was: -2.49. Finally, the real difference observed was somewhat less than what the model predicted (48.3 days), as the second individual was cured 28 days before the first one, who had worse conditions. Interactions with random effects Next, it is relevant to test in the final models built whether the effects of the random factors introduced are homogeneous or if, on the contrary, there are interactions. These interactions could lead to a modulation in a variable's effect, which may be interesting to interpret. Figure 3 shows a collection of graphs that reflect the interactions found between some interesting variables (protocol, presence of comorbidities, sex, severity) with the Week (in red) and Travel time (in blue) variables, which were introduced as random effects in the final models. Tables S4-S9 provide a complete view of the numerical evolution of the mean random effects in each category. MUAC: Mid-Upper Arm Circumference; LOS: Length of Stay; SAM: Severe Acute Malnutrition. Figure 3. Behaviour of mean random effects in different categories of interest in the final MUAC and LOS models for Mali and Niger. It is worth nothing that the importance that both random factors acquire in the models seems to be very different between both contexts. This fact is contrasted by the number of interactions found; while in Niger, the interactions are mostly with the Travel time variable, in Mali, is rather with the Week variable that we find a greater number of interactions. Therefore, while in Niger, the factor of travel time to the health site seems to have an appreciable weight, in Mali, a more noticeable seasonal effect on the variables of interest is present. For the interactions found in Niger, first, we highlight an effect of Travel time in the MUAC model upon admission of individuals who present a comorbidity at the time of their diagnosis of acute malnutrition (Fig. 3a). Thus, those individuals whose travel time to the health site is less than 15 minutes (category 1) see their MUAC increase on average by 2.65 mm (CI: 0.52; 5.14) compared to the rest of the individuals with a comorbidity. That is, being closer to the health site when they are sick seems to imply arriving with less severity. Nevertheless, the trend of the graph shows that the MUAC decreases when the Travel time increases; the confidence intervals, however, do not allow us to be really sure of this effect of increased severity. A second interaction affecting MUAC was found between Week and sex (Fig. 3b), indicating that boys recorded an improvement in their severity of 1.26 mm (CI: 0.05; 2.63), an effect that was not recorded in girls. Another interesting effect observed in Niger occurs in the LOS for recovery model (Fig. 3c), where individuals diagnosed with a higher degree of severity of acute malnutrition (SAM) reduce on their LOS by an average of 2.80 days (CI: 0.23; 5.70) when they are 15–30 minutes from the health site (category 2), while those individuals who are at the greatest travel time category, more than 2 hours from the health site, see an increase in their LOS by an average of 5.49 days (CI: 0.21; 12.67). This effect was not found among the group of treated children diagnosed with a lower severity (MAM) at the beginning of their treatment. Another interesting interaction in Niger, which corresponds to the LOS for recovery model, involves the presence of comorbidities (Fig. 3d). In this case, the behaviour of the random effects in the Travel time categories indicates that being 15–30 minutes from the health site (category 2) reduces the time in treatment in a child with no comorbidities by an average of 2.65 days (CI: 0.49; 4.97). No significant effects were found for the other Travel time categories, nor in any of the children with comorbidities. Mali results show for the MUAC upon admission model, a temporary effect in the individuals who were treated with the Standard Protocol iCCM (Fig. 3e). This effect was not found in individuals treated with either the Control CMAM Protocol or the Simplified Protocol. In this graph, it can be seen that around week 18 after the start of the intervention (October), the average MUAC value upon admission declines, reaching its lowest value at week 27 (November), with an average decrease of 9.29 mm (CI: 4.91; 14.08). At this point, the trend reverses, and the value begins to increase until weeks 40–50 (April-May), where it stabilizes with an average MUAC increase of around 5 mm (CI: 3.90; 9.86) compared to the rest of the weeks. A second interaction found in the MUAC upon admission model in Mali shows a pattern very similar to the one previously described. In this case, the category involved is the female sex (Fig. 3f). It can be seen how the temporal effect on the MUAC value in the group of girls is very clear throughout the study. In such a way that by week 29, the lowest value is reached, with an average reduction in MUAC of 5.91 mm (CI: 2.95; 9.37), and from this moment, the trend of the effect reverses until week 39 (April) when the effect becomes positive, reaching the highest average value in week 43 with 4.60 mm (CI: 1.62; 8.00). This pattern of change was not found in the group of boys. Regarding the interactions to be highlighted in the Mali model of LOS for recovery, the first of them involves the category of greatest severity (SAM) (Fig. 3g), where a temporary effect of increasing LOS for recovery was observed for boys and girls who began their treatment at weeks 15–19 (September-October), resulting in the greatest effect being about 6.34 days longer on average (CI: 0.65; 12.55). This pattern was not found in MAM individuals. However, the MAM group showed a significant decrease in LOS for recovery from week 45 (May), reaching values of up to 20 days less for LOS on average (CI: 11.55; 32.76) (Table S8). Another interaction found in the LOS for recovery model in Mali, and that combines the different behaviours of SAM and MAM children, is the one that involves in the boys (Fig. 3h). Therefore, they present a temporary effect during weeks 15–22 (September-November) of increase in LOS about 6.95 days on average (CI: 1.64; 12.50), with a subsequent decrease starting at week 45. Discussion To fully address a global public health problem as serious as acute child malnutrition, understanding its causes and the health-disease process requires a multidimensional approach. The classic models proposed by Laframboise ( 1973 ) and Lalonde ( 1974 ) point out the involvement of four main groups of health determinants: human biology, the health system, environment, and lifestyle. Following these theories, approaching and identifying these determinants of child acute malnutrition in each context, in addition to using biological (anthropometric) diagnostic criteria, will allow for a greater knowledge of the disease and increase the effectiveness of future interventions. The final models for MUAC upon admission have shown a mixture of factors of different natures associated with the severity of the treated child, in addition to differences between the contexts of Mali and Niger. In general, the age of the individual seems to be a decisive factor in both cases, which is reflected in the WHO growth standards which show an increase in MUAC with age (WHO, 2006). While in the Mali model only the age of the mother is added as another determining factor in the severity of the child, it is in younger mothers where the levels of severity increase, as has been confirmed in a broader analysis that included a total of 55 low- and middle-income countries. This analysis associated a higher risk of infant mortality and poor child health outcomes with children of adolescent mothers (Finlay et al. 2011 ). In the case of Niger, the final model describes a more complex reality, aiming to understand the influences on MUAC upon admission of treated children. Healthcare-related aspects such as the presence of comorbidities (diarrhea, vomiting, ARI) and correct vaccination appear as determining factors. In scientific literature, the vicious circle between infectious comorbidities and acute child malnutrition is well known, mediated by a series of physiological and immune reactions in the body (Humphries et al. 2021 ). Vaccination is a palliative measure that can help break this vicious circle, a protective effect that has also been proven in previous studies across different scenarios (Altare et al. 2016 ; Ambadekar and Zodpey, 2017 ). Strikingly, another variable that accumulated greater importance is breastfeeding. This scenario has been identified in different studies and systematic reviews as a protective factor against morbidity and mortality in the first two years of a child’s life. Numerous interventions have focused on promoting its adequate practice, based on its positive effects at a nutritional and immunological level (Horta and Victora, 2013; Khan and Islam, 2017 ). Finally, different consumption patterns in dietary diversity also appeared to be linked to MUAC upon admission. Various studies have shown that poor dietary diversity is associated with higher odds of wasting (Li et al. 2020 ; Aboagye et al. 2021 ). There are different factors such as socioeconomic level, food security, childcare, etc., which are related and all of which, in turn, further shape dietary intake and diversity. Moreover, another recent study better characterized this association, stating that the likelihood of wasting was 0.22 times lower for children who received minimum dietary diversity (MDD) and minimum meal frequency (MMF) (Sheikh et al. 2020 ). Specifically, in our model, Food Diversity PC1, which has a negative effect on MUAC, was related to greater consumption of fruits rich in vitamin A, vegetables especially rich in vitamin A, roots and tubers, and legumes, while Food Diversity PC2, which has a positive effect, was related to greater consumption of fats, dairy products, sugar products and condiments. These very different effects, depending on the pattern, are supported by a better quality in terms of caloric density and macro- and micronutrient content of the foods included in PC2. This nutritional concept, used by quantitative indices of dietary diversity (WFP, 2008), assigns greater importance to foods such as meat, fish, and dairy products. LOS modelling has enabled the identification of factors associated with individuals taking longer to achieve recovery, which can be very useful in prioritizing and improving their care. In both the Niger and Mali contexts, individuals with greater severity upon admission, as identified by the MUAC, presented longer LOS. The relationship between anthropometric severity upon admission and treatment outcome is widely documented (Collins et al. 2006 ; Dah et al. 2022 ). Studies such as that of Mamo et al. ( 2019 ), using another statistical approach, highlight that comorbidities and routine medicine provision are factors that impact time to recovery. Our models also reach this result, linking it through the MUAC upon admission. Another aspect associated with LOS in both contexts was related to the source of water consumption. In the case of Niger, greater distance was associated with an increase in LOS. On the other hand, in Mali, the quality of water was the most relevant variable. This highlights the great importance of having good access to a safe water source that is not only accessible but also drinkable and of high quality. Such quality water aids children in treatment to respond better to it. This deficiency in access to drinking water has been associated in numerous studies with child malnutrition (Kamiya, 2011 ; Bitew et al. 2022 ). Likewise, there is a great consensus that good quality of consumed water reduces the incidence of comorbidities that impair recovery, especially diarrhea (Bhutta et al. 2013 ). There is also consensus in both contexts regarding dietary diversity, as both models indicate that Food Diversity PC4 contributes to an increase in LOS. This can be explained by the negative association of this component with the consumption of eggs and meat. These animal products are energy-dense and contain multiple micronutrients such as iron, zinc, vitamin A, vitamin B12, etc. Their consumption is associated with improved nutritional status outcomes in observational studies (Hetherington et al. 2017 ; Larson et al. 2019). The LOS values of children treated in Niger were found to be influenced by the simplified treatment protocol. This protocol stands out compared to the conventional CMAM protocol, used mostly in the country, for decentralizing treatment and bringing it closer to families and a series of simplifications in the diagnosis and management of cases (Charle-Cuéllar et al. 2023 ). The WHO, in its most recent guideline on the prevention and management of wasting (WHO, 2023), recognizes CHWs as an effective tool based on currently existing evidence. Different studies have demonstrated its effectiveness in improving treatment coverage, a reduction in severity upon admission and an increase in the recovery rate (Álvarez-Morán et al. 2018 ; Charle-Cuéllar et al. 2018 ; Wilunda et al. 2021 ). Moreover, CHWs will lead to moderate savings in terms of resources (Rogers et al. 2018 ; Cichon et al. 2023 ). The great advantage of CHWs is that they reduce the distance to treatment. With health sites being less saturated, there is more time to treat each individual, allowing comprehensive treatment of other comorbidities such as diarrhea, acute respiratory infections (ARI), malaria, etc., which negatively affect severity and LOS (López-Ejeda et al. 2020 ). A previous study by Dougnon et al. ( 2021 ) in rural Niger also found a shorter LOS in SAM children treated by CHWs, attributing it to earlier detection of cases, as their severity was lower. The achieved models, in addition to be able to identify and to quantify risk factors associated with our variables of interest, have the great potential to predict, with a certain level of confidence, the value an individual could present based on the initial covariates. This capability can be particularly useful in the case of LOS for recovery. In this regard different profiles could be established to identify children at a higher risk of inadequate treatment response, and consequently, of remaining malnourished for a longer period, with adverse consequences for their health. The utility of its application in the field is evident through the detailed examples used for analysing and comparing various factors associated with each case. These examples involve crossing them with probability distributions and understanding the practicality of applying it in the field. These