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Background CD4 cell count has been identified to be an essential component in monitoring HIV treatment outcome. However, CD4 cell count monitoring sometimes fails to predict virological failure resulting in unnecessary switch of treatment lines which causes drug resistance and limitations of treatment options. This study assesses the use of both viral load (HIV RNA) and CD4 cell count in the monitoring of HIV/AIDS progression. Methods Time-homogeneous Markov models were fitted, one on CD4 cell count monitoring and the other on HIV RNA monitoring. Effects of covariates; gender, age, CD4 baseline, HIV RNA baseline and adherence to treatment were assessed for each of the fitted models. Assessment of the fitted models was done using prevalence plots and the likelihood ratio tests. The analysis was done using the “msm” package in R. Results Results from the analysis show that viral load monitoring predicts deaths of HIV/AIDS patients better than CD4 cell count monitoring. Assessment of the fitted models shows that viral load monitoring is a better predictor of HIV/AIDS progression than CD4 cell count. Conclusion From this study one can conclude that although patients take more time to achieve a normal CD4 cell count and less time to achieve an undetectable viral load, once the CD4 cell count is normal, mortality risks are reduced. Therefore, both viral load monitoring and CD4 count monitoring can be used to provide useful information which can be used to improve life expectance of patients living with HIV. However, viral load monitoring is a better predictor of HIV/AIDS progression than CD4 cell count and hence viral load is deemed superior.

The aim of this paper is to determine if the Loggamma distribution model in a Generalised Linear Model (GLM) setup is a better model than the traditional simple linear regression model and the Lognormal-based GLM when fitted to nitrogen dioxide (NO2) emissions data generated during the production of electricity from 13 Eskom’s coal-fuelled power stations in South Africa. The variables explaining the NO2 emissions data are selected using backward stepwise variable selection techniques. The variables considered include the power station itself, the amount of electricity generated from the power station, the age in years of the power station, the abatement technology (filter) used at the particular power station, and the month of the year. Interaction terms between the variables are also considered. The maximum likelihood estimation (MLE) method is used to estimate parameters of the GLM, and ordinary least squares is used to estimate parameters for the regression model. The Normal, Lognormal, and Loggamma distribution models with identity link function are fitted to the NO2 emissions data. The variance of the NO2 emissions increases with mean emissions and the Loggamma model plots, and the explained variance metrics (the variance-function-based R2 and adjusted R2) confirm the best fit to the data over the Normally distributed regression model and Lognormal-based GLM. Thus, NO2 emissions at Eskom in South Africa can be explained and predicted by employing the Loggamma-based GLM model. The findings will assist in providing information for the development of effective strategies for mitigating air pollution and promoting sustainable practices within the energy sector in South Africa.

Background In South Africa (SA), stroke is the second highest cause of mortality and disability. Apart from being the main killer and cause of disability, stroke is an expensive disease to live with. Stroke costs include death and medical costs. Little is known about the stroke burden, particularly the stroke direct costs in SA. Identification of stroke costs predictors using appropriate statistical methods can help formulate appropriate health programs and policies aimed at reducing the stroke burden. Analysis of stroke costs have in the main, concentrated on mean regression, yet modelling with quantile regression (QR) is more appropriate than using mean regression. This is because the QR provides flexibility to analyse the stroke costs predictors corresponding to quantiles of interest. This study aims to estimate stroke direct costs, identify and quantify its predictors through QR analysis. Methods Hospital-based data from 35,730 stroke cases were retrieved from selected private and public hospitals between January 2014 and December 2018. The model used, QR provides richer information about the predictors on costs. The prevalence-based approach was used to estimate the total stroke costs. Thus, stroke direct costs were estimated by taking into account the costs of all stroke patients admitted during the study period. QR analysis was used to assess the effect of each predictor on stroke costs distribution. Quantiles of stroke direct costs, with a focus on predictors, were modelled and the impact of predictors determined. QR plots of slopes were developed to visually examine the impact of the predictors across selected quantiles. Results Of the 35,730 stroke cases, 22,183 were diabetic. The estimated total direct costs over five years were R7.3 trillion, with R2.6 billion from inpatient care. The economic stroke burden was found to increase in people with hypertension, heart problems, and diabetes. The age group 55–75 years had a bigger effect on costs distribution at the lower than upper quantiles. Conclusions The identified predictors can be used to raise awareness on modifiable predictors and promote campaigns for healthy dietary choices. Modelling costs predictors using multivariate QR models could be beneficial for addressing the stroke burden in SA.

