Short-term forecasting of COVID-19 using support vector regression: An application using Zimbabwean data.

BACKGROUND: This study aims to show that including pairwise hierarchical interactions of covariates and combining forecasts from individual models improves prediction accuracy. METHODS: The least absolute shrinkage and selection operator via hierarchical pairwise interaction is used in selecting variables that are not correlated and with the greatest predictive power in single forecast models (Gradient boosting method [GBM], Generalized additive models [GAMs], Support vector regression [SVR]) are used in the analysis. The best model was selected based on the mean absolute error (MAE), the best key performance indicator for skewed data. Forecasts from the 5 models were combined using linear quantile regression averaging (LQRA). Box and Whiskers plots are used to diagnose the overall performance of fitted models. RESULTS: Single forecast models (GBM, GAMs, and SVRs) show that including pairwise interactions improves forecast accuracy. The SVR model with interactions based on the radial basis kernel function is the best from single forecast models with the lowest MAE. Combining point forecasts from all the single forecast models using the LQRA approach further reduces the MAE. However, based on the Box and Whiskers plot, the SVR model with pairwise interactions has the smallest range. CONCLUSIONS: Based on the key performance indicators, combining predictions from several individual models improves forecast accuracy. However, overall, the SVM with pairwise hierarchical interactions outperforms all the other models.

ARIMA model in predicting of COVID-19 epidemic for the Southern Africa region

Background: Coronavirus pandemic, a serious global public health threat, affects the Southern African countries more than any other country on the continent. The region has become the epicenter of the coronavirus with South Africa accounting for the most cases. To cap the deadly effect caused by the pandemic, we apply a statistical modelling approach to investigate and predict COVID-19 incidence. Methods: Using secondary data on the daily confirmed COVID-19 cases per million for Southern Africa Development Community (SADC) member states from March 5, 2020, to July 15, 2021, we model and forecast the spread of coronavirus in the region. We select the best ARIMA model based on the log-likelihood, AIC, and BIC of the fitted models. Results: The ARIMA (11,1,11) model for the complete data set was finally selected among ARIMA models based upon the parameter test and the Box­Ljung test. The ARIMA (11,1,9) was the best candidate for the training set. A 15-day forecast was also made from the model, which shows a perfect fit with the testing set. Conclusion: The number of new COVID-19 cases per million for the SADC shows a downward trend, but the trend is characterized by peaks from time to time. Tightening up of the preventive measures continuously needs to be adapted in order to eradicate the coronavirus epidemic from the population.

Short-term forecasting of confirmed daily COVID-19 cases in the Southern African Development Community region.

Background: The coronavirus pandemic has resulted in complex challenges worldwide, and the Southern African Development Community (SADC) region has not been spared. The region has become the epicentre for coronavirus in the African continent. Combining forecasting techniques can help capture other attributes of the series, thus providing crucial information to address the problem. Objective: To formulate an effective model that timely predicts the spread of COVID-19 in the SADC region. Methods: Using the Quantile regression approaches; linear quantile regression averaging (LQRA), monotone composite quantile regression neural network (MCQRNN), partial additive quantile regression averaging (PAQRA), among others, we combine point forecasts from four candidate models namely, the ARIMA (p, d, q) model, TBATS, Generalized additive model (GAM) and a Gradient Boosting machine (GBM). Results: Among the single forecast models, the GAM provides the best model for predicting the spread of COVID-19 in the SADC region. However, it did not perform well in some periods. Combined forecasts models performed significantly better with the MCQRNN being the best (Theil's U statistic=0.000000278). Conclusion: The findings present an insightful approach in monitoring the spread of COVID-19 in the SADC region. The spread of COVID-19 can best be predicted using combined forecasts models, particularly the MCQRNN approach.

Effects of Antiretroviral Therapy on CD4+ Cell Count, HIV Viral Load and Death in a South African Cohort: A Modelling Study.

BACKGROUND AND OBJECTIVE: Combination antiretroviral therapy (cART) has improved the survival of HIV infected patients significantly. However, in some patients, survival is not guaranteed due to several factors that are either individual-based or cART based. This study presents an HIV, AIDS, Death (HAD) model to analyse the survival of patients on cART. MATERIALS AND METHODS: Continuous-time Markov models are fitted based on the states occupied for an HIV, AIDS and Death (HAD) model. These states are based on CD4 cell count. Factors that affect the survival of HIV-infected patients on cART are also analyzed. These, among others, include age, gender, routinely collected viral load, time on treatment, non-adherence and peripheral neuropathy. RESULTS: Patients with higher viral loads than expected are 11.1 times more likely to be at risk of HIV progression to the AIDS state and 1.1 times more likely to be at risk of mortality from a CD4 cell count state above 200 cell/mm3compared to patients with lower viral loads. Non-adherence to treatment increases the risk of transition from CD4 cell count state above 200 cell/mm3 to the AIDS state by 2.2 folds. Patients who were non-adherent to treatment are 3.8 times more likely to transit from the CD4 state above 200 cell/mm3 to death compared to patients who were adherent to treatment. Patients are expected to recover from the AIDS state after one year of treatment. CONCLUSIONS: Recovery from AIDS state by HIV infected patients on cART is likely to occur after one year of cART treatment. However, if the viral load remains higher than expected, this increases risks of immune deterioration even after having achieved normal CD4 cell counts and consequently, mortality risks are increased.

A superiority of viral load over CD4 cell count when predicting mortality in HIV patients on therapy.

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.

Correction to: A Markov Model to Estimate Mortality Due to HIV/AIDS Using Viral Load Levels-Based States and CD4 Cell Counts: A Principal Component Analysis Approach.