models are of great interest because they incorporate the week of admission to treatment (reflecting seasonality) and travel time to the health site (reflecting accessibility to treatment) as random factors in their adjustment. This allows the incorporation of potential interactions they may have with other key factors. In Mali, a clear seasonal influence was observed, while the analyses did not indicate this in Niger, possibly due to the narrower time frame of their data. Specifically, in the case of Mali, the highest severity levels (lowest MUAC upon admission) were observed in weeks 0 and 24 of the study, coinciding with children admitted to treatment in June and November. This result aligns with a recent secondary analysis of 15 years of SMART survey data, indicating two peaks of wasting in African drylands such as Mali. The primary peak occurs in April to May, and the second peak occurs in September to October, influenced by peaks in temperature and precipitation (Venkat et al. 2023 ). This temporal difference with the identified prevalence peaks could respond to the time necessary for these most critical situations of food insecurity to be reflected in an increase in the severity of MUAC. It is important to take this seasonality into account in African drylands, where production systems highly depend on climatic conditions characterized by extreme and erratic rainfall. Seasonal temperatures are consistently above 20ºC and can reach as high as 40 or 50ºC (Young, 2020 ). Furthermore, considering this data will be particularly relevant in the future context of climate change, which is expected to worsen water scarcity and accelerate desertification, thereby influencing food production and nutrition security, which will amplify health challenges (Agostoni et al. 2023 ). In this sense, the study carried out by Baker and Anttila-Hughes ( 2020 ) estimated the effect of temperature on key child nutrition outcomes through a pooled statistical model that controlled for household and regional characteristics. They then forecasted the impact of future warming on child malnutrition levels, determining that the western Africa region would see a 37% increase in the prevalence of wasting by 2100. The random effects models presented significant interactions within the study sample in each context. In Niger, we observed that children with comorbidities experience a reduction in their severity on admission (MUAC) if they are very close to treatment. This benefit of proximity to treatment over severity has already been evidenced in studies that included CHWs as treatment prividers outside health centers closer to the communities (López-Ejeda et al. 2020 ; Dougnon et al. 2021 ). The results of our study seem to indicate that this effect could be especially important when comorbidities are present, as reducing the distance, one of the greatest barriers to accessing treatment, would lead to earlier detection and treatment of comorbidities, potentially reducing their severity upon admission. Another significant interaction detected in severity in Niger was between week and sex, with boys showing a greater MUAC compared to girls. This finding appears somewhat contradictory to the existing literature (Myatt et al. 2018 ; Costa et al. 2021 ). In a recent meta-analysis of 44 studies, Thurstans et al. ( 2020 ) demonstrated that boys are more likely to be wasted than girls (odds ratio: 1.26 [95% CI: 1.13–1.40]). This is biologically explained by the sexual differences that already exist from the first months of life, both in growth patterns and body composition, with less adipose accumulation and gain in boys (Davis et al. 2019 ). All of this is influenced by hormonal differences already noticeable in infants and affect their metabolism (Kiviranta et al. 2016 ). Regarding the LOS in Niger, an effect of travel time was also observed in the SAM group. Those further away from treatment had a greater LOS, which is directly related to the effect already observed on MUAC in this context. This effect, reflected in the LOS, suggests that in a treatment involving weekly visits, greater distance may impact the effectiveness of treatment adherence, leading to increased missed visits, which could ultimately result in default (Hitchings et al. 2022 ). This same explanation can be applied to the interaction observed between Travel time and the non-comorbidities group, as their LOS is reduced when near treatment but increases when distant. The lack of an effect seen on LOS in the comorbidities group may be attributed to the reduced sample size. In the context of Mali, interactions were observed in the MUAC model, with very similar behaviours, between the Week and the treatment protocol, and, on the other hand, between the Week and the sex variable. Firstly, individuals treated with the Standard Protocol experienced a decrease in their MUAC between weeks 20 and 30 of the study (November-December), coinciding with one of the wasting peaks identified in the literature. The very similar behavior observed in the values of the group of girls indicates that these seasonal effects were also associated with sex, as they were not appreciated in the group of boys. Both contexts have shared an association between sex and seasonality in MUAC, with a negative effect observed only for girls, which has already been mentioned as biologically contradictory. Therefore, it is necessary to consider the possible presence of social factors related to gender in both contexts, which may explain these results. Previous studies have demonstrated this influence in southeast Asian countries (Raj et al. 2015 ), wherein having more brothers increased the odds of severe wasting (AOR: 1.31 [CI = 1.11, 1.55]) for girls but not boys. This is likely due to situations of food insecurity, where there is a preference for feeding male children over female children (Biswas and Bose, 2011 ). A recent study by Thurstans et al. ( 2023 ) indicated a greater average daily weight gain in girls. However, in many settings, the adjusted odds ratios (AORs) noted that girls were less likely to recover than boys. Likewise, a study based on big data by country identified a strong and statistically significant association of the Gender Inequality Index with excess under-five female mortality in low-income and middle-income countries, including the Sahel region (Iqbal et al. 2018 ). In terms of LOS in Mali, a seasonal effect was also detected, with the group of SAM males showing an increase in LOS in specific weeks of the study (14–23) during September to November. These findings are based on the characteristics of this specific group of individuals, as it comprises the most severe group of boys (SAM). Therefore, this increased severity is added to the already mentioned disadvantageous biological characteristics of sexual dimorphism (Davis et al. 2019 ). Furthermore, being admitted to treatment during this time frame means that individuals have to undergo treatment during the second wasting peak of the year identified in the Sahel drylands (Venkat et al. 2023 ). This period coincides with worsening food security due to increasing temperatures and reduced access to sufficient, safe, and nutritious food to meet their dietary needs, which directly affect the nutritional status of individuals, resulting in longer LOS values comparable to those recorded in our study, where some SAM boys required more than 100 days to achieve recovery. Therefore, this period is particularly critical, requiring heightened attention to the most vulnerable groups, who suffer for an extended period from severe malnutrition. Finally, there are some issues that need to be stated as potential limitations of our approach. The most obvious is that the Niger data presented a narrower time frame and could not cover an entire year, limiting the results in correctly identifying the possible effect of seasonality on the variables of interest in this context. Another limitation would be the lack of response in some variables and the handling of missing values. In light of the results obtained, it is appropriate to highlight the need for further research, applying an integrative approach involving various biological, socioeconomic, ecological and clinical aspects related to the disease, but in different contexts from those analysed here. Therefore, caution is important when attempting to extrapolate the results obtained here to regions that may present very different characteristics. Conclusions The present study has quantified, using a Bayesian approach, the association of the variables with an increase in severity on admission (MUAC) and Length of stay (LOS) of children treated for acute malnutrition in two rural contexts in Niger and Mali. We showed how aspects such as seasonality and time to the treatment site can act as modulators, interacting differently among groups of individuals. Relevant differences were shown between contexts, apart from the greater influence of seasonality in Mali and, travel time to treatment in Niger. Firstly, regarding severity, in both contexts, there was an influence of the child's age, and it was in Niger that factors such as comorbidity, dietary diversity, and breastfeeding were influential. Secondly, for the LOS, in both contexts, the severity of admission and dietary diversity were relevant. In Niger, we found the distance to the water source and the protocol, but in Mali, the quality of the water source was more important. This study highlights the importance of applying a multidisciplinary analysis to encompass various factors that may have a more or less significant influence, directly or indirectly through interactions, on child malnutrition in different contexts. This approach allows for a better understanding of the environmental factors surrounding the disease. Declarations Conflict of Interest The authors declare no conflict of interest. Funding This research project was funded by Elrha's Research for Health in Humanitarian Crisis (R2HC) programme. R2HC aims to improve health outcomes for people affected by crises by strengthening the evidence base for public health interventions. The R2HC programme is funded by the UK Foreign, Commonwealth and Development Office (FCDO), Wellcome and the UK National Institute for Health Research (NIHR). LJ S-M was granted with a predoctoral fellowship from the Complutense University and Banco Santander. Author Contribution Conceptualization: LJS-M, NL-E, CLH, CF; Methodology: LJS-M, CF; Formal analysis and investigation: LJS-M, CF; Writing - original draft preparation: LJS-M; Writing - review and editing: NL-E, CLH, PC-C; Funding acquisition: NL-E, PC-C; Resources: SS, MNS, AB, MB, AAG, AS, NO, RHL; Supervision: SS, MNS, AB, MB, AAG, AS, NO, RHL. Acknowledgement The authors would like to express their gratitude to all medical staff and patients who participated in this study at Niger and Mali. References Aboagye RG, Seidu AA, Ahinkorah BO, Arthur-Holmes F, Cadri A, Dadzie LK, Hagan JE, Eyawo O, Yaya O (2021) Dietary Diversity and Undernutrition in Children Aged 6–23 Months in Sub-Saharan Africa. Nutrients. https://doi.org/10.3390/nu13103431 Adhikari T, Yadav J, Tolani H, Tripathi N, Kaur H, Rao MVV (2022) Spatio-temporal modeling for malnutrition in tribal population among states of India a Bayesian approach. https://doi.org/10.1016/j.sste.2021.100459 . 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Int J Environ Res Public Health. https://doi.org/10.3390/ijerph8041174 Rogers E, Martínez K, Álvarez-Morán JL, Alé FGB, Charle-Cuéllar P, Guerrero S, Puett C (2018) Cost-effectiveness of the treatment of uncomplicated severe acute malnutrition by community health workers compared to treatment provided at an outpatient facility in rural Mali. Hum Resour Health. https://doi.org/10.1186/s12960-018-0273-0 Rogers E, Myatt M, Woodhead S, Guerrero S, Alvarez JL (2015) Coverage of Community-Based Management of Severe Acute Malnutrition Programmes in Twenty-One Countries, 2012–2013. PLoS ONE. https://doi.org/10.1371/journal.pone.0128666 Rue H, Martino S, Chopin N (2009) Approximate Bayesian inference for latent Gaussian models using integrated nested Laplace approximations. 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Matern Child Nutr. https://doi.org/10.1111/mcn.13246 UNICEF, WHO, World Bank Group (2023) Levels and trends in child malnutrition. https://www.who.int/publications/i/item/9789240073791 . Accessed 20 September 2024 United Nations Children's Fund (‎‎UNICEF)‎ (2020) UNICEF Conceptual Framework on Maternal and Child Nutrition. https://www.unicef.org/documents/conceptual-framework-nutrition . Accesssed 10 September 2024 Vaitla B, Devereux S, Swan SH (2009) Seasonal hunger: a neglected problem with proven solutions. PLoS Med. https://doi.org/10.1371/journal.pmed.1000101 van Cooten MH, Bilal SM, Gebremedhin S, Spigt M (2019) The association between acute malnutrition and water, sanitation, and hygiene among children aged 6–59 months in rural Ethiopia. Matern Child Nutr. https://doi.org/10.1111/mcn.12631 Venkat A, Marshak A, Young H, Naumova EN (2023) Seasonality of Acute Malnutrition in African Drylands: Evidence From 15 Years of SMART Surveys. Food Nutr Bull. https://doi.org/10.1177/03795721231178344 Vollmer S, Harttgen K, Kupka R, Subramanian SV (2017) Levels and trends of childhood undernutrition by wealth and education according to a Composite Index of Anthropometric Failure: evidence from 146 Demographic and Health Surveys from 39 countries. BMJ Glob Health. https://doi.org/10.1136/bmjgh-2016-000206 Watanabe S, Opper M (2010) Asymptotic equivalence of Bayes cross validation and widely applicable information criterion in singular learning theory. J Mach Learn Res. https://doi.org/10.48550/arXiv.1004.2316 Waterlow JC, Buzina R, Keller W, Lane JM, Nichaman MZ, Tanner JM (1977) The presentation and use of height and weight data for comparing the nutritional status of groups of children under the age of 10 years. Bull World Health Organ 55(4):489–498 Weiss DJ, Nelson A, Gibson HS, Temperley W, Peedell S, Lieber A, Hancher M, Poyart E, Belchior S, Fullman N et al (2018) A global map of travel time to cities to assess inequalities in accessibility in 2015. Nature. https://doi.org/10.1038/nature25181 Wilunda C, Mumba FG, Putoto G, Maya G, Musa E, Lorusso V, Magige C, Leyna G, Manenti F, Riva DD et al (2021) Effectiveness of screening and treatment of children with severe acute malnutrition by community health workers in Simiyu region, Tanzania: a quasi-experimental pilot study. Sci rep. https://doi.org/10.1038/s41598-021-81811-6 World Food Programme (WFP) (2008) Vulnerability Analysis