Background The discrepancy between blood supply and demand requires accurate forecasts of the blood supply at any blood bank. Accurate blood donation forecasting gives blood managers empirical evidence in blood inventory management. The study aims to model and predict blood donations in Zimbabwe using hierarchical time series. The modelling technique allows one to identify, say, a declining donor category, and in that way, the method offers feasible and targeted solutions for blood managers to work on. Methods The monthly blood donation data covering the period 2007 to 2018, collected from the National Blood Service Zimbabwe (NBSZ) was used. The data was disaggregated by gender and blood groups types within each gender category. The model validation involved utilising actual blood donation data from 2019 and 2020. The model's performance was evaluated through the Mean Absolute Percentage Error (MAPE), uncovering expected and notable discrepancies during the Covid-19 pandemic period only. Results Blood group O had the highest monthly yield mean of 1507.85 and 1230.03 blood units for male and female donors, respectively. The top-down forecasting proportions (TDFP) under ARIMA, with a MAPE value of 11.30, was selected as the best approach and the model was then used to forecast future blood donations. The blood donation predictions for 2019 had a MAPE value of 14.80, suggesting alignment with previous years' donations. However, starting in April 2020, the Covid-19 pandemic disrupted blood collection, leading to a significant decrease in blood donation and hence a decrease in model accuracy. Conclusions The gradual decrease in future blood donations exhibited by the predictions calls for blood authorities in Zimbabwe to develop interventions that encourage blood donor retention and regular donations. The impact of the Covid-19 pandemic distorted the blood donation patterns such that the developed model did not capture the significant drop in blood donations during the pandemic period. Other shocks such as, a surge in global pandemics and other disasters, will inevitably affect the blood donation system. Thus, forecasting future blood collections with a high degree of accuracy requires robust mathematical models which factor in, the impact of various shocks to the system, on short notice.

Background. Blood cannot be artificially manufactured, and there is currently no substitute for human blood. The supply of blood in transfusion facilities requires constant and timely collection of blood from donors. Modeling and forecasting trends in blood collections are critical for determining both the current and future capacity requirements and appropriate models of adequate blood provision. Objectives. The objective of this study is to determine blood collection or donation patterns and develop time-series models that can be updated and refined in predicting future blood donations in Zimbabwe when given the historical data. Materials and Methods. Monthly blood donation data for the period 2009 to 2019 were collected retrospectively from the National Blood Service Zimbabwe database. Time-series models (i.e., the Seasonal Autoregressive Integrated Moving Average [SARIMA] and Error, Trend and Seasonal [ETS]) models were applied and compared. The models were chosen because of their ability to handle the seasonality and other time-series components evident in the blood donation data. Expert opinions and experience were used in selecting the models and in making inferences in the analysis. Results. Time-series plots of blood donations showed seasonal patterns, with significant drops in blood donations in months associated with Zimbabwe’s school holidays (April, August, and December) and public holidays. During these holidays, there is a reduced number of school donors, while at about the same time, there is increasing blood demand as a result of road accidents. Model identification procedures established the SARIMA ( 1 , 1 , 2 ) ( 0 , 1 , 1 ) 12 model as the appropriate model for forecasting total blood donation in Zimbabwe. The results and forecasts show an upward trend in blood donations. According to the accuracy measures used, the SARIMA model outperforms the ETS model. Conclusions. Expert knowledge in the blood donation process, coupled with statistical models, can help explain trends exhibited in blood donation data in Zimbabwe. These findings help the blood authorities plan for blood donor campaign drives. The findings are key indicators of where to allocate more resources toward blood donation and when to collect more blood units. The increasing blood donation projections ensure a stable blood bank inventory in the near future. Highlights A SARIMA model can be used to predict the flow of blood donations in Zimbabwe. The seasonal blood donation pattern peaks in the months of March, June/July, and September. The donations troughs are in the months of April, August, December, and January. These are the months coinciding with school holidays in Zimbabwe. Both the SARIMA and ETS models provided similar forecasts, but measures of fit and expert knowledge gave a slight preference to the SARIMA ( 1 , 1 , 2 ) ( 0 , 1 , 1 ) 12 model in predicting the flow of blood donations in Zimbabwe. These model results are useful for guiding allocation of blood donation resources and blood donation drive timing.

