School of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal, Durban, South Africa.
J Health Popul Nutr. 2020 Nov 6;39(1):8. doi: 10.1186/s41043-020-00217-8.
Anaemia and malaria are the leading causes of sub-Saharan African childhood morbidity and mortality. This study aimed to explore the complex relationship between anaemia and malaria in young children across the districts or counties of four contiguous sub-Saharan African countries, namely Kenya, Malawi, Tanzania and Uganda, while accounting for the effects of socio-economic, demographic and environmental factors. Geospatial maps were constructed to visualise the relationship between the two responses across the districts of the countries.
A joint bivariate copula regression model was used, which estimates the correlation between the two responses conditional on the linear, non-linear and spatial effects of the explanatory variables considered. The copula framework allows the dependency structure between the responses to be isolated from their marginal distributions. The association between the two responses was set to vary according to the district of residence across the four countries.
The study revealed a positive association between anaemia and malaria throughout the districts, the strength of which varied across the districts of the four countries. Due to this heterogeneous association between anaemia and malaria, we further considered the joint probability of each combination of outcome of anaemia and malaria to further reveal more about the relationship between the responses. A considerable number of districts had a high joint probability of a child being anaemic but not having malaria. This might suggest the existence of other significant drivers of childhood anaemia in these districts.
This study presents an alternative technique to joint modelling of anaemia and malaria in young children which assists in understanding more about their relationship compared to techniques of multivariate modelling. The approach used in this study can aid in visualising the relationship through mapping of their correlation and joint probabilities. These maps produced can then help policy makers target the correct set of interventions, or prevent the use of incorrect interventions, particularly for childhood anaemia, the causes of which are multiple and complex.
在撒哈拉以南非洲,贫血症和疟疾是导致儿童发病和死亡的主要原因。本研究旨在探索四个相邻撒哈拉以南非洲国家(肯尼亚、马拉维、坦桑尼亚和乌干达)各地区或县内贫血症和疟疾之间的复杂关系,同时考虑社会经济、人口和环境因素的影响。构建了地理空间图,以可视化两国各地区之间这两个反应之间的关系。
使用联合双变量 Copula 回归模型,该模型根据所考虑的解释变量的线性、非线性和空间效应来估计两个反应之间的相关性。Copula 框架允许将两个反应之间的依赖结构与其边际分布隔离开来。将两个反应之间的关联设置为根据四个国家中各地区的居住情况而变化。
研究表明,贫血症和疟疾在整个地区之间存在正相关,其强度在四个国家的地区之间有所不同。由于贫血症和疟疾之间存在这种异质关联,我们进一步考虑了贫血症和疟疾每种结果组合的联合概率,以进一步揭示这两个反应之间的关系。相当多的地区贫血症儿童的联合概率很高,但没有疟疾。这可能表明在这些地区存在其他导致儿童贫血的重要因素。
本研究提出了一种替代技术,用于联合建模贫血症和儿童疟疾,与多元建模技术相比,这有助于更好地了解它们之间的关系。本研究中使用的方法可以通过绘制它们的相关性和联合概率来帮助可视化它们之间的关系。然后可以生成这些地图,以帮助决策者针对正确的干预措施集,或防止使用不正确的干预措施,特别是对于原因复杂的儿童贫血症。