and Mapping. Food Consumption Analysis. Calculation and 523 use of the food consumption score in food security analysis. https://documents.wfp.org/stellent/groups/public/documents/manual_guide_proced/wfp197216.pdf . Accessed 19 September 2024 World Health Organization (WHO) (2006) WHO child growth standards: length/height-for-age, weight-for-age, weight-for-length, weight-for-height and body mass index-for-age: methods and development. https://www.who.int/publications/i/item/924154693X . Accessed 19 September 2024 World Health Organization (WHO) (2007) Joint Statement on Community-Based Management of Severe Acute Malnutrition. https://www.who.int/publications/i/item/9789280641479 . Accessed 10 September 2024 World Health Organization (WHO) (2023) Guideline: WHO guideline on the prevention and management of wasting and nutritional oedema (acute malnutrition) in infants and children under 5 years. https://app.magicapp.org/#/guideline/noPQkE . Accessed 23 September 2024 Young H (2020) Nutrition in Africa’s Drylands: A Conceptual Framework for Addressing Acute Malnutrition. Feinstein International Center. https://fic.tufts.edu/publication-item/nutrition-in-africas-drylands-a-conceptual-framework-for-addressing-acute-malnutrition/ . Accessed 17 October 2024 Additional Declarations No competing interests reported. Supplementary Files Supplementarymaterial.docx Cite Share Download PDF Status: Published Journal Publication published 05 Sep, 2025 Read the published version in Environmental and Ecological Statistics → Version 1 posted Editorial decision: Revision requested 28 Mar, 2025 Reviews received at journal 26 Jan, 2025 Reviewers agreed at journal 24 Dec, 2024 Reviewers agreed at journal 29 Nov, 2024 Reviewers invited by journal 25 Nov, 2024 Editor assigned by journal 17 Nov, 2024 Submission checks completed at journal 12 Nov, 2024 First submitted to journal 11 Nov, 2024 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-5434736","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":383507061,"identity":"84dfd4fb-bea2-40d7-bc0c-f1ef19dab96a","order_by":0,"name":"Luis Javier Sánchez-Martínez","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAvUlEQVRIiWNgGAWjYBACPgbGBgYJBgk5fqK1sEG02BhLNhCvBQzSEjccIFqLRHLzB4uaw4ybbyQ/3cBQUUeMlsQ2CYljh5nNbqSZ3WA4c5g4LQwSbIfZzG7ksN1gbCPCeUAtzR8k/h3mMZ4B0vKPOIc1SEi2pUkYSIC0NDAToYXnYZuEZJ+NgcSZZ2Y3Eo4R4Rd+9vTHnyW+SdT3tyc/u/GhhgiHgQCzBIyVQJwGBgbGD8SqHAWjYBSMgpEJAABPNrA2bJYVAAAAAElFTkSuQmCC","orcid":"","institution":"Complutense University of Madrid","correspondingAuthor":true,"submittingAuthor":false,"prefix":"","firstName":"Luis","middleName":"Javier","lastName":"Sánchez-Martínez","suffix":""},{"id":383507062,"identity":"424a401a-1fe0-47ef-a9f8-e9d3a420223d","order_by":1,"name":"Christel Faes","email":"","orcid":"","institution":"Hasselt University","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"Christel","middleName":"","lastName":"Faes","suffix":""},{"id":383507063,"identity":"1183482b-de08-4c68-baba-29cc32cb4bb2","order_by":2,"name":"Pilar Charle-Cuéllar","email":"","orcid":"","institution":"Action Against Hunger","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"Pilar","middleName":"","lastName":"Charle-Cuéllar","suffix":""},{"id":383507064,"identity":"2c3b3dfc-65be-4aa6-969f-486f75e03576","order_by":3,"name":"Salimata Samake","email":"","orcid":"","institution":"Action Against Hunger. 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Locally estimated scatterplot smoothing (LOESS) was applied to each country data.\u003c/p\u003e","description":"","filename":"floatimage181.png","url":"https://assets-eu.researchsquare.com/files/rs-5434736/v1/f5875e9a61fa9fc7789c11bc.png"},{"id":71607651,"identity":"24c5a29e-417d-42c1-8151-b21830e48a2f","added_by":"auto","created_at":"2024-12-17 06:24:19","extension":"jpeg","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":468282,"visible":true,"origin":"","legend":"\u003cp\u003eRelationships between the Principal Components and the frequency variables of consumption of food groups. The side legend shows the numerical correspondence of the correlation value with a colour gradient.\u003c/p\u003e","description":"","filename":"floatimage224.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-5434736/v1/71e0073745e8f2f9aa662f3a.jpeg"},{"id":71606239,"identity":"755d70b9-3b15-4b22-9c21-3a79a020ef40","added_by":"auto","created_at":"2024-12-17 06:16:19","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":259584,"visible":true,"origin":"","legend":"\u003cp\u003eBehaviour of mean random effects in different categories of interest in the final MUAC and LOS models for Mali and Niger.\u003c/p\u003e","description":"","filename":"floatimage355.png","url":"https://assets-eu.researchsquare.com/files/rs-5434736/v1/fe6ceb3c6687f5920e5b9350.png"},{"id":90828186,"identity":"859c8634-18f0-492b-9288-32188335f1cd","added_by":"auto","created_at":"2025-09-08 16:06:02","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1817344,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-5434736/v1/75c4cafd-6095-4905-8b74-10f8e024c68c.pdf"},{"id":71606240,"identity":"b10ebf27-947c-45d7-92f8-d50504d07458","added_by":"auto","created_at":"2024-12-17 06:16:19","extension":"docx","order_by":2,"title":"","display":"","copyAsset":false,"role":"supplement","size":570707,"visible":true,"origin":"","legend":"","description":"","filename":"Supplementarymaterial.docx","url":"https://assets-eu.researchsquare.com/files/rs-5434736/v1/4fb036c2600ca401c76db73e.docx"}],"financialInterests":"No competing interests reported.","formattedTitle":"Bayesian mixed effect models to account for environmental modulators of acute malnutrition treatment in children","fulltext":[{"header":"Introduction","content":"\u003cp\u003e\u0026ldquo;\u003cem\u003eEvery child has the right to good nutrition. Well-nourished children grow and develop to their full potential. They are better equipped to lead healthy lives, to be free from poverty, to learn and participate, and to continue thriving across the life course, with benefits that continue over generations\u003c/em\u003e\u0026rdquo;. This is how the latest worldwide report on levels and trends in child malnutrition published by UNICEF, the World Health Organization (WHO) and The World Bank (2023) begins. One of the main messages to take into account in this report is that millions of children under five years do not achieve the aforementioned right of having a good nutrition. Of them, 45\u0026nbsp;million are affected by wasting, the form of malnutrition that poses the greatest risks to health (Black et al. \u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e2008\u003c/span\u003e; McDonald et al. \u003cspan citationid=\"CR49\" class=\"CitationRef\"\u003e2013\u003c/span\u003e; Thurstans et al. \u003cspan citationid=\"CR68\" class=\"CitationRef\"\u003e2022\u003c/span\u003e). However, the values provided by recent cross-sectional surveys may not faithfully reflect the actual figures, which could be much higher (cumulative incidence) throughout a year (Isanaka et al. \u003cspan citationid=\"CR35\" class=\"CitationRef\"\u003e2021\u003c/span\u003e; Mertens et al. \u003cspan citationid=\"CR51\" class=\"CitationRef\"\u003e2023\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eFurthermore, the anthropometric criteria for diagnosing and treating acute malnutrition have varied over the decades, with each employed indicator showing a different relationship with body composition and clinical indicators (Bhutta et al. \u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e2017\u003c/span\u003e). First, weight-for-age began to be used (\u0026lt;\u0026thinsp;60% of a reference value), later the WHO, to avoid including children with growth retardation, established Weight-for-Height as a criterion (Z-score \u0026lt; -2) (Waterlow et al. \u003cspan citationid=\"CR76\" class=\"CitationRef\"\u003e1977\u003c/span\u003e), and afterwards, with the aim of simplifying the protocols, the Middle Upper-Arm Circumference was introduced (WHO, 2007). Currently, the WHO recognizes two well-differentiated states of severity within wasting: Moderate Acute Malnutrition (MAM) and Severe Acute Malnutrition (SAM). The latter is characterized by greater anthropometric severity: WHZ\u0026thinsp;\u0026lt;\u0026thinsp;\u0026minus;\u0026thinsp;3 and/or MUAC\u0026thinsp;\u0026lt;\u0026thinsp;115 mm and/or nutritional oedema (WHO, 2023).\u003c/p\u003e \u003cp\u003eTo prevent and effectively ameliorate levels of child wasting, it is essential to know the causes and main risk factors associated with it. Although poor infant feeding practice is usually pointed out as the main determinant of nutritional status, the complex reality is that there are multiple factors that interrelate with each other and have an important impact on it. These factors include socioeconomic status, level of food insecurity, burden of comorbidities, and access to water and sanitation, among others (Rodr\u0026iacute;guez et al. \u003cspan citationid=\"CR59\" class=\"CitationRef\"\u003e2011\u003c/span\u003e; Vollmer et al. \u003cspan citationid=\"CR74\" class=\"CitationRef\"\u003e2017\u003c/span\u003e; van Cooten et al. \u003cspan citationid=\"CR72\" class=\"CitationRef\"\u003e2019\u003c/span\u003e). A holistic point of view to understand these underlying causes allows a better approach to the problem to achieve lasting and sustainable solutions in the real world (Agostoni et al. \u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e2023\u003c/span\u003e). In this sense, there are other external factors that are neither biological, nutritional, nor socioeconomic on their own but that also influence the levels of child malnutrition in a region over time. From an epidemiological point of view, environmental exposures can be broadly categorized into those that are proximate (e.g., directly leading to a health condition) and those that are distal (e.g., indirectly leading to a health condition), such as socioeconomic conditions and climate change. Other broad-scale environmental aspects can cause adverse health conditions directly by altering proximate exposures and indirectly through changes in ecosystems and other systems related to human health (Merrill, \u003cspan citationid=\"CR50\" class=\"CitationRef\"\u003e2008\u003c/span\u003e). These concepts have recently been introduced into the conceptual framework of maternal and child nutrition by UNICEF (2020).\u003c/p\u003e \u003cp\u003eIn this sense, the aforementioned trends report also highlights that nearly 90% of all global child wasting cases are concentrated in the tropical areas of Africa and Asia (UNICEF et al. 2023). These regions experience marked periods of dry seasons and floods, which negatively affect various aspects such as agriculture, economic production, and access to drinking water (Asmall et al. \u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e2021\u003c/span\u003e). A strong negative association has been documented between child weight and the average monthly variation in temperature across Sub-Saharan region, indicating a mean loss of 0.1 WHZ for every 1 \u0026ordm;C increase (Baker and Anttila-Hughes, \u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e2020\u003c/span\u003e). To these annual effects, other climatic phenomena with a more stochastic occurrence are added, such as the El Ni\u0026ntilde;o Southern Oscillation (ENSO). Studies have highlighted that warmer conditions during ENSO are globally accompanied by an increase in the severity of child malnutrition in the tropics (Anttila-Hughes et al. \u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e2021\u003c/span\u003e). Additionally, studies have shown significant associations between drought conditions and both wasting and underweight prevalence (Lieber et al. \u003cspan citationid=\"CR43\" class=\"CitationRef\"\u003e2022\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eThe most recent evidence on the study of child wasting seasonality, considering 15 years of SMART surveys from 19 countries in the northern region of the African continent, points out to the existence of two wasting peaks during the year. The highest peak of prevalence is estimated to begin in April to May, coinciding with the first increase in temperatures. A second peak of wasting is observed from August to October, coinciding with the primary peak of rainfall (Venkat et al. \u003cspan citationid=\"CR73\" class=\"CitationRef\"\u003e2023\u003c/span\u003e). A local study in eastern Chad also identified two annual peaks of wasting and severe wasting at the end of the dry season. The smaller peak corresponds to the start of the harvest period, with the lowest prevalence occurring during the start of the dry season (Marshak et al. \u003cspan citationid=\"CR48\" class=\"CitationRef\"\u003e2023\u003c/span\u003e). This research demonstrates the importance of being cautious regarding the child wasting seasonality in a region, since the existence of a wet and dry season will not necessarily translate into a single hunger season, as has been accepted in previous scenarios (Vaitla et al. \u003cspan citationid=\"CR71\" class=\"CitationRef\"\u003e2009\u003c/span\u003e; Nonterah et al. \u003cspan citationid=\"CR54\" class=\"CitationRef\"\u003e2022\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eEnvironmental geographic variability also directly affects the availability, access, and utilization of basic services, such as health service around the world (Weiss et al. \u003cspan citationid=\"CR77\" class=\"CitationRef\"\u003e2018\u003c/span\u003e). Various studies have focused on mapping the levels of child acute malnutrition in countries such as Ethiopia and South Africa using data from national surveys. These studies demonstrate a non-uniform distribution of its prevalence across the country, highlighting the existence of specific spatial patterns and inequalities between administrative areas that respond to different factors (Sartorius et al. \u003cspan citationid=\"CR64\" class=\"CitationRef\"\u003e2020\u003c/span\u003e; Atalell et al. \u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e2023\u003c/span\u003e). Moreover, a cross-country study found an association, at the population level, of a higher prevalence of wasting in rural versus urban areas in 13 countries from the East and southern African region, also relating it to socioeconomic inequalities at the household level (Caleyachetty et al. \u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e2023\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eConcerning child wasting, an aspect repeatedly identified as a barrier to accessing correct diagnosis