In the original publication, the following text was missing from the beginning of the Methods section in the main text "This study uses similar methods to those previously published.

A Markov Model to Estimate Mortality Due to HIV/AIDS Using Viral Load Levels-Based States and CD4 Cell Counts: A Principal Component Analysis Approach.

INTRODUCTION: Improvement of health in human immunodeficiency virus/acquired immunodeficiency syndrome (HIV/AIDS) patients on antiretroviral therapy (ART) is characterised by an increase in CD4 cell counts and a decrease in viral load to undetectable levels. In modelling HIV/AIDS progression in patients, researchers mostly deal with either viral load levels only or CD4 cell counts only, as they expect these two variables to be collinear. In this study, both variables will be in one model. METHODS: Principal component variables are created by fitting a regression model of CD4 cell counts on viral load levels to improve the efficiency of the model. The new orthogonal covariate is included to represent the CD4 cell counts covariate for the continuous time-homogeneous Markov model defined. Viral load levels are categorised to define the states for the Markov model. RESULTS: The likelihood ratio test and the estimated AICs show that the model with the orthogonal CD4 cell counts covariate gives a better prediction of mortality than the model in which the covariate is excluded. The study further revealed high accelerated mortality rates from undetectable viral load levels as well as accelerated risks of viral rebound from undetectable viral level for patients with lower CD4 cell counts than expected. CONCLUSION: Inclusion of both viral load levels and CD4 cell counts, monitoring and management in time homogeneous Markov models help in the prediction of mortality in HIV/AIDS patients on ART. Higher CD4 cell counts improve the health and consequently survival of HIV/AIDS patients.

Determinants of viral load rebound on HIV/AIDS patients receiving antiretroviral therapy: results from South Africa.

BACKGROUND: Antiretroviral therapy (ART) has become the standard of care for patients with HIV infection in South Africa and has led to the reduction in AIDS related morbidity and mortality. In developing countries, the nucleosides reverse transcriptase inhibitors (NRTIs) class are widely used because of their low production costs. However patients treated with NRTIs develop varying degree of toxicity after long-term therapy. For this study patients are administered with a triple therapy of two NRTIs and one non-nucleoside reverse transcriptase inhibitor (NNRTI). METHOD: In this study the progression of HIV in vivo is divided into some viral load states and a continuous time-homogeneous model is fitted to assess the effects of covariates namely gender, age, CD4 baseline, viral load baseline, lactic acidosis, peripheral neuropathy, non-adherence and resistance to treatment on transition intensities between the states. Effects of different drug combinations on transition intensities are also assessed. RESULTS: The results show no gender differences on transition intensities. The likelihood ratio test shows that the continuous time Markov model for the effects of the covariates including combination give a significantly better fit to the observed data. From almost all states, rates of viral suppression were higher than rates of viral rebound except for patients in state 2 (viral load between 50 and 10,000 copies/mL) where rates of viral rebound to state 3 (viral load between 10,000 and 100,000 copies/mL) were higher than rates of viral suppression to undetectable levels. For this transition, confidence intervals were very small. This was quite notable for patients who were administered with AZT-3TC-LPV/r and FTC-TDF-EFV. Although patients on d4T-3TC-EFV also had higher rates of viral rebound from state 2 than suppression, the difference was not significant. CONCLUSION: From these findings, we can conclude that administering of any HIV drug regimen is better when based on the viral load level of an HIV+ patient. Before initiation of treatment, patients should be well equipped on how antiretroviral drugs operate including possibilities of toxicity in order to reduce chances of non-adherence to treatment. There should also be a good relationship between patient and health-care-giver to ensure proper adherence to treatment. Uptake of therapy by young patients should be closely monitored by adopting pill counting every time they come for review.

Time-homogeneous Markov process for HIV/AIDS progression under a combination treatment therapy: cohort study, South Africa.

BACKGROUND: As HIV enters the human body, its main target is the CD4 cell which it turns into a factory that produces millions of other HIV particles. These HIV particles target new CD4 cells resulting in the progression of HIV infection to AIDS. A continuous depletion of CD4 cells results in opportunistic infections, for example tuberculosis (TB). The purpose of this study is to model and describe the progression of HIV/AIDS disease in an individual on antiretroviral therapy (ART) follow up using a continuous time homogeneous Markov process. A cohort of 319 HIV infected patients on ART follow up at a Wellness Clinic in Bela Bela, South Africa is used in this study. Though Markov models based on CD4 cell counts is a common approach in HIV/AIDS modelling, this paper is unique clinically in that tuberculosis (TB) co-infection is included as a covariate. METHODS: The method partitions the HIV infection period into five CD4-cell count intervals followed by the end points; death, and withdrawal from study. The effectiveness of treatment is analysed by comparing the forward transitions with the backward transitions. The effects of reaction to treatment, TB co-infection, gender and age on the transition rates are also examined. The developed models give very good fit to the data. RESULTS: The results show that the strongest predictor of transition from a state of CD4 cell count greater than 750 to a state of CD4 between 500 and 750 is a negative reaction to drug therapy. Development of TB during the course of treatment is the greatest predictor of transitions to states of lower CD4 cell count. Transitions from good states to bad states are higher on male patients than their female counterparts. Patients in the cohort spend a greater proportion of their total follow-up time in higher CD4 states. CONCLUSION: From some of these findings we conclude that there is need to monitor adverse reaction to drugs more frequently, screen HIV/AIDS patients for any signs and symptoms of TB and check for factors that may explain gender differences further.