Estimating risk determinants of HIV and TB in South Africa.

Antenatal HIV and syphilis incidence surveys have been used to monitor HIV prevalence in South Africa. The pattern of HIV in South Africa remained the same even in later years (Department of Health, 2006).

Figure 1.1: Projected HIV prevalence in South Africa from 1987 to 2015 (Source:WHO)

Tuberculosis in the World and South Africa

In South Africa, all forms of tuberculosis are detectable, except for XDR-TB, which is associated with a high case fatality rate (CFR) due to its short incubation period, making it difficult to contain and mitigate the disease. In 2002, Statistics South Africa (StatsSA) reported that Western Cape had the highest incidence of tuberculosis.

Table 1.1: Incidence estimates of TB in South Africa in 2004

Relationship between HIV and TB

It is clear that as HIV prevalence started to increase, TB notifications also started to increase drastically. An individual infected with HIV can take about 5 years before becoming infected with TB.

Figure 1.3: HIV prevalence in South African adults and TB notification rate per 10 000 000 population since early 1980s

Objectives of this Research

Research hypothesis

Predominantly African and socially disadvantaged communities have a higher proportion of unemployment, and/or a higher migrant population consequently have a disproportionately higher prevalence of HIV and TB burdens. High population density or poor areas are associated with high burden of HIV and TB infections.

The Data

Sample Weights

In the final step, individual-level information was integrated and the final sample weight was calculated for each data record. Thus, our analyzes will be primarily at the individual level rather than at the aggregate (community) level.

Statistical Methods

Generalized Linear Models

The generalization of the systematic part allows the linear predictor to be a monotonic function of the mean. This strictly linear model can be further generalized by allowing other smooth functions of the mean.

Binary Response

Thus, β1 is a measure of the linear effect of x on the logarithm of the probability of the event of interest. Confidence intervals for odds ratios can be used to estimate the significance of parameters of interest.

Thesis overview

The first approach to understanding data is to perform exploratory analysis using tools such as crosstabs and graphs. Descriptive results are presented in tabular form, namely Table 2.1 presents socio-demographic factors, Table 2.2 presents sexual behavior determinants, Table 2.3 presents biomedical factors and Table 2.4 presents substance use factors.

Descriptive Analysis of HIV

On the relationship with STIs, the analysis shows that those who had STIs are more likely to be HIV positive than those who did not have STIs. The prevalence for those who reported having one, two, and more than two acts per month is 20%, respectively.

Descriptive analysis of TB

Interaction of TB and HIV

On the other hand, the risk of HIV infection is higher among individuals infected with tuberculosis than among uninfected individuals. Our descriptive analysis of the data currently suggests that the prevalence of HIV infection is higher among TB-infected individuals than among TB-uninfected individuals.

Logistic Regression Modelling

Model results for HIV data

The chance of becoming infected with HIV if you are a man is 0.66 times smaller than the chance of becoming infected with HIV if you are a woman. This means that the effect of race on HIV prevalence differs at different levels of education. In summary, it should be noted that some confidence intervals are quite wide, making the point estimate less reliable.

Model results for TB

Discussion

Human Immune Virus
Tuberculosis
Introduction
Modelling Correlated Binary Data
Results of GEEs

HIV Results from GEEs
TB Results from GEEs

The results show that men have a lower risk of HIV infection than women, table 3.1. The results show that those in good health have a lower risk of HIV infection than those in poor health. Results show that men are at higher risk of contracting TB compared to their female counterparts.

Individuals who are in good health have a lower risk of contracting tuberculosis.

Generalized Linear Mixed Models

Introduction

Modelling binary response using GLMMs

Quasi-likelihood

The parameter estimation is not that different from that of a GLM (fixed effects only), except that now the linear predictor includes an additional term representing the random effects. As usual, solving the model parameters is numerically intensive, so there is a need for better modified methods that can be used to evaluate the solutions. There are two different variance estimators that can be estimated using a quasi-likelihood approach.

The quasi-likelihood method can be used to analyze overdispersed data without making any distributional assumptions, but only using the specification of the mean and variance.

Results of GLMMs

GLMMs HIV Results
GLMMs TB results

Those who have primary education or no education are at greater risk of becoming infected with tuberculosis, OR = 7.84 compared to those who have tertiary education. Individuals with secondary or secondary education are more likely to be infected with tuberculosis, OR=4.01. Those who are unemployed are at greater risk of becoming infected with tuberculosis than those who are working.

People who are in good health are less likely to become infected with tuberculosis (OR=0.19).