and treatment is the distance to the health site (Puett and Guerrero, \u003cspan citationid=\"CR56\" class=\"CitationRef\"\u003e2015\u003c/span\u003e; Rogers et al. \u003cspan citationid=\"CR61\" class=\"CitationRef\"\u003e2015\u003c/span\u003e). Consequently, some geospatial analyses in various regions have highlighted this problem and its association with the burden of wasting. In Niger, the geographic distribution of community health posts was reported as inefficient. An estimated 58.5% of its population, which is 10.4\u0026nbsp;million people predominantly living in rural areas, remained beyond a 60-minute catchment of community health posts (Oliphant et al. \u003cspan citationid=\"CR55\" class=\"CitationRef\"\u003e2021\u003c/span\u003e). Additionally, a geospatial coverage analysis conducted in the three largest districts of the Kayes Region in Mali revealed that there exists a high proportion of children living more than 5 km from the nearest health site, estimated at 70.4%. Moreover, a high proportion of children in rural communities were not screened for SAM, estimated at 52.2% (Charle-Cu\u0026eacute;llar et al. \u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e2022\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eTraditionally, these analyses and studies have been based on association models typical of classical frequentist statistics. However, the complexity of the contexts being studied, the rapid and abrupt changes that occur in them, as well as the underlying interrelationships between variables require more complete approaches. In this sense, the Bayesian approach is especially interesting and has been widely used in recent studies (Sartorius et al. \u003cspan citationid=\"CR64\" class=\"CitationRef\"\u003e2020\u003c/span\u003e; Adhikari et al. \u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2022\u003c/span\u003e; Atalell et al. \u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e2023\u003c/span\u003e), since they provide the advantages of being able to integrate prior knowledge with the observed data and are more flexible when it comes to updating the results as more data is obtained. Additionally, they explicitly incorporate uncertainty by providing posterior probability distributions for the parameters, which facilitates decision-making, allowing risk assessment and optimization of results.\u003c/p\u003e \u003cp\u003eThe objective of the present study is to determine, in an explanatory manner, which variables, incorporating seasonality and travel time to the treatment provider, are associated with greater severity upon admission and a longer stay in treatment for children diagnosed with acute malnutrition in rural regions of Niger and Mali, considered emergency contexts.\u003c/p\u003e"},{"header":"Material and methods","content":"\u003cdiv id=\"Sec3\" class=\"Section2\"\u003e \u003ch2\u003eStudy design\u003c/h2\u003e \u003cp\u003eThe present study is a secondary analysis derived from controlled trials, which aimed to test different protocols for the treatment of acute child malnutrition (6\u0026ndash;59 months) (Charle-Cu\u0026eacute;llar et al. \u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e2023\u003c/span\u003e; S\u0026aacute;nchez-Mart\u0026iacute;nez et al. \u003cspan citationid=\"CR63\" class=\"CitationRef\"\u003e2023\u003c/span\u003e; L\u0026oacute;pez-Ejeda et al. \u003cspan citationid=\"CR46\" class=\"CitationRef\"\u003e2024\u003c/span\u003e). The intervention was carried out in the Diffa region, in Niger, during the months of December 2020 to April 2021, including a total of 6 different health sites. Meanwhile, in the Gao region, in Mali, the intervention spanned from June 2020 to June 2021, involving a total of 27 health sites. Further details regarding the spatial distribution of the considered health site can be found in Figure \u003cspan refid=\"MOESM1\" class=\"InternalRef\"\u003eS1\u003c/span\u003e.\u003c/p\u003e \u003cp\u003eA three-arm cluster randomized controlled trial was applied in Mali. In the control group, children were treated by specialized health personnel in health sites, using the standard protocol approved by the Ministry of Health of Mali (Community Management of Acute Malnutrition (CMAM) group). The first intervention group applied the same treatment protocol but added Community Health Workers (CHWs) as treatment providers in villages, at a minimum distance of 30 km from the reference health site (Integrated Community Case Management (iCCM) standard group). The second intervention group included, in a decentralized manner, both types of treatment providers (nurses and CHWs) but applied the combined simplified protocol known as the ComPAS protocol (Bailey et al. \u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e2020\u003c/span\u003e). On the other hand, a non-randomized controlled trial with only two groups was conducted in Niger, both of them including nurses and CHWs. The control group was treated under the country's standard protocol (CMAM protocol), while in the intervention group the combined-simplified ComPAS protocol was applied.\u003c/p\u003e \u003cp\u003eIn addition to measuring anthropometric variables for diagnosing acute malnutrition (MUAC and WHZ), several information was collected, including sex and age, the presence of comorbidities (fever, vomiting, diarrhoea, malaria, acute respiratory infection), and their vaccination status. Furthermore, the present study was based on a subsample of treated children on which a socioeconomic survey was carried out. Specifically, a total of 676 families in Mali and 771 in Niger were interviewed. The socioeconomic survey was conducted by interviewing the child's caregiver at the treatment facility upon admission, covering 58 variables organized into four dimensions of living conditions: demographics (9), livelihoods (14), food security and diversity (26), and access to healthcare (9). After the completion of each child's treatment, information regarding the treatment outcome was also collected (recovery, default, discharge error, etc) which then enables to select only recovered children. Only cured children were included in the present study.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec4\" class=\"Section2\"\u003e \u003ch2\u003eData cleaning and exploratory analyses\u003c/h2\u003e \u003cp\u003eData analysis was carried out using R software v. 4.3.2 (R Core Team, \u003cspan citationid=\"CR57\" class=\"CitationRef\"\u003e2023\u003c/span\u003e). Initially, data cleaning was performed, by considering negative numbers or values beyond four standard deviations away from the mean as transcription errors or extreme outliers, and, hence, being replaced by NA. In addition, for categorical variables, those cases showing less than five observations were either eliminated or combined with another if there was an ordinal relationship. Afterwards, missing values were handled, to reach comparable datasets for the model building step. Firstly, variables with total missing values equal to or greater than 10% (12) were removed from the analysis, remaining a total of 46 (Table \u003cspan refid=\"MOESM1\" class=\"InternalRef\"\u003eS1\u003c/span\u003e). Subsequently, individuals with any missing values were also removed. This procedure ensures that all participants have information on the same variables without missing values. Finally, after cleaning the data, the total sample set consisted of 413 children from Mali and 439 children from Niger with a mean age of 13.89\u0026thinsp;\u0026plusmn;\u0026thinsp;7.07 months (Figure S2).\u003c/p\u003e \u003cp\u003eThe dependent variables modelled were Mid-Upper Arm Circumference (MUAC) at admission and Length of Stay (LOS) for recovery as proxies of severity and treatment effectiveness respectively. As a temporal variable, the day of the child's admission to treatment was included, which was later grouped into a new variable indicating the week (starting from the day of the beginning of the study of Mali in June) on which each child was admitted to treatment. Regarding the spatial variable, information is available on the travel time from the child's home to the health site where treatment was provided, grouped into 7 categories progressively increasing travel time (1: Less than 15 min, 2: 15\u0026ndash;30 min, 3: 30\u0026ndash;90 min, 4: 90\u0026ndash;120 min, 5: 120\u0026ndash;150 min, 6: 150\u0026ndash;180 min, 7: more than 3 hour). This temporal data is considered the most suitable proxy for operationalizing accessibility (Weiss et al., \u003cspan citationid=\"CR77\" class=\"CitationRef\"\u003e2018\u003c/span\u003e). Initially, an exploratory analysis was conducted to examine the relationships between this set of variables in both contexts.\u003c/p\u003e \u003cp\u003eAn initial descriptive graph was created using a locally estimated scatterplot smoothing (LOESS) function to model the relationship between the MUAC and LOS variables over time (weeks) and travel time to the health site. In this sense, Pearson correlation coefficients were calculated, stratified by key variables, to better understand the underlying interrelations and modulation effects. Following this, with the objective of reducing the dimensionality of the data, a Principal Component Analysis was conducted on the frequency values of the dietary diversity survey. The calculation was performed by a singular value decomposition of the centered and scaled data, retaining the first four Principal Components, which became new variables in the dataset. To interpret the relationships in the diet data, it was represented a correlation matrix along with its dendrogram, generated through a Hierarchical Cluster Analysis (HCA) using Euclidean distances as metrics.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec5\" class=\"Section2\"\u003e \u003ch2\u003eVariables selection\u003c/h2\u003e \u003cp\u003ePrior to modelling, the covariates were ordered based on their importance in analyzing each dependent variable. For this purpose, several univariate models were built, one for each covariate and country independently. The Watanabe Akaike Information Criteria (WAIC) was then calculated for model comparison. The models with the lowest WAIC values were chosen to establish the order of importance among the covariates. Moreover, the WAIC value is considered a measure of model accuracy (Watanabe and Opper, \u003cspan citationid=\"CR75\" class=\"CitationRef\"\u003e2010\u003c/span\u003e). All univariate models were performed using the subsample of individuals without missing values, incorporating the temporal variable of week and the spatial variable of travel time to the health site as random effects. This ensured homogeneity in the information available for each model, enabling their WAIC values to be comparable.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec6\" class=\"Section2\"\u003e \u003ch2\u003eDefining Bayesian model\u003c/h2\u003e \u003cp\u003eBayesian inference is a valuable method for data modelling that allows to estimate posterior distributions of model parameters \u003cem\u003eβ\u003c/em\u003e by updating prior distributions with information from recorded observations \u003cem\u003ey\u003c/em\u003e using Bayes\u0026rsquo; Theorem:\u003cdiv class=\"BlockQuote\"\u003e\u003cp\u003e \u003cspan class=\"InlineEquation\"\u003e \u003cspan class=\"mathinline\"\u003e\\(\\:\\pi\\:\\left(\\beta\\:|y\\right)=\\:\\frac{\\pi\\:\\left(y|\\beta\\:\\right)\\:\\pi\\:\\left(\\beta\\:\\right)}{\\pi\\:\\left(y\\right)}\\:\\propto\\:\\:\\pi\\:\\left(y|\\beta\\:\\right)\\:\\pi\\:\\left(\\beta\\:\\right),\\)\u003c/span\u003e \u003c/span\u003e (Moraga et al. \u003cspan citationid=\"CR52\" class=\"CitationRef\"\u003e2021\u003c/span\u003e)\u003c/p\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eThe models implemented in the present study were performed using the Integrated Nested Laplace Approximation (INLA) approach through the open-source R-INLA package (Rue et al., \u003cspan citationid=\"CR62\" class=\"CitationRef\"\u003e2009\u003c/span\u003e). INLA avoids sampling by accurately approximating posterior marginal distributions, making it an efficient alternative to Markov Chain Monte Carlo (MCMC) methods (Lindgren and Rue, \u003cspan citationid=\"CR44\" class=\"CitationRef\"\u003e2015\u003c/span\u003e). Mixed-effects models were specifically chosen for their ability to model and incorporate complex relationships between variables, as they allow the inclusion of both linear fixed effects and random effects of different natures (G\u0026oacute;mez-Rubio, \u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e2020\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eRegarding the Bayesian parameters of the model, the prior distribution for fixed effects (regression coefficients and global intercept) was specified as Gaussian, centered on 0, and with a large variance (minimally informative). For health site variables, travel time to the health site and week of admission, we assumed nonlinear relationships with the response variable by including them in the model as random effects. To evaluate what type of random effect to implement for the temporal and travel time variables in each model, the WAIC of the possible combinations was calculated (Table S2). The possibilities considered included random walks of orders 1 and 2 (rw1 and rw2), while for the health site, it was established as independent (iid). These random walk processes are very suitable for modelling biological and natural processes, allowing a certain degree of randomness and dependence on previous values (Codling et al. \u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e2008\u003c/span\u003e). Finally, the prior distribution for random effects was specified as a Half-Cauchy distribution, as it yielded a better WAIC than using the default multivariate Gaussian distribution with zero mean and precision matrix τΣ.\u003c/p\u003e \u003cp\u003eTherefore, in the present study the INLA models were fit for each variable of interest as follows:\u003cdiv id=\"Equa\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equa\" name=\"EquationSource\"\u003e\n$$\\:{{\\eta\\:}}_{i}=\\alpha\\:+\\sum\\:_{j=1}^{{n}_{\\beta\\:}}{\\beta\\:}_{j}\u0026middot;\\:{x}_{ij}+\\:\\sum\\:_{k=1}^{{n}_{f}}{f}^{\\left(k\\right)}\\left({u}_{ki}\\right);\\:i=1,\\dots\\:n$$\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003ewhere \u003cem\u003eη\u003c/em\u003e\u003csub\u003e\u003cem\u003ei\u003c/em\u003e\u003c/sub\u003e is the linear predictor, α is the intercept, \u003cem\u003eβ\u003c/em\u003e\u003csub\u003e\u003cem\u003ej\u003c/em\u003e\u003c/sub\u003e\u003cem\u003ex\u003c/em\u003e\u003csub\u003e\u003cem\u003eij\u003c/em\u003e\u003c/sub\u003e are the covariate parameters and covariates, \u003cem\u003ef\u003c/em\u003e \u003csup\u003e\u003cem\u003e(k)\u003c/em\u003e\u003c/sup\u003e are the random effects terms on some covariates \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\left\\{{u}_{k}\\right\\}}_{k=1}^{{n}_{f}}\\)\u003c/span\u003e\u003c/span\u003e, and i\u0026thinsp;=\u0026thinsp;1, \u0026hellip;, n are the variables of interest.