Theses and Dissertations (Statistics)

Bayesian modelling of malaria cases through the elicitation of prior distribution

Wed, 01 Jan 2025 00:00:00 GMT

Bayesian modelling of malaria cases through the elicitation of prior distribution Sehlabana, Makwelantle Asnath Climate change plays a critical role in shaping both the geographic spread and intensity of malaria outbreaks. Recent research demonstrates that climaterelated factors surpass epidemiological, socio-economic, and environmental contributors in driving malaria resurgence. Progress towards malaria elimination has been further hindered by the COVID-19 pandemic, which disrupted control programmes globally. In South Africa, despite implementation of the National Malaria Elimination Strategic Plan (NMESP), malaria elimination targets remain unmet, partly due to limitations in surveillance and predictive systems. This thesis addresses the underutilisation of subjective Bayesian methods in epidemiology, which incorporate expert knowledge into disease models. While objective priors are commonly used due to their simplicity, subjective priors informed by expert judgment offer richer, context-specific insights. However, the process of prior elicitation is often hindered by complexity and resource constraints. To overcome this, the thesis introduces a novel, efficient approach that combines the Analytic Hierarchy Process (AHP) with statistical validation techniques to incorporate expert knowledge into Bayesian models. The approach provides a simple, time and resource efficient framework for eliciting and applying subjective priors in Bayesian epidemiological models. This thesis utelised both primary and secondary data. Primary data were collected through a purposive sampling approach using a questionnaire to support expert elicitation, with participants recruited nationally and internationally. Secondary data included malaria case records (2018–2022) from the South African ii National Department of Health, climatological data from the South African Weather Services, and environmental data from EarthExplorer platform, covering the provinces of KwaZulu-Natal, Limpopo, and Mpumalanga. The major contribution of this thesis is the development of a robust Bayesian malaria prediction model that integrates both climate data and expert-informed prior distributions. Comparative analysis indicates that subjective priors outperform objective priors in enhancing model performance. These findings underscore the value of expert knowledge in improving predictive accuracy and guiding public health responses. The analysis reveals that malaria transmission intensifies in regions with temperatures between 20–30°C, rainfall ranging from 0–200 mm, and Normalised Difference Vegetation Index (NDVI) values of 0.5–0.8. Those conditions are associated with 200 to 1000 predicted malaria cases. Ehlanzeni (Mpumalanga), uMkhanyakude (KwaZulu-Natal), Vhembe, and Mopani (Limpopo) districts are identified as high-risk areas with elevated malaria counts. Malaria incidence peaks in summer and autumn, especially in regions experiencing temperatures of 12–20°C during the night, moderate rainfall (100–200 mm), and NDVI levels exceeding 0.6. This implies that malaria transmission intensify after cumulative rainfall creates optimal mosquito breeding conditions. These findings support the development of early warning systems and targeted vector control interventions. Future research should explore the integration of Bayesian machine learning and further evaluate the comparative performance of different priors across various epidemiological contexts. Thesis (Ph.D. (Statistics)) -- University of Limpopo, 2025

Statistics of extremes with application to extreme floods in Kwazulu Natal Province, South Africa

Wed, 01 Jan 2025 00:00:00 GMT

Statistics of extremes with application to extreme floods in Kwazulu Natal Province, South Africa Lutombo, Hulisani Extreme rainfall has become a prevailing natural disaster in the region of Southern Africa. Flooding is one of the natural disasters that pose damage to property, infrastructure, and human lives. This study conducted a comprehensive extreme value analysis of monthly maximum rainfall recorded at five selected meteorological stations in KwaZulu-Natal province, South Africa; namely Mandini, Mount Edgecombe, Richards Bay Airport, Port Edward, and Virginia, using data spanning from 1952 to 2022 as provided by the South African Weather Service (SAWS). The aimed to compare the performance of advanced extreme value theory (EVT) models, specifically the generalised extreme value distribution (GEVD), generalised extreme value distribution for r-largest order statistics (GEVDr) and the blended generalised extreme value distribution (bGEVD), in modelling extreme rainfall events. Stationarity assessments using the Augmented Dickey-Fuller (ADF), Kwiatkowski-Phillips- Schmidt-Shin (KPSS), and Phillips-Perron (PP) tests produced mixed results, while the Mann-Kendall (M-K) trend test indicated a monotonic decreasing trend in rainfall. Parameter estimation for the GEVD was performed using maximum likelihood estimation (MLE) and Bayesian Markov Chain Monte Carlo (MCMC) methods, both yielding positive shape parameters consistent with the Fr´echet class of distributions. Goodness-of-fit evaluations through Anderson-Darling (A-D) and Kolmogorov-Smirnov (K-S) tests, alongside diagnostic plots, confirmed the suitability of the GEVD model for the data. Additionally, the Shapiro-Wilk test demonstrated the non-normality of the rainfall datasets. Optimal block sizes for the r-largest order statistics model varied across stations, with r-values ranging from 2 to 4. Both the standard GEVD and r-largest GEVD models provided consistent return level estimates, suggesting strong model performance. The bGEVD model further revealed a negative time trend in rainfall maxima, resulting in lower return level estimates compared to the other models. Return levels were calculated for return periods ranging from 5 to 250 years, highlighting that extreme rainfall events become increasingly likely with longer return periods. Overall, the findings of the study offer valuable insights into the behaviour of extreme rainfall in KwaZulu-Natal province, with significant implications for risk management, infrastructure planning, and disaster preparedness. Thesis (M. Sc. (Statistics)) -- University of Limpopo, 2025

