Accelerated failure time modelling of Tuberculosis predictors in HIV/AIDS patients in Albert Luthuli Municipality of South Africa

Background: Tuberculosis (TB) is one of the most common opportunistic diseases and leading cause of death among Human immunodeficiency virus and acquired immune deficiency syndrome (HIV/AIDS) patients. There has been a drastic rise of TB infection associated with the pandemic occurrence of HIV/AIDS infection in South Africa and other resource-limited countries world-wide. South Africa faces an immense burden on health care systems posed by diagnostic and therapeutic challenges resulting from the concomitant HIV and TB epidemics. This study aimed to determine the prevalence and the factors associated with TB and HIV coinfection for patients attending clinical care at rural public health facilities in Albert Luthuli municipality of South Africa. Methods : A cohort of HIV/AIDS patients was retrospectively followed from inception in 2010 to 2017 until TB was diagnosed or until the end of the study. Accelerated Failure Time (AFT) model was used to analyse survival data on HIV/AIDS patients. Factors associated to TB were modelled using log-logistic AFT model and further analysis of the significant factors was done using Kaplan-Meier, log-rank and hazard ratios. Results : From 357 HIV/AIDS patients, 65 patients (18.2%) had TB. Out of the 65 HIV/AIDS patients with TB, 15 (23.1%) of them died. Thus, of the 41 HIV/AIDS patients who died during the follow-up period, 15 of them (36.6%) had TB. Log-logistic AFT model determined factors associated with TB at significance level of 0.05 as: hospital, WHO stage, treatment (regimen 1), ART adherence, follow-up CD4 count, baseline haemoglobin, follow-up white blood cell count, baseline viral load, baseline sodium and follow-up alanine transaminase. Discussion: Although antiretroviral therapy is effective in reducing the risk of developing TB, the overall burden of TB in HIV/AIDS community may not substantially diminish. Conclusion: TB/HIV co-infection is of the serious public health problems in Albert Collaborative TB/HIV activities in form of early diagnosis of both TB and HIV need a holistic approach in order to reduce drug resistance, drug toxicity, co-morbidities and mortalities which are associated with TB/HIV co-infection. < 0.0001), (EFV+AZT+3TC) relative to (NVP+3TC+TDF) (TR=0.4409, p-value < 0.0005); (EFV+3TC+TDF) relative to (NVP+3TC+TDF) (TR=0.6580, p-value < 0.0296); poor relative to good ART adherence (TR=0.3268, p-value < 0.0001); fair relative to good ART adherence (TR=0.5718, p-value < 0.0001); baseline haemoglobin (TR=0.9356, p-value < 0.0005); follow-up white blood cell count (TR=0.9569, p-value < 0.0245); ln (baseline viral load) (TR=0.9388, p-value < 0.0001); baseline sodium (TR=0.9804, p-value < 0.0003) and follow-up Alanine Transaminase (TR=0.9939, p-value < 0.0007). A decrease in viral load is associated with an increase in survival probability from the onset of TB. Thus, a one unit decrease in ln (baseline viral load) makes a patient’s average survival time from the hazard of TB decrease by about 6.1%, after adjusting for other factors.


Introduction
Tuberculosis is the leading cause of death in South Africa (South Africa National AIDS Council, 2017). The country has the world's sixth largest tuberculosis (TB) epidemic, with a TB incidence rate of 438,000 in 2016 (South Africa National AIDS Council, 2017). The HIV epidemic in South Africa fuels the TB epidemic because people living with HIV are at a far higher risk of developing TB due to weakened immune systems. It is estimated that 60% of Data based evidence show that TB is worryingly prevalent in Albert Luthuli municipality.
Consequently, the main objective of the study was to assess the impact of HIV/AIDS and TB coinfection on survival of patients after adjusting for potential explanatory variables.

