Predicting the loss to follow-up of HIV-infected patients on ART in a rural area in South Africa using generalized gamma distributions

Background - Long-term regular follow-up and high retention are the anticipated outcomes for the wellness and longevity of HIV/AIDS patients on antiretroviral treatment. However, these anticipated outcomes are marred by patient loss to follow-up (LTFU) which is currently exacerbated by the COVID-19 pandemic. This study aims to determine the prevalence and predictors of LTFU among HIV/AIDS patients on ART at two rural district hospitals in South Africa. Methods — This is an observational study whereby a cohort of HIV/AIDS patients was retrospectively followed from 2010 to 2017 until loss to follow-up occurred or until the end of the observation period at Carolina and Embhuleni hospitals. A study was undertaken among children, adolescents and adults living with HIV/AIDS and attending ART clinic between January 1, 2010 and June 30, 2017. Loss to follow up was defined as not taking an ART refill for a period of 90 days or longer from the last attendance for refill and not yet classified as ‘dead’ or ‘transferred - out’ . Patient information was obtained from the routine hospitals’ records, and the data were analysed using Generalized gamma distribution to identify the predictors of loss to follow-up among HIV/AIDS patients while Kaplan-Meier model was used to estimate and compare the LTFU survival probabilities of heterogenous groups among the patients. [HR: 2.9 CI;(1.3 – 6.4)], regimen EFV+3TC+TDF [HR: 10.0 CI;(3.9 – 25.9)], regimen NVP+3TC+TDF [HR: 10.6 CI;(1.8 – 62.4)], follow up CD4 [HR: 1.0 CI;(1.0 – 1.0)], log(follow up viral load) [HR: 0.8 CI;(0.7 – 0.9)], marital status (married) [HR: 0.4 CI;(0.3 – 0.8)], marital status (cohabitation) [HR: 0.6 CI;(0.3 – 0.9)], ART adherence (fair) [HR: 2.4 CI;(1.3 – 3.4)], ART adherence (good) [HR: 4.6 CI;(2.2 – 9.5)] and age [HR: 1.02 CI;(1.0 – 1.04)]. Discussion — Effective control and tracing measures in the at-risk population and in defaulters need to be stepped up especially during this COVID-19 pandemic period, to improve retention in hospitals. There is also need for careful adherence counseling and assessment of medication supplies. Conclusion — LTFU is more pronounced among females and is highest among adolescents. Patients with increased risk for LTFU were consistent with ART regimens, viral load, age, CD4 count, adherence and marital status.


Background
HIV/AIDS has been a major health problem worldwide for more than three decades now.
According to the UNAIDS global statistics; since the beginning of the epidemic, 75.7 million people have been infected with the HIV virus, about 32.7 million people have died of HIV and 38 million people were living with HIV at the end of 2019. According to Avert (2018), South Africa has the biggest and most high-profile HIV epidemic in the world, with estimated 7.7 million living with HIV in 2019. South Africa's Mpumalanga province has the second highest HIV prevalence rate after KwaZulu-Natal province. Gert Sibande district which is in Mpumalanga province is leading all districts in the country with 46.1% HIV prevalence rate (Motsoaledi, 2013). Gert Sibande district has Albert Luthuli as one of its municipalities whose HIV prevalence stood at 43.2% (Nkosi, 2017). HIV prevalence in South Africa currently stands at 20.4% (Avert, 2018).
The ART treatment has shown promising results in the reduction of HIV transmission and in HIV/AIDS related morbidity and mortality. According to WHO report, ART has prevented an consequences, such as discontinuation of treatment, drug toxicity, treatment failure due to poor adherence and drug resistance (Kaplan et al., 2000;Taiwo, 2009). The LTFU results in an increased risk of death of up to 40% as in studies of patients LTFU in sub-saharan Africa (Chammartin et al., 2018 ;Brinkhof et al., 2009). It is essential to understand how and why people drop out of treatment programmes, since the retention of people on ART and ensuring adherence to treatment are critical determinants of successful long-term outcomes (Berheto et al., 2014  The variables which form part of the routine hospital records in Albert Luthuli municipality were used in this study and are described as follows. Loss to follow-up (LTFU) status is the dependent variable for the study. It was recorded in terms of LTFU status (yes, no) and time until its onset.