Detection of metabolic disorders for African women in a rural South African setting : a case of Ga-Dikgale Limpopo Province, South Africa

Mon, 01 Jan 2024 00:00:00 GMT

Detection of metabolic disorders for African women in a rural South African setting : a case of Ga-Dikgale Limpopo Province, South Africa Phaho, Mmalehu Francin The waist circumference cut-off point for diagnosing metabolic syndrome in Sub-Saharan Africa is based on standards established for European populations. The purpose of this study was to determine the prevalence of metabolic syndrome and other related disorders and to determine the waist circumference cut-off point that effectively discriminates between African women with and without metabolic syndrome. Initially, the study participants with metabolic syndrome were identified using the National Cholesterol Education Program - Third Adult Treatment Panel criteria, which was subsequently adapted to the International Diabetes Federation definition. According to the National Cholesterol Education Program - Third Adult Treatment Panel definition, metabolic syndrome is present if at least three of the following criteria are met: Triglycerides ≥1.7 mmol/L, High-density lipoprotein cholesterol <1.29 mmol/L, Glucose ≥5.6 mmol/L, Systolic Blood Pressure ≥ 130 mmHg, or Diastolic Blood Pressure ≥ 85 mmHg. The prevalence of metabolic syndrome and obesity (body mass index ≥30 kg) were 19% and 30%, respectively. The optimal waist circumference for diagnosing metabolic syndrome was obtained using receiver operating characteristic curve analysis and was found to be 88 cm. Machine learning methods, including logistic regression, linear discriminant analysis and random forest were employed to further validate the cut-off point. The 88 cm cut-off point demonstrated superior performance compared to the European 80 cm cut-off pint, based on prediction accuracy, specificity and positive predictive value. The study highlights how important ii it is to have population-specific cut-off points for correctly diagnosing metabolic syndrome in order to reduce the risk of misdiagnosis and related complications. The findings advocate for using the 88 cm cut-off point, which differs with the recommended cut-off point of 80 cm. This is a as a quick and cost-effective measure for identifying obesity, potentially improving public health interventions for African populations. Thesis (M. Sc. (Statics)) -- University of Limpopo, 2024

Application of survival analysis and machine learning models to age at first marriage among women in South Africa

Mon, 01 Jan 2024 00:00:00 GMT

Application of survival analysis and machine learning models to age at first marriage among women in South Africa Komane, Malahlane Magdaline Understanding factors influencing the age at first marriage is crucial for addressing social issues, promoting gender equality, and ensuring women’s wellbeing. This research aims to identify key determinants of age at first marriage for South African women. The discrete survival tree approach is applied to analyze data and identify factors influencing women’s age at first marriage. Key individual variables, such as birth year, ethnicity, education level, age at first marriage, and province, are used in the analysis. The performance of this model is compared with that of Random Forests and Classification and Regression Trees using the C-index to determine the best-performing model.” All three models provided valuable insights, but Random Forest emerged as the most accurate age predictor at first marriage. Key determinants identified were province of residence, birth year, and educational level. These findings can contribute to policy-making aimed at improving the well-being of women in South Africa through targeted interventions. Thesis (M. Sc. (Statistics)) -- University of Limpopo, 2024