A thesis submitted to the Faculty of Science, University of the Witwatersrand, Johannesburg, in fulfilment of the requirements for the degree of Doctor of Philosophy. 21 October, 2014. / Three decades ago, the discovery of the Human Immunodeficiency Virus (HIV) was announced. The subsequent HIV pandemic has continued to devastate the global community, and many countries have set ambitious HIV reduction targets over the years. Reliable methods for measuring incidence, the rate of new infections, are essential for monitoring the virus, allocating resources, and assessing interventions. The estimation of incidence from single cross-sectional surveys using tests that distinguish between ‘recent’ and ‘non-recent’ infection has therefore attracted much interest. The approach provides a promising alternative to traditional estimation methods which often require more complex survey designs, rely on poorly known inputs, and are prone to bias. More specifically, the prevalence of HIV and ‘recent’ HIV infection, as measured in a survey, are used together with relevant test properties to infer incidence. However, there has been a lack of methodological consensus in the field, caused by limited applicability of proposed estimators, inconsistent test characterisation (or estimation of test properties) and uncertain test performance. This work aims to address these key obstacles. A general theoretical framework for incidence estimation is developed, relaxing unrealistic assumptions used in earlier estimators. Completely general definitions of the required test properties emerge from the analysis. The characterisation of tests is then explored: a new approach, that utilises specimens from subjects observed only once after infection, is demonstrated; and currently-used approaches, that require that subjects are followed-up over time after infection, are systematically benchmarked. The first independent and consistent characterisation of multiple candidate tests is presented, and was performed on behalf of the Consortium for the Evaluation and Performance of HIV Incidence Assays (CEPHIA), which was established to provide guidance and foster consensus in the field. Finally, the precision of the incidence estimator is presented as an appropriate metric for evaluating, optimising and comparing tests, and the framework serves to counter existing misconceptions about test performance. The contributions together provide sound theoretical and methodological foundations for the application, characterisation and optimisation of recent infection tests for HIV incidence surveillance, allowing the focus to now shift towards practical application.

The HIV and AIDS epidemic has remained one of the leading causes of death in the world and has been destructive in Africa with Sub-Saharan Africa remaining the epidemiological locus of the epidemic. HIV and AIDS hinders development by erasing decades of health, economic and social progress, reducing life expectancy by years and deepening poverty [57].The most urgent public-health problem globally is to devise effective strategies to minimize the destruction caused by the HIV and AIDS epidemic. Due to the problems caused by HIV and AIDS, well defined endpoints to evaluate treatment benefits are needed. The surrogate and true endpoints for a disease need to be specified. The purpose of a surrogate endpoint is to draw conclusions about the effect of intervention on true endpoint without having to observe the true endpoint. It is of great importance to understand the surrogate validation methods. At present the question remains as to whether CD4 count and viral load are good surrogate markers for death in HIV or there are some better surrogate markers. This dissertation was undertaken to obtain some clarity on this question by adopting a mathematical model for HIV at immune system level and the impact of treatment in the form of reverse transcriptase inhibitors (RTIs). For an understanding of HIV, the dissertation begins with the description of the human immune system, HIV virion structure, HIV disease progression and HIV drugs. Then a review of an existing mathematical model follows, analyses and simulations of this model are done. These gave an insight into the dynamics of the CD4 count, viral load and HIV therapy. Thereafter surrogate marker validation methods followed. Finally generalized estimating equations (GEEs) approach was used to analyse real data for HIV positive individuals, from the Centre for the AIDS Programme of Research in South Africa (CAPRISA). Numerical simulations for the HIV dynamic model with treatment suggest that the higher the treatment efficacy, the lower the infected cells are left in the body. The infected cells are suppressed to a lower threshold value but they do not completely disappear, as long as the treatment is not 100% efficacious. Further numerical simulations suggest that it is advantageous to have a low proportion of infectious virions (ω) at an individual level because the individual would produce few infectious virions to infect healthy cells. Statistical analysis model using GEEs suggest that CD4 count< 200 and viral load are highly associated with death, meaning that they are good surrogate markers for death. An interesting finding from the analysis of this particular data from CAPRISA was that low CD4 count and high viral loads as surrogates for HIV survival act independently/additively. The interaction effect was found to be insignificant. Individual characteristics or factors that were found to be significantly associated with HIV related death are weight, CD4 count< 200 and viral load. / Thesis (M.Sc.)-University of KwaZulu-Natal, Pietermaritzburg, 2010.

Where HIV/AIDS has had its greatest adverse impact is on TB. People with TB that are infected with HIV are at increased risk of dying from TB than HIV. TB is the leading cause of death in HIV individuals in South Africa. HIV is the driving factor that increases the risk of progression from latent TB to active TB. In South Africa no coherent analysis of the risk determinants of HIV and TB has been done at the national level this study seeks to mend that gab. This study is about estimating risk determinants of HIV and TB. This will be done using the national household survey conducted by Human Sciences Research Council in 2005. Since individuals from the same household and enumerator area more likely to be more alike in terms of risk of disease or correlated among each other, the GEEs will be used to correct for this potential intraclass correlation. Disease occurrence and distribution is highly heterogeneous at the population, household and the individual level. In recognition of this fact we propose to model this heterogeneity at community level through GLMMs and Bayesian hierarchical modelling approaches with enumerator area indicating the community e ect. The results showed that HIV is driven by sex, age, race, education, health and condom use at sexual debut. Factors associated with TB are HIV status, sex, education, income and health. Factors that are common to both diseases are sex, education and health. The results showed that ignoring the intraclass correlation can results to biased estimates. Inference drawn from GLMMs and Bayesian approach provides some degree of con dence in the results. The positive correlation found at an enumerator area level for both HIV and TB indicates that interventions should be aimed at an area level rather than at the individual level. / Thesis (M.Sc.)-University of KwaZulu-Natal, Pietermaritzburg, 2009

The effects of gender and age on the behavioral risk of HIV/AIDS are not clearly understood as previous distinct studies which have been carried out, have given disputable and contradictory outcomes. This study therefore, discusses the statistical methods which can be used to model the influence of age and gender on the behavioral risk factors of HIV/AIDS. In general, generalized linear models are the main methods which can be applied to depict the impact of age and gender on the behavioral risk of becoming infected with HIV/AIDS virus. In this study, the main methods used were logistic regression, log-linear regression and multiple regressions. Behavioral risk was taken as the dependent variable while age, gender, number of sexual partners, religious beliefs and alcohol and drug abuse were fitted as predictor variables. The three statistical methods gave significant results for gender and insignificant results for age. Furthermore, comparisons were made on the three regression methods and the logistic regression gave the best results. It was therefore concluded that gender plays a significant role on the behavioral risk of HIV/AIDS. The results of the study showed that gender of the student and number of sexual partners had a significant effect on the risk behavior of the university students. In future, it may be very important to find out why age is not a significant factor on risk behavior of HIV/AIDS among university students.