Study design and setting
The categorical independent variables were gender, hospital (Carolina, Embhuleni), WHO stage (1,2,3,4), HIV disclosure (yes, no), marital status (single, married, cohabitation, widowed/divorced), treatments (regimen 1)(NVP+D4T+3TC, EFV+D4T+3TC, EFV+AZT+3TC, EFV+3TC+TDF and NVP+3TC+TDF) and ART adherence (poor, fair, good). The continuous independent variables for the study except for age were classified into baseline and follow-up variables were mass, CD4 cell count, haemoglobin, lymphocyte, white blood cell count, viral load, creatinine, total protein, sodium and alanine transaminase. The cohort for this study was made up of children, adolescents and adults as in Moshago et al. (2014), however, it is recommended to have cohorts made up of participants with ages from 16 years and above as in most retrogressive follow-up studies. Diabetes and hypertension were excluded because their records were found in very few patient files. HIV/AIDS patients with missing essential records such as ART regimen, gender and date of birth or age were excluded from the study.

Sample size and sampling procedure
Sample size was determined by using sample size calculation formula for survival analysis by considering the following assumptions on HIV-infected patients: an average of 14.8% prevalence rate of LTFU among ART naïve patients (Seifu et al., 2018), 5% precision or margin error, 95% level of confidence interval and 0.45 loss (Damtew et al., 2015). The sample size which was calculated using the formula = 2 (1− ) 2 , (Eneyew et al., 2016), where N = sample size, Z = 1.96 (critical value at 95% level of confidence), p = proportion of LTFU and = type-1 error (0.05) was 357. The estimated total sample size was proportionally and randomly allocated to the two study sites (Embhuleni and Carolina hospitals with proportions of 79% and 21% respectively) and according to the age and gender proportions.

Ethical considerations
The ethical approval for this study was granted by UNISA Ethics Review Committee with the approval number being 2017/SSR ERC/005. The permission to conduct the study at Carolina and Embhuleni hospitals was obtained from Mpumalanga Department of Health with the permission number being MP_201708_013. All data related to the patients were handled with utmost confidentiality in all the stages of the research. In addition, no reference to an individual respondent was made as all results were handled in aggregate format. The electronic documents carrying confidential information on patients are all protected by some encryption and will be destroyed as per research policy.

Determination of loss to follow up status
Loss to follow up was defined as not taking an ART refill for a period of 90 days or longer from the last attendance for refill and not yet classified as 'dead' or 'transferred-out' (Seifu et al., 2018).
Patients who after meeting the criterion for LTFU came for refilling would be treated as patients attending the clinic for the first time.

Exploratory data analysis
Of the 357 patients, 60.5% were females. The mean (SD) age of the cohort was 36.2 (14.1), 15.4

Fitting the Weibull distribution
The best fitting model was obtained by using the goodness-of-fit criteria as shown in Table 2. Table 2 shows AIC, AICc, BIC and log likelihood statistics for the four parametric models which were applied to the survival data. These goodness of fit criteria were used to select the best fitting parametric model. According to these criteria, the Weibull model achieved the lowest AIC, AICc and log likelihood values and was therefore the best model for predicting LTFU among HIV/AIDS patients on ART.     Key: Reference levels: 'NVP+D4T+3TC' for Treatment (Regimen 1); 'Poor' for ART adherence, 'Single' for marital status up CD4 is positively associated with LTFU and clinically significant, it does not have a statistical impact on LTFU. An increase in follow-up viral load among the patients has the effect of decreasing the hazard to LTFU by about 20%, and this effect can be as low as 30% to 7%. Being married and being in cohabitation relative to being single, each has the effect of decreasing the hazard to LTFU by about 0.4 times and 0.6 times respectively. Lastly, an increase in the age of a patient by one year has the effect of increasing the hazard to LTFU by about 1.02 times, and this effect can be as high as 1.04 times to 1 times.