In both developed and developing nations, with South Africa (SA) being one of the latter, the motor vehicle industry is one of the most important sectors. The SA automobile industry was not unaffected by the 2007/2008 global financial crisis (GFC). This study aims to assess the impact of the GFC on new car sales in SA through statistical modeling, an impact that has not previously been investigated or quantified. The data obtained indicate that the optimal model for assessing the aforementioned impact is the SARIMA (0,1,1)(0,0,2)12 model. This model’s suitability was confirmed using Akaike information criterion (AIC) and Bayesian information criterion (BIC), as well as the root mean square error (RMSE) and the mean absolute percentage error (MAPE). An upward trend is projected for new car sales in SA, which has positive implications for SA and its economy. The projections indicate that the new car sales rate has increased and has somewhat recovered, but it has not yet reached the levels expected had the GFC not occurred. This shows that SA’s new car industry has been negatively and severely impacted by the GFC and that the effects of the latter still linger today. The findings of this study will assist new car manufacturing companies in SA to better understand their industry, to prepare for future negative shocks, to formulate potential policies for stocking inventories, and to optimize marketing and production levels. Indeed, the information presented in this study provides talking points that should be considered in future government relief packages.

We modelled the mean annual rainfall for data recorded in Zimbabwe from 1901 to 2009. Extreme value theory was used to estimate the probabilities of meteorological droughts. Droughts can be viewed as extreme events which go beyond and/or below normal rainfall occurrences, such as exceptionally low mean annual rainfall. The duality between the distribution of the minima and maxima was exploited and used to fit the generalised extreme value distribution (GEVD) to the data and hence find probabilities of extreme low levels of mean annual rainfall. The augmented Dickey Fuller test confirmed that rainfall data were stationary, while the normal quantile-quantile plot indicated that rainfall data deviated from the normality assumption at both ends of the tails of the distribution. The maximum likelihood estimation method and the Bayesian approach were used to find the parameters of the GEVD. The Kolmogorov-Smirnov and Anderson-Darling goodness-of-fit tests showed that the Weibull class of distributions was a good fit to the minima mean annual rainfall using the maximum likelihood estimation method. The mean return period estimate of a meteorological drought using the threshold value of mean annual rainfall of 473 mm was 8 years. This implies that if in the year there is a meteorological drought then another drought of the same intensity or greater is expected after 8 years. It is expected that the use of Bayesian inference may better quantify the level of uncertainty associated with the GEVD parameter estimates than with the maximum likelihood estimation method. The Markov chain Monte Carlo algorithm for the GEVD was applied to construct the model parameter estimates using the Bayesian approach. These findings are significant because results based on non-informative priors (Bayesian method) and the maximum likelihood method approach are expected to be similar. KEYWORDS: minima; return level; mean annual rainfall; Bayesian approach; severe meteorological drought