\u003c/p\u003e \u003cp\u003eThe selection of the final model was carried out in a stepwise manner to optimize prediction error. Therefore, variables were introduced one by one according to the order of the lowest WAIC established previously by the univariate models. When introducing a new variable into the model, if the WAIC of this expanded model decreased by more than three units compared to the previous one, the variable remained in the model. Otherwise, the variable was removed from the model, and the next one was tested. This procedure was repeated until two of these stepwise phases were completed to reach the final model.\u003c/p\u003e \u003c/div\u003e"},{"header":"Results","content":"\u003cp\u003ePreliminary exploratory analysis suggests that MUAC values and LOS for recovery differ across the categories of the variables of time from the health site and week of child\u0026rsquo;s treatment admission. Likewise, a difference is also noticeable in the behaviour of the data in both contexts, as shown in Fig.\u0026nbsp;1. This variation between the data from Mali and Niger appears to be particularly pronounced in the LOS values, both along the travel time and for the week variable categories, with higher values recorded in individuals from Mali.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eMUAC: Mid-Upper Arm Circumference; LOS: Length of Stay.\u003c/p\u003e \u003cp\u003e \u003cb\u003eFigure 1.\u003c/b\u003e Scatter plots showing the relationship between MUAC upon admission and LOS with the Week and Travel time category variables for Mali and Niger. Locally estimated scatterplot smoothing (LOESS) was applied to each country data.\u003c/p\u003e \u003cp\u003eNext, for quantifying the observed relationship, the sample set was to key factors that may impact the variables of interest. Table S3 shows the results of these correlations, and despite the limitation that only linear relationships have been evaluated, some relevant results that are worth highlighting were observed when comparing both countries and the categories of the stratification variables. In general, we observe that all the values obtained show weak linear relationships (\u0026lt;\u0026thinsp;0.4), and in many cases, they are not significant. However, we found interesting differences between the categories of some key variables. Firstly, in Niger, we observed an initial effect of severity on the relationship established between MUAC and LOS with Week, such that MAM children present significant correlations while SAM do not. There is also a quite notable effect of the presence of comorbidities, with significant effects observed in individuals who presented any. On the other hand, Mali stands out compared to Niger for presenting a large number of significant correlations between the MUAC and Week variables. Therefore, it seems to exhibit a fairly evident temporal effect in its evolution. Likewise, we found differential relationships between groups of categories in the treatment protocol, in the degree of severity, in the presence of comorbidities, and in the fact of being vaccinated or not. However, the sex and the age of the individual did not appear to have any effect, as the relationships were significant in both groups.\u003c/p\u003e \u003cp\u003eFigure 2 shows the interrelations established in Mali and Niger between the variables of food consumption frequency and each of the first four Principal Components (PC) computed with Principal Component Analysis. The correlations between all these pairs of variables were placed in a correlation matrix, and then a dendrogram was constructed, which showed relevant groups according to the dietary pattern in the population:\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003ePC: Principal Component.\u003c/p\u003e \u003cp\u003e \u003cb\u003eFigure 2.\u003c/b\u003e Relationships between the Principal Components and the frequency variables of consumption of food groups. The side legend shows the numerical correspondence of the correlation value with a colour gradient.\u003c/p\u003e \u003cp\u003eIn Mali, a clear pattern in the consumption of certain foods is associated with PC2, indicating a relationship in the consumption of fish and seafood, cereals, dairy products, fats, condiments, and sugar products. On the other hand, PC3 and PC4 are associated with a greater consumption of animal organs such as kidney or liver and fruits rich in vitamin A. Another interesting association is found with the consumption of meat, eggs, other fruits, roots and tubers, and other vegetables. Finally, it should be noted that PC1 presents negative correlations, pointing that an increase in its values ​​would result a general reduction in the frequency of food consumption.\u003c/p\u003e \u003cp\u003eIf we pay attention to the relationships of food consumption in Niger, we find slightly different associations. First of all, PC1 is associated with the consumption of fruits rich in vitamin A, vegetables especially rich in vitamin A, roots and tubers, and legumes. Another interesting association is found with PC2 and the consumption of fats, dairy products, sugar products, and condiments. Finally, PC3 and PC4 are associated with cereal consumption and negatively associated with the rest. A final interesting pattern indicates a group of children who have increased their protein consumption, with a higher frequency of eggs, meat, fish, seafood, animal organs, and other fruits and vegetables in their diets\u003c/p\u003e \u003cdiv id=\"Sec8\" class=\"Section2\"\u003e \u003ch2\u003eFinal models for MUAC\u003c/h2\u003e \u003cp\u003eThe parameters of the final models on the MUAC upon admission for Mali and Niger are presented in Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e. The number of variables introduced in the final model for Niger was five, and this model reached a WAIC of 2617.18. On the other hand, in the case of Mali, the final model was simpler, containing two variables, with a corresponding WAIC of 2691.22. Although one variable is shared in both models, our results seem to indicate two different situations to understand the severity (MUAC) of children upon admission to treatment depending on the context.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab1\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eFinal model of MUAC upon admission in Niger and Mali: INLA posterior mean estimates (including standard deviations) and its credible interval are presented.\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"5\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eCountry\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eParameter\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eMean\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eSD\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eCI\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"6\" rowspan=\"7\"\u003e \u003cp\u003eNiger\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eIntercept\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e109.713\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e1.788\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e(106.188; 113.240)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eComorbidities Yes\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e-2.529\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.575\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e(-3.657; -1.402)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eFood Diversity PC1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e-0.508\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.131\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e(-0.765; -0.252)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eAge Admission (months)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.145\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.047\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e(0.052; 0.237)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eReceiving breastfeed now Yes\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e3.329\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e1.099\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e(1.173; 5.485)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eVaccination Yes\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e1.365\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.471\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e(0.442; 2.290)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eFood Diversity PC2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.544\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.164\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e(0.222; 0.867)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"2\" rowspan=\"3\"\u003e \u003cp\u003eMali\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eIntercept\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e107.739\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e1.773\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e(104.265; 111.219)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eAge mother pregnant (years)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.139\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.051\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e(0.040; 0.238)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eAge Admission (months)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.160\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.038\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e(0.086; 0.235)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003ePC: Principal Component; SD: Standard Deviation; CI: Credible Interval.\u003c/p\u003e \u003cp\u003eIf we pay attention to the Niger model, we find variables of different natures involved in determining the MUAC upon admission. A first group seems to be related to the health status of the individual. Presenting any comorbidity negatively affects the MUAC, modifying its values ​​by -2.529 mm (CI: -3.657; -1.402). Likewise, the vaccination has a positive effect on the MUAC value, increasing it on average by 1.365 mm (CI: 0.442; 2.290). A second group of variables are associated with the child's diet. Firstly, breastfeeding is a quite positive factor according to the model on the MUAC value, if it is present in the child's diet, it causes the MUAC to increase on average by 3.329 mm. (CI: 1.173; 5.485). Furthermore, dietary diversity also seems to have an interesting effect. Since PC1 (vegetables and fruits) and PC2 (fats and dairy products) are present in the model, the first one seems to have a negative effect on the MUAC, since for each unit that increases its value, the MUAC is reduced in the individual by 0.508 mm (CI: -0.765; -0.252). On the other hand, the effect of the PC2 is positive on the MUAC value, so that for each unit that increases its value, the MUAC increases by 0.544 mm (CI: 0.222; 0.867). Another variable present in the model in the case of Niger is the age of the individual, which has a positive effect on the MUAC, observing an average increase of 0.145 mm (CI: 0.052; 0.237) for each month.\u003c/p\u003e \u003cp\u003eRegarding the final model of MUAC upon admission in Mali, which stands out for being much simpler than the one of Niger, we can highlight the shared presence of the variable age upon admission, which acquires a very similar effect, so that for each month that the child turns, his MUAC upon admission increases by 0.160 mm (CI: 0.086; 0.235). Another variable that participates in the model is the age at which the mother began her pregnancy with the treated child, which also appears as a positive factor on the MUAC value. For each year that the mother's age increases, the child's MUAC upon admission increases on average by 0.139 mm (CI: 0.040; 0.238).\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec9\" class=\"Section2\"\u003e \u003ch2\u003eFinal models for LOS\u003c/h2\u003e \u003cp\u003eTable\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e show the parameters of the final models of LOS for recovery in Niger and Mali. Once again, the Niger model presents a greater number of variables. It reaches a WAIC of 3269.66 with these five variables. On the other hand, the model in Mali with three variables shows a WAIC of 2952.29. In the case of the LOS for recovery variable, both the Niger and Mali models seem to identify very similar factors related to the study variable in both contexts.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab2\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 2\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eFinal model of LOS for recovery in Niger and Mali: INLA posterior mean estimates (including standard deviations) and its credible interval are presented.