Nonparametric inferences about the survivor functions
The cohort of HIV+ terminal patients in this study is not homogeneous with respect to their characteristics that may affect their survival from LTFU. Hence, it will be necessary to test the equality of survivor functions among groups (strata) of patients. The function 'survdiff()' was used to test for the differences in survival between two groups using a log-rank test. Log-rank tests and the Kaplan-Meier functions presented in this section are for ART treatments, ART adherence, Follow-up CD4, Follow-up viral load, Marital status and age.
The parametric plots for all modelled covariates ( figure 1 to figure 6) approximate K-M plots meticulously for high LTFU survival probabilities (above 50%), while for low LTFU survival probabilities (below 50%), all the three parametric plots ( Weibull, Exponential and Generalized gamma) deviate significantly from the associated K-M plots. In addition, the Weibull plots for all the modelled covariates approximate the K-M plots better than Exponential and Generalized gamma distributions.

Kaplan-Meier survival functions
The K-M plot (Figure 1) shows that regimens EFV+3TC+TDF and NVP+3TC+TDF are associated with higher probability of LTFU than EFV+D4T+3TC and EFV+AZT+3TC whose survival probabilities from LTFU are above 90%. The treatment groups are significantly different as the log rank p-value is less than 0.05. The marital status groups as shown in figure 2 are significantly different as depicted by the log rank p-value (0.0014).
Married and cohabitating patients relative to single patients survive LTFU better.
As shown in Figure 3, patients with good or fair ART adherence are more likely to get lost to follow-up than patients with poor ART adherence.
The groups of patients according to ART adherence are statistically different (log rank p-value =0.0000).
CD4 and viral load were categorised as done in the standard Laboratory report in South African hospitals. Figure 4 shows that survivor functions for Follow-up viral load are statistically different at 0.05 significance level (log rank p-value=0.0000) and this confirms that Follow-up viral load strata are associated with LTFU hazard. Figure 5 shows that survivor functions for Follow-up CD4 are statistically different at 0.05 significance level (log rank p-value = 0.0000) and this confirms that CD4 strata are associated with LTFU hazard.
Lastly, in Figure 6, the survivor functions for Age are marginally not statistically different at 0.05 significance level (log rank p-value = 0.0576) and this confirms that Age strata are statistically marginally not associated with LTFU hazard. As shown in Figure 3, patients with good or fair ART adherence are unexpectedly more likely to get lost to follow-up than patients with poor ART adherence. The implication is that patients who fully adhere to the use of ART drugs are the once who are more likely to get lost to follow-up.
Could this be the case, then the highly probable culprit drugs could be EFV+3TC+TDF and NVP+3TC+TDF as shown in Figure 1. As shown in Figure 6 Lastly, Nakhaee and Law (2011) used four parametric survival models (exponential, Weibull, lognormal and log-logistic) for survival analysis of HIV/AIDS patients in Australia, and the Weibull model just as in this study, was found to be the best parametric model. Although the Cox model is frequently used in survival analysis, parametric models may fit data better and give more precise estimates of the quantities of interest (Hamidi et al., 2017).

Conclusion
Patients with increased risk for LTFU were consistent with ART regimens, viral load, age, CD4 count, adherence and marital status. The identification of the patients at risk to LTFU at an early stage helps in putting control mechanisms in place before LTFU goes out of hand. Stringent measures are supposed to be employed to curtail LTFU, especially during this COVID-19 pandemic period.     Kaplan Meier and parametric plots for estimated probabilities for the association bet ween ART adherence and loss to follow up Kaplan Meier and parametric plots for estimated probabilities for the association between viral load and loss to follow up  Kaplan Meier and parametric plots for estimated probabilities for the association between age group and loss to follow up