Discussion

In this chapter, the focus will be on the Markov Chain Monte Carlo (MCMC) methods for simulating data. Definition of the n-step transition probability p(n)ij as the probability that the process is in state j given that it started in state in the first step ago, i.e. 4.3) A Markov chain is said to be irreducible if there exists a positive integer such that p(nijij) > 0 for all i, j. A Markov chain can reach a stationary distribution π∗ where the vector of probabilities of being in any given state is independent of the initial state.

If equation (4.4) holds for all (i, j), the Markov chain is said to be reversible, so equation (4.4) is called the reversibility condition.

Table 3.1: GEEs HIV model: Parameter Estimates (Standard Error)

Direct Sampling Methods

Acceptance-Rejection Sampling

Since the expected number of iterations of steps 1 and 2 to achieve a tie is given by c−1, the rejection method is optimized by setting.

Markov Chain Monte Carlo

The Metropolis-Hastings Algorithm

Convergence Diagnostics
A Metropolis-Hastings Acceptance-Rejection Algo-

The Metropolis-Hastings (M-H) update scheme was first described by Hastings (1970) as a generalization of the Metropolis algorithm. As mentioned, the candidate generating distribution can be tuned to adjust the mixing and especially the acceptance probability of the chain. The probability of acceptance can be increased by reducing the standard deviation of the candidate generating distribution (Draper 2000).

If the chain is stationary, the means of the two samples should be equal.

The Gibbs Sampler

Gibbs sampler as a special case of the M-H algorithm 85

Each iteration of Gibbs sampling cycles through the subvectors of θ, drawing each subset conditional on the value of all the others. The power of Gibbs sampling to address a wide variety of statistical issues has been studied (Gelfand and Smith 1990). Any feature of interest to the marginals can be computed from m realizations of the Gibbs sequence.

A measure of the effects of autocorrelation between elements in the sampler is the effective chain size.

Graphical Modelling

This implies that the joint distribution of both parameters in the model, say νV, and the data can be factored as This involves marrying the parents by inserting the edge between the parents of each node ν in the graph. This graph provides us with all the information about the relationships between the parameters in the model.

Therefore, the graph of conditional independence makes it easy to see which other parameters are required in the specification of the full conditional distributions for each parameter, thus simplifying the implementation of MCMC algorithms for such models.

Analysis of the data

It is also clear that black people are more likely to contract HIV than Indians. In this study, individuals in good health were less likely to become infected with HIV than those in poor health. Individuals who are infected with HIV are more likely to be infected with TB than those who are HIV negative.

Individuals who are unemployed are more likely to be infected with TB than those who receive income from other sources (grants, donations, pensions, etc.).

Figure 4.1: History: Complete trace plots for HIV fixed effects parameters

Discussion

South African youth are severely affected by poverty-related problems (Eaton et al. 2003). A number of studies have shown that Africans are at greater risk of HIV infection than any other racial group (Eaton et al. 2003). Thus, poor/disadvantaged communities are associated with a high risk of HIV infection (Kalichman et al. 2006).

Most sexually active individuals use condoms inconsistently or not at all (Eaton et al. 2003).

Table 4.1: HIV model: Parameter Estimates and Standard Errors

Tuberculosis

This is consistent with the study by Harlinget al.(2008), which showed that there is a 10% reduction in the chances of being infected with tuberculosis for an additional year of completed education. TB is mostly perceived as a disease of people of low social status (Harling et al. 2008). Harling et al.(2008) report that there is a 40% reduction in the chances of contracting TB for those individuals who were employed in the past year.

Some studies have shown that income inequality is associated with different health outcomes, especially in settings with high inequality (Subramanianet al. 2004; Kawachiet al. 2000).

Intervention Implications

So this means that the risk of contagion will be significantly reduced if everyone can achieve higher education standards. If individuals can be detected and treated early for tuberculosis, this will reduce the mortality rate of individuals who are infected with HIV but die from tuberculosis. Treatment of tuberculosis in HIV-infected individuals is difficult, as some of them are also already taking antiretroviral drugs, which could lead to complications in adherence.

The government and those in charge should develop job opportunities for those who have no job as it is clear in this study that people who are unemployed are at higher risk of contracting TB.

Different Statistical approaches

The results will therefore provide a better understanding of the spread of the two epidemics in South Africa, namely HIV and TB. The purpose of the study is to examine risk determinants for HIV and TB and identify factors common to both epidemics. The results will therefore provide a better understanding of the spread of these two epidemics in South Africa.

In Figures 5.1 and 5.2, the red line for each variable converges to 1, while the total width and the width within the interval converge to stability, indicating the significant convergence.