\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"5\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eCountry\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eParameter\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eMean\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eSD\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eCI\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"7\" rowspan=\"8\"\u003e \u003cp\u003eNiger\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eIntercept\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e166.883\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e12.208\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e(142.934; 190.835)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eMUAC Admission (mm)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e-1.061\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.107\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e(-1.270; -0.853)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eProtocol Simplified\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e-10.849\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e1.463\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e(-13.719; -7.980)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eFood Diversity PC4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e1.801\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.560\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e(0.703; 2.899)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eDistance to collect water 100\u0026ndash;300m\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e3.756\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e1.495\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e(0.824; 6.690)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eDistance to collect water 300\u0026ndash;500m\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e5.372\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e1.764\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e(1.911; 8.835)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eDistance to collect water more than 500m\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e1.839\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e2.101\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e(-2.282; 5.961)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eTravel Health site one day Yes\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e-3.726\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e1.707\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e(-7.075; -0.377)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"9\" rowspan=\"10\"\u003e \u003cp\u003eMali\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eIntercept\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e83.646\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e19.634\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e(45.084; 122.141)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eMUAC Admission (mm)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e-0.407\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.167\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e(-0.734; -0.078)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eFood Diversity PC4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e2.402\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e1.060\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e(0.321; 4.480)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eWater supply other\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e7.584\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e11.00\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e(-14.009; 29.163)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eWater supply water tanker\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e1.822\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e16.917\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e(-31.372; 35.004)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eWater supply rain water\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e21.651\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e9.907\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e(2.207; 41.085)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eWater supply surface water\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e-4.922\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e4.366\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e(-13.494; 3.640)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eWater supply unprotected well\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e11.762\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e3.830\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e(4.241; 19.273)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eWater supply protected well\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e8.545\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e3.278\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e(2.109; 14.974)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eWater supply community tap\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e6.180\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e3.807\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e(-1.293; 13.647)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003e \u003cdiv class=\"BlockQuote\"\u003e \u003cp\u003eMUAC: Mid-Upper Arm Circumference; mm: millimetres; PC: Principal Component; SD: Standard Deviation; CI: Credible Interval.\u003c/p\u003e \u003c/div\u003e \u003c/p\u003e \u003cp\u003eIn Niger (see Table\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e), the protocol variable stands out with the highest value of posterior mean estimate. So, when the child is treated with the simplified protocol, its LOS is reduced by 10.849 days (CI: -13.719; -7.980) compared with the national Standard protocol. Another relevant variable is that referring to the travel health site, which seems to indicate that being able to travel on the same day would have a positive effect on the shortening of the time in treatment, modifying the LOS on average by -3.726 days (CI: -7.075; -0.377). On the other hand, we found the MUAC upon admission, which reflects the severity with which the child began treatment. This last variable indicates in the model that a greater MUAC participates favourably in shortening the time in treatment, since for each millimetre that it increases, the LOS for recovery decreases by 1.061 days (CI: -1.270; -0.853). We also see how the PC4 of diet diversity (fruits) intervenes to lengthen the LOS for recovery in Niger; according to the model, for each unit that increases this variable, it results in an increase in the LOS of 1.801 days (CI: 0.703; 2.899). Finally, the distance to the drinking water source also has an important influence. Being 100\u0026ndash;300 m or 300\u0026ndash;500 m compared to the reference category, which is less than 100 m, causes an increase in LOS of 3.756 days (CI: 0.824; 6.690) and 5.372 days (CI: 1.911; 8.835) respectively. However, for the longest distance category, the impact was not significant, possibly because of a small sample size.\u003c/p\u003e \u003cp\u003eThe final LOS for recovery model in Mali includes very similar variables to those selected in the case of Niger. Firstly, MUAC upon admission also has a positive effect in reducing LOS for recovery, so that for each millimetre of increase, the reduction is 0.429 days (CI: -0.756; -0.101). A second variable shared in both models is the fourth Principal Component of dietary diversity, which in the case of Mali, an increase also has a negative effect on the LOS, since for each unit of increase, the LOS increases by 2.457 days. (CI: 0.369; 4.545). Finally, the third variable considered in the model is related to drinking water, in this case, its source. We observe how the categories of rain water, unprotected well, and protected well have an appreciable effect, compared to the reference category which is home tap, they increase the LOS for recovery, with the first of them being the most harmful since they represent an average increase of 21.091 days (CI: 1.663; 40.485), followed by unprotected well that increases LOS by 11.482 days (CI: 3.929; 19.023), and protected well by 8.403 days (CI: 1.919; 14.877), respectively.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec10\" class=\"Section2\"\u003e \u003ch2\u003eModel prediction\u003c/h2\u003e \u003cp\u003eIn the specific case of the final model of LOS for recovery in Niger (Table \u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e), we found quite a difference in the effects of each variable and their respective weights in the model. Figure S3, which shows the posterior distributions of all these parameters, shows us the estimated probability (y axes) that each coefficient has of taking on a specific value (x axes), providing a better comparison for understanding the distribution of effects that contribute to the predictions made by the model.\u003c/p\u003e \u003cp\u003eFor the sample of boys and girls treated in Niger, a paradigmatic case of prediction can be proposed: the maximum LOS value predicted by our model was 65.39 days (58.53; 72.27). This prediction corresponds to an 8-month-old girl whose MUAC was 90 mm. She could not make the travel to the health site in a single day, was treated with the simplified protocol, the source of water consumption was located 100\u0026ndash;300 m away, and her value in the PC4 of dietary diversity was: 0.84. The opposite extreme case is found in a 17-month-old boy, for whom the model predicts the lowest LOS for recovery: 17.09 days (12.64; 21.53). This individual had a MUAC of 120 mm, he could make the travel to the health site in a single day, was treated with the simplified protocol, the source of water consumption was located less than 100 m, and his value in the PC4 of diet diversity was: -2.49. Finally, the real difference observed was somewhat less than what the model predicted (48.3 days), as the second individual was cured 28 days before the first one, who had worse conditions.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec11\" class=\"Section2\"\u003e \u003ch2\u003eInteractions with random effects\u003c/h2\u003e \u003cp\u003eNext, it is relevant to test in the final models built whether the effects of the random factors introduced are homogeneous or if, on the contrary, there are interactions. These interactions could lead to a modulation in a variable's effect, which may be interesting to interpret. Figure\u0026nbsp;3 shows a collection of graphs that reflect the interactions found between some interesting variables (protocol, presence of comorbidities, sex, severity) with the Week (in red) and Travel time (in blue) variables, which were introduced as random effects in the final models. Tables S4-S9 provide a complete view of the numerical evolution of the mean random effects in each category.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eMUAC: Mid-Upper Arm Circumference; LOS: Length of Stay; SAM: Severe Acute Malnutrition.\u003c/p\u003e \u003cp\u003e \u003cb\u003eFigure 3.\u003c/b\u003e Behaviour of mean random effects in different categories of interest in the final MUAC and LOS models for Mali and Niger.\u003c/p\u003e \u003cp\u003eIt is worth nothing that the importance that both random factors acquire in the models seems to be very different between both contexts. This fact is contrasted by the number of interactions found; while in Niger, the interactions are mostly with the Travel time variable, in Mali, is rather with the Week variable that we find a greater number of interactions. Therefore, while in Niger, the factor of travel time to the health site seems to have an appreciable weight, in Mali, a more noticeable seasonal effect on the variables of interest is present.\u003c/p\u003e \u003cp\u003eFor the interactions found in Niger, first, we highlight an effect of Travel time in the MUAC model upon admission of individuals who present a comorbidity at the time of their diagnosis of acute malnutrition (Fig.\u0026nbsp;3a). Thus, those individuals whose travel time to the health site is less than 15 minutes (category 1) see their MUAC increase on average by 2.65 mm (CI: 0.52; 5.14) compared to the rest of the individuals with a comorbidity. That is, being closer to the health site when they are sick seems to imply arriving with less severity. Nevertheless, the trend of the graph shows that the MUAC decreases when the Travel time increases; the confidence intervals, however, do not allow us to be really sure of this effect of increased severity. A second interaction affecting MUAC was found between Week and sex (Fig.\u0026nbsp;3b), indicating that boys recorded an improvement in their severity of 1.26 mm (CI: 0.05; 2.63), an effect that was not recorded in girls.\u003c/p\u003e \u003cp\u003eAnother interesting effect observed in Niger occurs in the LOS for recovery model (Fig.\u0026nbsp;3c), where individuals diagnosed with a higher degree of severity of acute malnutrition (SAM) reduce on their LOS by an average of 2.80 days (CI: 0.23; 5.70) when they are 15\u0026ndash;30 minutes from the health site (category 2), while those individuals who are at the greatest travel time category, more than 2 hours from the health site, see an increase in their LOS by an average of 5.49 days (CI: 0.21; 12.67). This effect was not found among the group of treated children diagnosed with a lower severity (MAM) at the beginning of their treatment. Another interesting interaction in Niger, which corresponds to the LOS for recovery model, involves the presence of comorbidities (Fig.\u0026nbsp;3d). In this case, the behaviour of the random effects in the Travel time categories indicates that being 15\u0026ndash;30 minutes from the health site (category 2) reduces the time in treatment in a child with no comorbidities by an average of 2.65 days (CI: 0.49; 4.97). No significant effects were found for the other Travel time categories, nor in any of the children with comorbidities.\u003c/p\u003e \u003cp\u003eMali results show for the MUAC upon admission model, a temporary effect in the individuals who were treated with the Standard Protocol iCCM (Fig.\u0026nbsp;3e). This effect was not found in individuals treated with either the Control CMAM Protocol or the Simplified Protocol. In this graph, it can be seen that around week 18 after the start of the intervention (October), the average MUAC value upon admission declines, reaching its lowest value at week 27 (November), with an average decrease of 9.29 mm (CI: 4.91; 14.08). At this point, the trend reverses, and the value begins to increase until weeks 40\u0026ndash;50 (April-May), where it stabilizes with an average MUAC increase of around 5 mm (CI: 3.90; 9.86) compared to the rest of the weeks. A second interaction found in the MUAC upon admission model in Mali shows a pattern very similar to the one previously described. In this case, the category involved is the female sex (Fig.\u0026nbsp;3f). It can be seen how the temporal effect on the MUAC value in the group of girls is very clear throughout the study. In such a way that by week 29, the lowest value is reached, with an average reduction in MUAC of 5.91 mm (CI: 2.95; 9.37), and from this moment, the trend of the effect reverses until week 39 (April) when the effect becomes positive, reaching the highest average value in week 43 with 4.60 mm (CI: 1.62; 8.00). This pattern of change was not found in the group of boys.\u003c/p\u003e \u003cp\u003eRegarding the interactions to be highlighted in the Mali model of LOS for recovery, the first of them involves the category of greatest severity (SAM) (Fig.