Likelihood based statistical methods for estimating HIV incidence rate.
Estimation of current levels of human immunodeficiency virus (HIV) incidence is essential for monitoring the impact of an epidemic, determining public health priorities, assessing the impact of interventions and for planning purposes. However, there is often insufficient data on incidence as compared to prevalence. A direct approach is to estimate incidence from longitudinal cohort studies. Although this approach can provide direct and unbiased measure of incidence for settings where the study is conducted, it is often too expensive and time consuming. An alternative approach is to estimate incidence from cross sectional survey using biomarkers that distinguish between recent and non-recent/longstanding infections. The original biomarker based approach proposes the detection of HIV-1 p24 antigen in the pre-seroconversion period to identify persons with acute infection for estimating HIV incidence. However, this approach requires large sample sizes in order to obtain reliable estimates of HIV incidence because the duration of antigenemia before antibody detection is short, about 22.5 days. Subsequently, another method that involves dual antibody testing system was developed. In stage one, a sensitive test is used to diagnose HIV infection and a less sensitive test such is used in the second stage to distinguish between long standing infections and recent infections among those who tested positive for HIV in stage one. The question is: how do we combine this data with other relevant information, such as the period an individual takes from being undetectable by a less sensitive test to being detectable, to estimate incidence? The main objective of this thesis is therefore to develop likelihood based method that can be used to estimate HIV incidence when data is derived from cross sectional surveys and the disease classification is achieved by combining two biomarker or assay tests. The thesis builds on the dual antibody testing approach and extends the statistical framework that uses the multinomial distribution to derive the maximum likelihood estimators of HIV incidence for different settings. In order to improve incidence estimation, we develop a model for estimating HIV incidence that incorporate information on the previous or past prevalence and derive maximum likelihood estimators of incidence assuming incidence density is constant over a specified period. Later, we extend the method to settings where a proportion of subjects remain non-reactive to a less sensitive test long after seroconversion. Diagnostic tests used to determine recent infections are prone to errors. To address this problem, we considered a method that simultaneously makes adjustment for sensitivity and specificity. In addition, we also showed that sensitivity is similar to the proportion of subjects who eventually transit the “recent infection” state. We also relax the assumption of constant incidence density by proposing linear incidence density to accommodate settings where incidence might be declining or increasing. We extend the standard adjusted model for estimating incidence to settings where some subjects who tested positive for HIV antibodies were not tested by a less sensitive test resulting in missing outcome data. Models for the risk factors (covariates) of HIV incidence are considered in the last but one chapter. We used data from Botswana AIDS Impact (BAIS) III of 2008 to illustrate the proposed methods. The general conclusion and recommendations for future work are provided in the final chapter.