Cryptocurrencies are said to be very risky, and so are the currencies of emerging economies, including the South African rand. The steady rise in the movement of South Africans’ investments between the rand and BitCoin warrants an investigation as to which of the two currencies is riskier. In this paper, the Generalised Pareto Distribution (GPD) model is employed to estimate the Value at Risk (VaR) and the Expected Shortfall (ES) for the two exchange rates, BitCoin/US dollar (BitCoin) and the South African rand/US dollar (ZAR/USD). The estimated risk measures are used to compare the riskiness of the two exchange rates. The Maximum Likelihood Estimation (MLE) method is used to find the optimal parameters of the GPD model. The higher extreme value index estimate associated with the BTC/USD when compared with the ZAR/USD estimate, suggests that the BTC/USD is riskier than the ZAR/USD. The computed VaR estimates for losses of$0.07, $ 0.09, and$0.16 per dollar invested in the BTC/USD at 90%, 95%, and 99% compared to the ZAR/USD’s $ 0.02,$0.02, and $ 0.03 at the respective levels of significance, confirm that BitCoin is riskier than the rand. The ES (average losses) of$0.11, $ 0.13, and$0.21 per dollar invested in the BTC/USD at 90%, 95%, and 99% compared to the ZAR/USD’s $ 0.02,$0.02, and $ 0.03 at the respective levels of significance further confirm the higher risk associated with BitCoin. Model adequacy is confirmed using the Kupiec test procedure. These findings are helpful to risk managers when making adequate risk-based capital requirements more rational between the two currencies. The argument is for more capital requirements for BitCoin than for the South African rand.

In this paper, a hybrid of a Wavelet Decomposition–Generalised Auto-Regressive Conditional Heteroscedasticity–Extreme Value Theory (WD-ARMA-GARCH-EVT) model is applied to estimate the Value at Risk (VaR) of BitCoin (BTC/USD) and the South African Rand (ZAR/USD). The aim is to measure and compare the riskiness of the two currencies. New and improved estimation techniques for VaR have been suggested in the last decade in the aftermath of the global financial crisis of 2008. This paper aims to provide an improved alternative to the already existing statistical tools in estimating a currency VaR empirically. Maximal Overlap Discrete Wavelet Transform (MODWT) and two mother wavelet filters on the returns series are considered in this paper, viz., the Haar and Daubechies (d4). The findings show that BitCoin/USD is riskier than ZAR/USD since it has a higher VaR per unit invested in each currency. At the 99% significance level, BitCoin/USD has average values of VaR of 2.71% and 4.98% for the WD-ARMA-GARCH-GPD and WD-ARMA-GARCH-GEVD models, respectively; and this is slightly higher than the respective 2.69% and 3.59% for the ZAR/USD. The average BitCoin/USD returns of 0.001990 are higher than ZAR/USD returns of −0.000125. These findings are consistent with the mean-variance portfolio theory, which suggests a higher yield for riskier assets. Based on the p-values of the Kupiec likelihood ratio test, the hybrid model adequacy is largely accepted, as p-values are greater than 0.05, except for the WD-ARMA-GARCH-GEVD models at a 99% significance level for both currencies. The findings are helpful to financial risk practitioners and forex traders in formulating their diversification and hedging strategies and ascertaining the risk-adjusted capital requirement to be set aside as a cushion in the event of the occurrence of an actual loss.

Sales forecasting is a crucial aspect of any successful manufacturing organisation as it provides the foundation for investment, employment development, and innovation. The Global Financial Crisis (GFC) had a negative impact on the manufacturing sector in South Africa (SA) and the rest of the world. The objective of this paper is to analyse the trend of manufacturing sales before, during, and after the GFC and to quantify the impact of the GFC on the total manufacturing sales in SA. The time-series-based Box-Jenkins methodology is used to achieve the objective. The study used Statistic South Africa's data on monthly total manufacturing sales in SA from January 1998 to December 2022. Total manufacturing sales exhibit strong seasonality. The ACF, PACF, and EACF plots, as well as the AIC, BIC, RMSE, and MAE, suggest the SARIMA(2,1,2)(2,1,1)12 model as the best model for explaining and forecasting manufacturing sales in SA. The SA manufacturing sector was negatively impacted by the GFC, as evidenced by the comparison between actual data and projections based on a historical path prior to the GFC. Manufacturing sales are recovering from the GFC but have not reached potential levels that could have been achieved without the crisis. The SA manufacturing sector may take time to reach the expected/projected sale levels that could have been achieved in the absence of the GFC.