\u0026nbsp;3g), where a temporary effect of increasing LOS for recovery was observed for boys and girls who began their treatment at weeks 15\u0026ndash;19 (September-October), resulting in the greatest effect being about 6.34 days longer on average (CI: 0.65; 12.55). This pattern was not found in MAM individuals. However, the MAM group showed a significant decrease in LOS for recovery from week 45 (May), reaching values of up to 20 days less for LOS on average (CI: 11.55; 32.76) (Table S8). Another interaction found in the LOS for recovery model in Mali, and that combines the different behaviours of SAM and MAM children, is the one that involves in the boys (Fig.\u0026nbsp;3h). Therefore, they present a temporary effect during weeks 15\u0026ndash;22 (September-November) of increase in LOS about 6.95 days on average (CI: 1.64; 12.50), with a subsequent decrease starting at week 45.\u003c/p\u003e \u003c/div\u003e"},{"header":"Discussion","content":"\u003cp\u003eTo fully address a global public health problem as serious as acute child malnutrition, understanding its causes and the health-disease process requires a multidimensional approach. The classic models proposed by Laframboise (\u003cspan citationid=\"CR39\" class=\"CitationRef\"\u003e1973\u003c/span\u003e) and Lalonde (\u003cspan citationid=\"CR40\" class=\"CitationRef\"\u003e1974\u003c/span\u003e) point out the involvement of four main groups of health determinants: human biology, the health system, environment, and lifestyle. Following these theories, approaching and identifying these determinants of child acute malnutrition in each context, in addition to using biological (anthropometric) diagnostic criteria, will allow for a greater knowledge of the disease and increase the effectiveness of future interventions.\u003c/p\u003e \u003cp\u003eThe final models for MUAC upon admission have shown a mixture of factors of different natures associated with the severity of the treated child, in addition to differences between the contexts of Mali and Niger. In general, the age of the individual seems to be a decisive factor in both cases, which is reflected in the WHO growth standards which show an increase in MUAC with age (WHO, 2006). While in the Mali model only the age of the mother is added as another determining factor in the severity of the child, it is in younger mothers where the levels of severity increase, as has been confirmed in a broader analysis that included a total of 55 low- and middle-income countries. This analysis associated a higher risk of infant mortality and poor child health outcomes with children of adolescent mothers (Finlay et al. \u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e2011\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eIn the case of Niger, the final model describes a more complex reality, aiming to understand the influences on MUAC upon admission of treated children. Healthcare-related aspects such as the presence of comorbidities (diarrhea, vomiting, ARI) and correct vaccination appear as determining factors. In scientific literature, the vicious circle between infectious comorbidities and acute child malnutrition is well known, mediated by a series of physiological and immune reactions in the body (Humphries et al. \u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e2021\u003c/span\u003e). Vaccination is a palliative measure that can help break this vicious circle, a protective effect that has also been proven in previous studies across different scenarios (Altare et al. \u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e2016\u003c/span\u003e; Ambadekar and Zodpey, \u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e2017\u003c/span\u003e). Strikingly, another variable that accumulated greater importance is breastfeeding. This scenario has been identified in different studies and systematic reviews as a protective factor against morbidity and mortality in the first two years of a child\u0026rsquo;s life. Numerous interventions have focused on promoting its adequate practice, based on its positive effects at a nutritional and immunological level (Horta and Victora, 2013; Khan and Islam, \u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e2017\u003c/span\u003e). Finally, different consumption patterns in dietary diversity also appeared to be linked to MUAC upon admission. Various studies have shown that poor dietary diversity is associated with higher odds of wasting (Li et al. \u003cspan citationid=\"CR42\" class=\"CitationRef\"\u003e2020\u003c/span\u003e; Aboagye et al. \u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e2021\u003c/span\u003e). There are different factors such as socioeconomic level, food security, childcare, etc., which are related and all of which, in turn, further shape dietary intake and diversity. Moreover, another recent study better characterized this association, stating that the likelihood of wasting was 0.22 times lower for children who received minimum dietary diversity (MDD) and minimum meal frequency (MMF) (Sheikh et al. \u003cspan citationid=\"CR65\" class=\"CitationRef\"\u003e2020\u003c/span\u003e). Specifically, in our model, Food Diversity PC1, which has a negative effect on MUAC, was related to greater consumption of fruits rich in vitamin A, vegetables especially rich in vitamin A, roots and tubers, and legumes, while Food Diversity PC2, which has a positive effect, was related to greater consumption of fats, dairy products, sugar products and condiments. These very different effects, depending on the pattern, are supported by a better quality in terms of caloric density and macro- and micronutrient content of the foods included in PC2. This nutritional concept, used by quantitative indices of dietary diversity (WFP, 2008), assigns greater importance to foods such as meat, fish, and dairy products.\u003c/p\u003e \u003cp\u003eLOS modelling has enabled the identification of factors associated with individuals taking longer to achieve recovery, which can be very useful in prioritizing and improving their care. In both the Niger and Mali contexts, individuals with greater severity upon admission, as identified by the MUAC, presented longer LOS. The relationship between anthropometric severity upon admission and treatment outcome is widely documented (Collins et al. \u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e2006\u003c/span\u003e; Dah et al. \u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e2022\u003c/span\u003e). Studies such as that of Mamo et al. (\u003cspan citationid=\"CR47\" class=\"CitationRef\"\u003e2019\u003c/span\u003e), using another statistical approach, highlight that comorbidities and routine medicine provision are factors that impact time to recovery. Our models also reach this result, linking it through the MUAC upon admission. Another aspect associated with LOS in both contexts was related to the source of water consumption. In the case of Niger, greater distance was associated with an increase in LOS. On the other hand, in Mali, the quality of water was the most relevant variable. This highlights the great importance of having good access to a safe water source that is not only accessible but also drinkable and of high quality. Such quality water aids children in treatment to respond better to it. This deficiency in access to drinking water has been associated in numerous studies with child malnutrition (Kamiya, \u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e2011\u003c/span\u003e; Bitew et al. \u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e2022\u003c/span\u003e). Likewise, there is a great consensus that good quality of consumed water reduces the incidence of comorbidities that impair recovery, especially diarrhea (Bhutta et al. \u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e2013\u003c/span\u003e). There is also consensus in both contexts regarding dietary diversity, as both models indicate that Food Diversity PC4 contributes to an increase in LOS. This can be explained by the negative association of this component with the consumption of eggs and meat. These animal products are energy-dense and contain multiple micronutrients such as iron, zinc, vitamin A, vitamin B12, etc. Their consumption is associated with improved nutritional status outcomes in observational studies (Hetherington et al. \u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e2017\u003c/span\u003e; Larson et al. 2019).\u003c/p\u003e \u003cp\u003eThe LOS values of children treated in Niger were found to be influenced by the simplified treatment protocol. This protocol stands out compared to the conventional CMAM protocol, used mostly in the country, for decentralizing treatment and bringing it closer to families and a series of simplifications in the diagnosis and management of cases (Charle-Cu\u0026eacute;llar et al. \u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e2023\u003c/span\u003e). The WHO, in its most recent guideline on the prevention and management of wasting (WHO, 2023), recognizes CHWs as an effective tool based on currently existing evidence. Different studies have demonstrated its effectiveness in improving treatment coverage, a reduction in severity upon admission and an increase in the recovery rate (\u0026Aacute;lvarez-Mor\u0026aacute;n et al. \u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e2018\u003c/span\u003e; Charle-Cu\u0026eacute;llar et al. \u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e2018\u003c/span\u003e; Wilunda et al. \u003cspan citationid=\"CR78\" class=\"CitationRef\"\u003e2021\u003c/span\u003e). Moreover, CHWs will lead to moderate savings in terms of resources (Rogers et al. \u003cspan citationid=\"CR60\" class=\"CitationRef\"\u003e2018\u003c/span\u003e; Cichon et al. \u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e2023\u003c/span\u003e). The great advantage of CHWs is that they reduce the distance to treatment. With health sites being less saturated, there is more time to treat each individual, allowing comprehensive treatment of other comorbidities such as diarrhea, acute respiratory infections (ARI), malaria, etc., which negatively affect severity and LOS (L\u0026oacute;pez-Ejeda et al. \u003cspan citationid=\"CR45\" class=\"CitationRef\"\u003e2020\u003c/span\u003e). A previous study by Dougnon et al. (\u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e2021\u003c/span\u003e) in rural Niger also found a shorter LOS in SAM children treated by CHWs, attributing it to earlier detection of cases, as their severity was lower.\u003c/p\u003e \u003cp\u003eThe achieved models, in addition to be able to identify and to quantify risk factors associated with our variables of interest, have the great potential to predict, with a certain level of confidence, the value an individual could present based on the initial covariates. This capability can be particularly useful in the case of LOS for recovery. In this regard different profiles could be established to identify children at a higher risk of inadequate treatment response, and consequently, of remaining malnourished for a longer period, with adverse consequences for their health. The utility of its application in the field is evident through the detailed examples used for analysing and comparing various factors associated with each case. These examples involve crossing them with probability distributions and understanding the practicality of applying it in the field.\u003c/p\u003e \u003cp\u003eThese models are of great interest because they incorporate the week of admission to treatment (reflecting seasonality) and travel time to the health site (reflecting accessibility to treatment) as random factors in their adjustment. This allows the incorporation of potential interactions they may have with other key factors. In Mali, a clear seasonal influence was observed, while the analyses did not indicate this in Niger, possibly due to the narrower time frame of their data. Specifically, in the case of Mali, the highest severity levels (lowest MUAC upon admission) were observed in weeks 0 and 24 of the study, coinciding with children admitted to treatment in June and November. This result aligns with a recent secondary analysis of 15 years of SMART survey data, indicating two peaks of wasting in African drylands such as Mali. The primary peak occurs in April to May, and the second peak occurs in September to October, influenced by peaks in temperature and precipitation (Venkat et al. \u003cspan citationid=\"CR73\" class=\"CitationRef\"\u003e2023\u003c/span\u003e). This temporal difference with the identified prevalence peaks could respond to the time necessary for these most critical situations of food insecurity to be reflected in an increase in the severity of MUAC.\u003c/p\u003e \u003cp\u003eIt is important to take this seasonality into account in African drylands, where production systems highly depend on climatic conditions characterized by extreme and erratic rainfall. Seasonal temperatures are consistently above 20\u0026ordm;C and can reach as high as 40 or 50\u0026ordm;C (Young, \u003cspan citationid=\"CR83\" class=\"CitationRef\"\u003e2020\u003c/span\u003e). Furthermore, considering this data will be particularly relevant in the future context of climate change, which is expected to worsen water scarcity and accelerate desertification, thereby influencing food production and nutrition security, which will amplify health challenges (Agostoni et al. \u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e2023\u003c/span\u003e). In this sense, the study carried out by Baker and Anttila-Hughes (\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e2020\u003c/span\u003e) estimated the effect of temperature on key child nutrition outcomes through a pooled statistical model that controlled for household and regional characteristics. They then forecasted the impact of future warming on child malnutrition levels, determining that the western Africa region would see a 37% increase in the prevalence of wasting by 2100.