Data sources
A cohort of HIV-infected patients from Embhuleni and Carolina district hospitals were retrospectively followed from 2010 to 2017 until TB was diagnosed or until the end of the study. Since the exact date of TB onset is not known, the event TB is known to lie in an interval that is the last available visit date and end of the study. Thus, the observed event leads to interval censored survival data. Albert Luthuli Local Municipality is a South African local municipality situated in the Gert Sibande District of Mpumalanga. Carolina and Embhuleni District hospitals, from where data was collected, render comprehensive health care service which includes HIV and TB treatments and support services to the surrounding communities in Albert Luthuli municipality. These hospitals are accredited antiretroviral (ARV) treatment initiation and on-going treatment sites. Both Hospitals serve mostly the rural population in Albert Luthuli Municipality. The target population which was used as a sampling frame included all HIV/AIDS patients admitted and started ART treatment in the two hospitals within the three-month period from the 1 st of January to the 31 st of March 2010. The variables which form part of the routine hospital records in Albert Luthuli municipality were used in this study and are described as follows. Being tuberculosis co-infected or not co-infected is the dependent variable for the study. It was recorded as TB history (yes, no). The categorical independent variables were gender, hospital (Carolina, Embhuleni), WHO stage (1,2,3,4), marital status ( single, married, staying together, widowed/separated/divorced), treatments (regimen 1)(NVP+D4T+3TC, EFV+D4T+3TC, EFV+AZT+3TC and EFV+3TC+TDF), ART adherence (poor, fair, good), transferred from hospital (yes, no) and lost to follow-up (yes, no).
The continuous independent variables for the study which except 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. Diabetes and hypertension were excluded because their records were found in very few patient files.

TB diagnosis and treatment
The clinical manifestations of TB vary but include prolonged fever, hemoptysis, productive

Model Comparison
In order to select best fit model, we have used -2 Log-likelihood, AIC, AICC and BIC. Loglogistic AFT model was adopted after comparison with Log-normal and Exponential by using AIC, BIC, AICC and Log-likelihood. The AIC guards against over fitting and it is defined as: where, p is the number of covariates in the model, with k = 1 for exponential and k = 2 for Weibull, log-logistic and log-normal models. The AIC penalizes the number of parameters less strongly than the BIC (Schwarz, 1978). BIC is defined as: where, ′ is a vector of regression coefficients, and are intercept and scale parameters respectively and the error term .This transformation leads to the Weibull, log-normal or loglogistic AFT models for (Collett, 2003).

Maximum Likelihood Estimation
Given = ( ) as in 1.2, then the density function of is given by

Modelling and analysis approaches
Variables with p-values less than 0.05 were incorporated into the multivariate model. Let . Log-rank test, Kaplan-Meier survivor functions and hazard ratios were used as analysis approaches in addressing homogeneity with respect to the characteristics of the cohort. Log-rank test was used to compare TB survival rates between two distinct groups using the hypothesis: Data were for the study were recorded on research tools and then captured on Microsoft excel database and checked against original records by two competent individuals. Data was analysed using SAS Version 9.4, Stata Version 15 and R Version 3.5.1.

Inclusion and Exclusion Criteria
This study considered all HIV/AIDS patients admitted and started ART treatment in the two hospitals within the three-month period from the 1 st of January to the 31 st of March 2010.
HIV/AIDS patients were excluded from the study if the patient medical register had missing essential records such as admission and last follow-up dates, TB history and date of birth or age.

Ethical consideration
The University of South Africa Ethics Review Committee and the Mpumalanga Department of Health approved the protocol for this study. All data related to the patient were handled with utmost confidentiality in all the stages of the research. In addition, no reference to an individual respondent was recorded and 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.

Fit statistics for data modelling using different regression models
From all the four fit statistics in Table 2 Table   3 in the following section.

Nonparametric inferences about the survivor functions on TB and HIV/AIDS
The cohort of HIV/AIDS patients in this study is not homogeneous with respect to their characteristics that may affect their survival. Hence, it will be necessary to test the equality of factors were found to be highly statistically significant in the log-logistic model (Table 1) and the difference their strata were also found to be highly significant (using log-rank test). Figure 1 shows that throughout the follow-up period, HIV/AIDS patients from Embhuleni hospital have lower TB survival probability than patients from Carolina hospital.

Kaplan-Meier survival functions for Hospitals
The hospital strata shown in the Figure 1 are statistically different as shown by both the logrank test (p-value = 0.00) and the 95% Wald Confidence Limits for hazard ratios which do not include '1', a value of no effect. As shown in Table 4 Figure 2 shows that throughout the follow-up period, HIV/AIDS patients taking (NVP+D4T+3TC) and those taking (EFV+3TC+TDF) experienced the least survival probability from TB while HIV/AIDS patients taking (NVP+3TC+TDF) experienced the highest survival probability from TB. The treatments shown in the Figure 2 are statistically different as shown by the log-rank test (p-value = 0.00). As shown in Table 5, the ascending order of TB hazard in terms of each researched ART treatment relative to NVP+D4T+3TC is:

