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School Mathematics, Statistics and Computer Science

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Browsing School Mathematics, Statistics and Computer Science by SDG "SDG3"

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    Flexible Bayesian hierarchical spatial modelling in disease mapping.
    (2022) Ayalew, Kassahun Abere.; Manda, Samuel.
    The Gaussian Intrinsic Conditional Autoregressive (ICAR) spatial model, which usually has two components, namely an ICAR for spatial smoothing and standard random effects for non-spatial heterogeneity, is used to estimate spatial distributions of disease risks. The normality assumption in this model may not always be correct and misspecification of the distribution of random effects could result in biased estimation of the spatial distribution of disease risk, which could lead to misleading conclusions and policy recommendations. Limited research studies have been done where the estimation of the spatial distributions of diseases under the ICAR-normal model were compared to those obtained from fitting ICAR-nonnormal model. The results from these studies indicated that the ICAR-nonnormal models performed better than the ICAR-normal in terms of accuracy, efficiency and predictive capacity. However, these efforts have not fully addressed the effect on the estimation of spatial distributions under flexible specification of ICAR models in disease mapping. The overall aim of this PhD thesis is to develop approaches that relax the normality assumption that is often used in modeling and fitting of ICAR models in the estimation of spatial patterns of diseases. In particular, the thesis considers the skew-normal and skew-Laplace distributions under the univariate, and skew-normal for the multivariate specifications to estimate the spatial distributions of either univariable or multivariable areal data. The thesis also considers non-parametric specification of the multivariate spatial effects in the ICAR model, which is a novel extension of an earlier work. The estimation of the models was done using Bayesian statistical approaches. The performances of our suggested alternatives to the ICAR-normal model are evaluated by simulating studies as well as with practical application to the estimation of district-level distribution of HIV prevalence and treatment coverage using health survey data in South Africa. Results from the simulation studies and analysis of real data demonstrated that our approaches performed better in the prediction of spatial distributions for univariable and multivariable areal data in disease mapping approaches. This PhD work shows the limitations of relying on the ICAR-normal model for the estimations of spatial distributions for all spatial analyses, even when the data could be asymmetric and non-normal. In such scenarios, skewed-ICAR and nonparametric ICAR approaches could provide better and unbiased estimation of the spatial pattern of diseases.
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    Statistical modelling on childhood anaemia, malaria and stunting in Malawi, Lesotho, and Burundi.
    (2023) Gaston, Rugiranka Tony.; Ramroop, Shaun.; Habyarimana, Faustin.
    The current research aimed to produce and expand statistical models in the discipline of biostatistics with a focus on childhood anaemia, malaria, and stunting. Malaria, anaemia, and stunting together continue to be public health issues worldwide in both industrialised and underdeveloped countries, particularly in children younger than 5 years (Osazuwa and Ayo, 2010; Kanchana et al., 2018). Malaria, anaemia, and stunting are dangerous, mostly in children from underdeveloped nations and they still remain the biggest contributor to morbidity and mortality. In addition, anaemia, malaria, and stunting are associated, and if not treated on time can damage children’s emotional, physical, mental status and poor performance at school (Gaston et al., 2022). The current study evaluates the link between anaemia, stunting, and malaria simultaneously. Furthermore, the study assessed whether socioeconomic, geographical, environmental, and child demographic variables have a significant effect on childhood malaria, anaemia, and stunting. This study used a national secondary cross-sectional data from Malawi Malaria Indicator Survey (MMIS); Lesotho Demographic Health Survey (LDHS); and Burundi Demographic Health Survey (BDHS). The data was collected based on multi-stage sampling, stratified, and cluster sampling with an unequal chance of sampling. It is for this reason we first used the survey logistic regression model in Chapter 3, which accounted for the complexity of sampling design and heterogeneity between observations from the same cluster. However, this model includes only the fixed effect and does not have the option of adding the random effect to model the correlation between observations. We extend the model in Chapter 4, to a generalised mixed additive model (GAMM) to include the random effect. The GAMM is also an extension of the generalised linear mixed model (GLMM) and enables the parametric fixed effects from GLMM to be modelled as a non-parametric model using the additive smooth function. These models were applied to single response variables, and we wanted to evaluate the relationship which might exist between anaemia, stunting, and malaria. We then explore the multivariate joint model under GLMM in Chapter 5 to simultaneously joint either malaria and anaemia or anaemia and stunting. Finally, we introduce a structural equation model (SEM) in Chapter 6, to evaluate the complex interrelationships between socioeconomics, demographics, and environmental factors, as well as their direct or indirect relationship with childhood malaria, anaemia and stunting co-morbidity. The previous chapters could not address these interrelationships among the variables of interest. Each model used in this study has its weaknesses and strengths which can depend on the goal of the xii researcher. However, the multivariate model under GLMM and the structural equation model were found to be more adaptive and attractive to researchers interested in innovative scientific research. The findings from this study revealed that the child’s nutrition status, age, the child with fever, diarrhoea, altitude, place of residence, toilet facility, access to electricity, children who slept under a mosquito bed net the night before the survey, mother's education level, and mother’s body mass index have a significant effect on both childhood anaemia and malaria. The age of a child, the mother’s educational status, place of residence, wealth index, and child weight at birth were the determinants of stunting or malnutrition. The findings also indicated that the geographical, geophysical, environmental, household and child demographic factors were statistically significant and have either a direct or an indirect effect on childhood co-morbidity factors. The geographical factors were statistically significant and had a positive direct effect on childhood malaria, anaemia, and stunting. The estimated indirect path for the impact of geophysical factors on childhood co-morbidity factors, as mediated by household factors was statistically significant and positive. However, the estimated indirect paths for the effect of geophysical factors on childhood co-morbidity factors, as mediated by environmental factors were statistically significant but negative. The child demographic factors revealed a direct statistically significant impact on childhood co-morbidity factors. Furthermore, the estimated indirect path effect on childhood comorbidity as mediated effect on household factors was statistically significant and negative. Moreover, household and environmental factors indicate a positive direct effect on childhood co-morbidity anaemia, malaria, and stunting. Finally, the results of this study revealed a positive relationship between stunting, anaemia, and malaria. This means that malaria, anaemia, and stunting increase or decrease in the same direction. Hence, controlling one or two between malaria, anaemia, and stunting can reduce the effect of other(s), which can assist the policymakers and government in the allocation of financial resources to fight against childhood comorbidity anaemia, malaria, and stunting. Furthermore, understanding the link between anaemia, malaria, and stunting other factors associated with them will assist in focusing on those areas and go a long way toward achieving the United Nations Sustainable Development Goals (SDGs3), known as the complete elimination of under-5 mortality by 2030.