Analysing lapsing rates among first-time blood donors at a blood centre in Zimbabwe using survival analysis.

Introduction: blood centres are often faced with the problem of donor lapsing resulting in loss of donors from the already strained donor pool. In Zimbabwe, 70% of the donated blood comes from younger donors aged 40 years and below, who at the same time, have high attrition rates. This study seeks to apply the concept of survival analysis in analysing blood donor lapsing rates. Methods: in analysing the donor lapsing and retention rates, data on 450 first-time blood donors at the National Blood Service Zimbabwe, in Harare´s blood bank for the period 2014 to 2017 was extracted from the donors´ database. The Cox proportional hazards (Cox PH) and Kaplan-Meier methods were applied in the analysis. Donor demographic characteristics suspected of having effect on donor lapsing and retention were identified and analysed. Results: the study findings show that 56.9% of the donors had lapsed by the end of the four-year study period. Results from the multiple Cox PH model indicate that donor age had a significant effect on blood donor retention time (p = 0.000918 < 0.05). The hazard ratio (HR) = 0.615 with 95% CI: (0.461; 0.820) shows that the relatively older donors had a lower hazard (38.5% lower) of lapsing compared to the hazard for younger donors. The effect of gender, blood donor group and donation time interval on donor retention and attrition were not statistically significant. Male donors had HR = 1.03; 95% CI (0.537; 1.99) with (p = 0.922 > 0.05) and donors with a 4-month interval between donations had HR = 1.31; 95% CI (0.667; 2.59) with (p = 0.430 > 0.05). Conclusion: the study confirmed the problem of donor attrition faced by blood centres. The age of the donor had a significant effect on the retention time of blood donors before lapsing. The older the blood donor, the lower the risk of lapsing. The Zimbabwe National Blood Service (NBSZ) Blood Centre authorities should have a critical mass of individuals above 40 years as potential blood donors because of their reliability in blood donation according to the study findings.

Blood donation projections using hierarchical time series forecasting: the case of Zimbabwe's national blood bank.

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.

The Impact of Age Group in Hierarchical Forecasting of Monthly Blood Donations in Zimbabwe.

Background: To meet the blood requirements for transfusion therapy, blood banks need to ensure that blood inventories are maintained at desirable levels. There is a rising global need for optimal ways to manage blood supply and demand using statistical models in blood inventory planning and management. Thus, blood donation forecasting using donor-specific characteristics such as donor type and age is critical in managing the blood bank inventory. Methods: The monthly blood donation data covering the period 2007 to 2018, collected from the National Blood Service Zimbabwe (NBSZ) was used in this study. The data is first disaggregated based on donor age, and further disaggregation is performed for each age group based on donor type. The hierarchical forecasting approaches, namely the bottom-up, top-down and the optimal combination methods were used in the data analysis. The Error-Trend-Seasonality (ETS) and Autoregressive Integrated Moving Average (ARIMA) methods are used in the hierarchical forecasting approaches to generate the forecasts. Results: New blood donors account for more than 55% of blood donations in Zimbabwe. The younger donors (16-29 years) dominate the blood donations, accounting for 89.2% of the donations. Young and new donors account for nearly 50% of the donations. The middle-aged and older donors have lower blood donations. The bottom-up approach under the ARIMA model outperformed all the other approaches. The future projections show that new and young donors will increase in blood donations, regular donations will decline slightly while the occasional donations are projected to remain constant. Conclusion: Hierarchical forecasting is a unique approach in that the different aggregation levels reveal important features of the blood donation data. The lower percentage of regular donations is worrisome to blood authorities as it points to new blood donors not returning for further donations. Blood authorities need to develop policies that will encourage new and young donor categories to become regular donors.

Application of Time-Series Analysis and Expert Judgment in Modeling and Forecasting Blood Donation Trends in Zimbabwe.

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.

A Markov jump process approach to modeling blood donor status: Donor retention and attrition rates at a blood service center in Zimbabwe.

Background: Blood service agencies depend upon the availability of regular blood donors for sustainability. The knowledge and understanding of the stochastic behavior of donors is the first step toward sustaining the blood supply. Analyzing the changes in the donor status within the donor pool will help the blood service authorities to manage the blood donation process. Objectives: The study presents a multistate Markov jump model in analyzing the changes in blood donor status during their blood donation career. Relevant covariates are used to aid in explaining the transitions. Materials and Methods: The status of a blood donor i that can be in one of four states S = {1; 2; 3; 4}. A new donor (s = 1), repeat/regular donor (s = 2), occasional donor (s = 3), and lapsed donor (s = 4). A Continuous-time Markov model was used to estimate blood donor progression during their blood donation career. Frequencies of blood donations made in a given time interval determines the state occupied. Results: In the early years of blood donation career, first-time donors have a higher likelihood of becoming regular donors. Donor attrition increases with time whilst donor retention decreases with time. The results show that when the jump process is currently in an occasional state, the probability that it moves into lapsed state when it leaves the occasional state is given as 69.06%. Similarly, donors are forecasted to spend 21.193 months (1.8 years) in the occasional state before lapsing. Repeat donors can spend 39.342 months (3.3 years) in the regular state before the transition to other states. The study established that donor-specific demographic factors such as age and gender are critical in donor status transitions. Conclusions: With the passage of time, donor status evolves, with trend inclined towards reduction in the frequency of blood donations as more donors become inactive or lapsed. The transition of donors in various states can be described by a time homogeneous Markov model.

Analysing and quantifying the effect of predictors of stroke direct costs in South Africa using quantile regression.

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.

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.