\u003c/p\u003e \u003cp\u003eThe random effects models presented significant interactions within the study sample in each context. In Niger, we observed that children with comorbidities experience a reduction in their severity on admission (MUAC) if they are very close to treatment. This benefit of proximity to treatment over severity has already been evidenced in studies that included CHWs as treatment prividers outside health centers closer to the communities (L\u0026oacute;pez-Ejeda et al. \u003cspan citationid=\"CR45\" class=\"CitationRef\"\u003e2020\u003c/span\u003e; Dougnon et al. \u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e2021\u003c/span\u003e). The results of our study seem to indicate that this effect could be especially important when comorbidities are present, as reducing the distance, one of the greatest barriers to accessing treatment, would lead to earlier detection and treatment of comorbidities, potentially reducing their severity upon admission. Another significant interaction detected in severity in Niger was between week and sex, with boys showing a greater MUAC compared to girls. This finding appears somewhat contradictory to the existing literature (Myatt et al. \u003cspan citationid=\"CR53\" class=\"CitationRef\"\u003e2018\u003c/span\u003e; Costa et al. \u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e2021\u003c/span\u003e). In a recent meta-analysis of 44 studies, Thurstans et al. (\u003cspan citationid=\"CR67\" class=\"CitationRef\"\u003e2020\u003c/span\u003e) demonstrated that boys are more likely to be wasted than girls (odds ratio: 1.26 [95% CI: 1.13\u0026ndash;1.40]). This is biologically explained by the sexual differences that already exist from the first months of life, both in growth patterns and body composition, with less adipose accumulation and gain in boys (Davis et al. \u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e2019\u003c/span\u003e). All of this is influenced by hormonal differences already noticeable in infants and affect their metabolism (Kiviranta et al. \u003cspan citationid=\"CR38\" class=\"CitationRef\"\u003e2016\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eRegarding the LOS in Niger, an effect of travel time was also observed in the SAM group. Those further away from treatment had a greater LOS, which is directly related to the effect already observed on MUAC in this context. This effect, reflected in the LOS, suggests that in a treatment involving weekly visits, greater distance may impact the effectiveness of treatment adherence, leading to increased missed visits, which could ultimately result in default (Hitchings et al. \u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e2022\u003c/span\u003e). This same explanation can be applied to the interaction observed between Travel time and the non-comorbidities group, as their LOS is reduced when near treatment but increases when distant. The lack of an effect seen on LOS in the comorbidities group may be attributed to the reduced sample size.\u003c/p\u003e \u003cp\u003eIn the context of Mali, interactions were observed in the MUAC model, with very similar behaviours, between the Week and the treatment protocol, and, on the other hand, between the Week and the sex variable. Firstly, individuals treated with the Standard Protocol experienced a decrease in their MUAC between weeks 20 and 30 of the study (November-December), coinciding with one of the wasting peaks identified in the literature. The very similar behavior observed in the values of the group of girls indicates that these seasonal effects were also associated with sex, as they were not appreciated in the group of boys. Both contexts have shared an association between sex and seasonality in MUAC, with a negative effect observed only for girls, which has already been mentioned as biologically contradictory. Therefore, it is necessary to consider the possible presence of social factors related to gender in both contexts, which may explain these results. Previous studies have demonstrated this influence in southeast Asian countries (Raj et al. \u003cspan citationid=\"CR58\" class=\"CitationRef\"\u003e2015\u003c/span\u003e), wherein having more brothers increased the odds of severe wasting (AOR: 1.31 [CI\u0026thinsp;=\u0026thinsp;1.11, 1.55]) for girls but not boys. This is likely due to situations of food insecurity, where there is a preference for feeding male children over female children (Biswas and Bose, \u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e2011\u003c/span\u003e). A recent study by Thurstans et al. (\u003cspan citationid=\"CR66\" class=\"CitationRef\"\u003e2023\u003c/span\u003e) indicated a greater average daily weight gain in girls. However, in many settings, the adjusted odds ratios (AORs) noted that girls were less likely to recover than boys. Likewise, a study based on big data by country identified a strong and statistically significant association of the Gender Inequality Index with excess under-five female mortality in low-income and middle-income countries, including the Sahel region (Iqbal et al. \u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e2018\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eIn terms of LOS in Mali, a seasonal effect was also detected, with the group of SAM males showing an increase in LOS in specific weeks of the study (14\u0026ndash;23) during September to November. These findings are based on the characteristics of this specific group of individuals, as it comprises the most severe group of boys (SAM). Therefore, this increased severity is added to the already mentioned disadvantageous biological characteristics of sexual dimorphism (Davis et al. \u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e2019\u003c/span\u003e). Furthermore, being admitted to treatment during this time frame means that individuals have to undergo treatment during the second wasting peak of the year identified in the Sahel drylands (Venkat et al. \u003cspan citationid=\"CR73\" class=\"CitationRef\"\u003e2023\u003c/span\u003e). This period coincides with worsening food security due to increasing temperatures and reduced access to sufficient, safe, and nutritious food to meet their dietary needs, which directly affect the nutritional status of individuals, resulting in longer LOS values comparable to those recorded in our study, where some SAM boys required more than 100 days to achieve recovery. Therefore, this period is particularly critical, requiring heightened attention to the most vulnerable groups, who suffer for an extended period from severe malnutrition.\u003c/p\u003e \u003cp\u003eFinally, there are some issues that need to be stated as potential limitations of our approach. The most obvious is that the Niger data presented a narrower time frame and could not cover an entire year, limiting the results in correctly identifying the possible effect of seasonality on the variables of interest in this context. Another limitation would be the lack of response in some variables and the handling of missing values. In light of the results obtained, it is appropriate to highlight the need for further research, applying an integrative approach involving various biological, socioeconomic, ecological and clinical aspects related to the disease, but in different contexts from those analysed here. Therefore, caution is important when attempting to extrapolate the results obtained here to regions that may present very different characteristics.\u003c/p\u003e"},{"header":"Conclusions","content":"\u003cp\u003eThe present study has quantified, using a Bayesian approach, the association of the variables with an increase in severity on admission (MUAC) and Length of stay (LOS) of children treated for acute malnutrition in two rural contexts in Niger and Mali. We showed how aspects such as seasonality and time to the treatment site can act as modulators, interacting differently among groups of individuals.\u003c/p\u003e \u003cp\u003eRelevant differences were shown between contexts, apart from the greater influence of seasonality in Mali and, travel time to treatment in Niger. Firstly, regarding severity, in both contexts, there was an influence of the child's age, and it was in Niger that factors such as comorbidity, dietary diversity, and breastfeeding were influential. Secondly, for the LOS, in both contexts, the severity of admission and dietary diversity were relevant. In Niger, we found the distance to the water source and the protocol, but in Mali, the quality of the water source was more important.\u003c/p\u003e \u003cp\u003eThis study highlights the importance of applying a multidisciplinary analysis to encompass various factors that may have a more or less significant influence, directly or indirectly through interactions, on child malnutrition in different contexts. This approach allows for a better understanding of the environmental factors surrounding the disease.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e \u003ch2\u003eConflict of Interest\u003c/h2\u003e \u003cp\u003eThe authors declare no conflict of interest.\u003c/p\u003e \u003c/p\u003e\u003ch2\u003eFunding\u003c/h2\u003e \u003cp\u003eThis research project was funded by Elrha's Research for Health in Humanitarian Crisis (R2HC) programme. R2HC aims to improve health outcomes for people affected by crises by strengthening the evidence base for public health interventions. The R2HC programme is funded by the UK Foreign, Commonwealth and Development Office (FCDO), Wellcome and the UK National Institute for Health Research (NIHR). LJ S-M was granted with a predoctoral fellowship from the Complutense University and Banco Santander.\u003c/p\u003e\u003ch2\u003eAuthor Contribution\u003c/h2\u003e\u003cp\u003eConceptualization: LJS-M, NL-E, CLH, CF; Methodology: LJS-M, CF; Formal analysis and investigation: LJS-M, CF; Writing - original draft preparation: LJS-M; Writing - review and editing: NL-E, CLH, PC-C; Funding acquisition: NL-E, PC-C; Resources: SS, MNS, AB, MB, AAG, AS, NO, RHL; Supervision: SS, MNS, AB, MB, AAG, AS, NO, RHL.\u003c/p\u003e\u003ch2\u003eAcknowledgement\u003c/h2\u003e\u003cp\u003e The authors would like to express their gratitude to all medical staff and patients who participated in this study at Niger and Mali.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\u003cli\u003e\u003cspan\u003eAboagye RG, Seidu AA, Ahinkorah BO, Arthur-Holmes F, Cadri A, Dadzie LK, Hagan JE, Eyawo O, Yaya O (2021) Dietary Diversity and Undernutrition in Children Aged 6\u0026ndash;23 Months in Sub-Saharan Africa. 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Accessed 17 October 2024\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"environmental-and-ecological-statistics","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"eest","sideBox":"Learn more about [Environmental and Ecological Statistics](http://link.springer.com/journal/10651)","snPcode":"10651","submissionUrl":"https://submission.nature.com/new-submission/10651/3","title":"Environmental and Ecological Statistics","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"Child wasting, undernutrition, MUAC, travel time, Bayesian, INLA models","lastPublishedDoi":"10.21203/rs.3.rs-5434736/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-5434736/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eAcute child malnutrition is a global public health problem influenced by very diverse factors, including socioeconomic and dietary aspects, but also seasonal and geographic factors. The present study is a secondary analysis that attempts to characterize which variables have influenced the Middle Upper-Arm Circumference (MUAC) upon admission and the Length of Stay (LOS) for treatment recovery. The sample of children analysed was 852. Initially, data cleaning and a reduction of the dimensionality of dietary diversity were carried out. A selection of the importance of the variables using the Watanabe Akaike Information Criteria (WAIC) was carried out prior to the adjustment of Bayesian mixed effects models, with the variables of travel time to health site and week of admission as random factors, on the MUAC and LOS variables. Clear differences were seen between both contexts. Highlighting significant interactions of travel time in Niger while the seasonal effect stood out in Mali. The MUAC models identified a positive effect of age in both contexts, and in Niger, influences of diet diversity, comorbidities, breastfeeding and vaccination appeared. On the other hand, the LOS models highlighted the severity upon admission, and in Niger also factors related to the treatment protocol and the distance to the water source, while in Mali, the quality of water was more decisive. The present study shows the importance of considering acute child malnutrition from a multidimensional and complex approach, where diverse factors (biological, socioeconomic, ecological, etc.) can influence directly or as modulators of the disease and its treatment.\u003c/p\u003e","manuscriptTitle":"Bayesian mixed effect models to account for environmental modulators of acute malnutrition treatment in children","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2024-12-17 06:16:14","doi":"10.21203/rs.3.rs-5434736/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Revision requested","date":"2025-03-28T15:06:35+00:00","index":"","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-01-26T16:03:58+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"64500143963544850869600935984895874182","date":"2024-12-24T18:45:07+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"226795207212008974090389909018460083016","date":"2024-11-29T14:35:09+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2024-11-25T05:23:21+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2024-11-17T14:35:45+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2024-11-12T10:57:45+00:00","index":"","fulltext":""},{"type":"submitted","content":"Environmental and Ecological Statistics","date":"2024-11-11T22:01:08+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"environmental-and-ecological-statistics","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"eest","sideBox":"Learn more about [Environmental and Ecological Statistics](http://link.springer.com/journal/10651)","snPcode":"10651","submissionUrl":"https://submission.nature.com/new-submission/10651/3","title":"Environmental and Ecological Statistics","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false}}],"origin":"","ownerIdentity":"87d5b59b-6baa-457a-8964-fb0adbc71e82","owner":[],"postedDate":"December 17th, 2024","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"published-in-journal","subjectAreas":[],"tags":[],"updatedAt":"2025-09-08T16:05:56+00:00","versionOfRecord":{"articleIdentity":"rs-5434736","link":"https://doi.org/10.1007/s10651-025-00674-6","journal":{"identity":"environmental-and-ecological-statistics","isVorOnly":false,"title":"Environmental and Ecological Statistics"},"publishedOn":"2025-09-05 15:57:41","publishedOnDateReadable":"September 5th, 2025"},"versionCreatedAt":"2024-12-17 06:16:14","video":"","vorDoi":"10.1007/s10651-025-00674-6","vorDoiUrl":"https://doi.org/10.1007/s10651-025-00674-6","workflowStages":[]},"version":"v1","identity":"rs-5434736","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-5434736","identity":"rs-5434736","version":["v1"]},"buildId":"FbvkV6FR0MCFSLy54lSbu","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}