Kaplan-Meier survival functions for Treatments
EFV+AZT+3TC, NVP+3TC+TDF and EFV+3TC+TDF. The ART treatment EFV+D4T+3TC relative to NVP+D4T+3TC is not significant since the 95% confidence limits (0.6539, 2.0771) include '1', which is a value of no effect.    shown by the log-rank test (p-value = 0.00). As shown in Table 7, patients with baseline viral load above 50 000 HIV RNA copies/ 3 relative to patients with baseline viral load less than 50 HIV RNA copies/ 3 are about 6 times likely to experience TB.     Figure 5 shows that throughout the follow-up period, AIDS patients with follow-up CD4 count < 200 cells/ 3 have higher TB hazard than HIV-infected patients with follow-up CD4 count ≤ 200 cells/ 3 .

Kaplan-Meier survival functions for Follow-up CD4 groups
The follow-up CD4 count strata in Figure 5 are statistically different as shown by the log-rank test (p-value = 0.00). As shown in Table 8, AIDS patients with Follow-up CD4 count < 200 cells/ 3 relative to HIV-infected patients with Follow-up CD4 count ≥ 200 cells/ 3 are about 3 times likely to experience TB, and this effect can be as low as 2 times and as high as 5 times.

Kaplan-Meier survival function for TB for Albert Luthuli HIV/AIDS data
As shown in Figure 6, the estimate of the survival graph (bold) and its 95% confidence intervals (dotted) graphs, the TB survival probability for the HIV/AIDS patients gradually declines over the follow-up period.
The decline in TB survival probability is associated to the factors in Table 3. At the end of the follow-up time, the estimate of TB survival probability as in Figure 6 was at 0.647 and this estimate could go as low as 0.535 and as high as 0.783.   Table 9: TB survival probability of HIV/AIDS patients Pleural fluid from coinfected subjects has higher viral titers (Toossi et al. 2001) and greater HIV heterogeneity than plasma from the same patients (Collins et al. 2002). As shown in Figure   4, HIV/AIDS patients with detectable viral load (>50 000 HIV RNA copies/mm 3 ) have lower survival probability than HIV/AIDS patients with non-detectable viral load (<50 HIV RNA copies/mm 3 ). Many studies found out that people living with HIV and with a low CD4 count are much more susceptible to active TB. As shown in Figure 5 and Table 8 and by Zenner et al. (2015), this study has shown that there are some ART regimens which are positively associated with hazards among TB patients. As shown in Table 5 (2003), there is concern that, although antiretroviral therapy is very effective in reducing an individual's risk of developing TB per unit time, the lifetime risk of the disease may not decrease. Thus, the overall burden of TB in the community may not substantially diminish, despite good antiretroviral coverage. Some other interventions that may also be important in reducing TB as suggested by Woldehanna and Volmink (2004) and Churchyard et al. (2003) include the use of primary and secondary isoniazid prophylaxis.
In addition to the predictors of TB, as shown in Table 3, ART adherence is a highly significant factor. Figure 3 and Table 6 show that HIV/AIDS patients with poor ART adherence relative to HIV/AIDS patients with good ART adherence are at higher risk to TB. Hospital is one of the factors associated with TB hazard. As shown in Finally, there are several reasons why the AFT model is better suited to this study than the Cox proportional hazards model. Clinically, the AFT model analyses the time to event directly rather than hazard ratios, making the interpretation of the output clinically relevant and meaningful (Orbe et al., 2002). AFT model has also been found to perform better prediction than Cox model for the right-hand distribution of the model (Saberifiroozi et al., 2006), which was the main research interest in this study. Some studies showed that parametric models resulted in a better fit than the Cox's regression model (Nardi & Schemper, 2003). When the proportionality assumption of Cox's regression model is not satisfied, the log-normal parametric model is the model of choice, moreover, simulation study showed that whether PH assumption is met or not, the log-logistic model is the best fitted model (Orbe et al., 2002).

Conclusion
In conclusion, the study presented the factors associated with TB among HIV/AIDS patients as: hospital, WHO stage, Treatment (regimen 1), ART adherence, follow-up CD4, baseline haemoglobin, follow-up white blood cell count, baseline viral load, baseline sodium and follow-up alanine transaminase. Thus, the study established diverse baseline statistics against which future research may be based. As the burden of HIV and TB co-infection in this study is relatively high, there is a need to increase funding to improve efforts for early detection and intervention for both HIV and TB. Understanding the key factors associated with TB in terms of death and non-death losses would assist in programmes evaluation and development.