A likelihood estimation of HIV incidence incorporating information on past prevalence

The prevalence and incidence of an epidemic are basic characteristics that are essential for monitoring its impact, determining public health priorities, assessing the effect of interventions, and for planning purposes. A direct approach for estimating incidence is to undertake a longitudinal cohort study where a representative sample of disease free individuals are followed for a specified period of time and new cases of infection are observed and recorded. This approach is expensive, time consuming and prone to bias due to loss-to-follow-up. An alternative approach is to estimate incidence from cross sectional surveys using biomarkers to identify persons recently infected as in (Brookmeyer and Quinn, 1995; Janssen et al., 1998). This paper builds on the work of Janssen et al. (1998) and extends the theoretical framework proposed by Balasubramanian and Lagakos (2010) by incorporating information on past prevalence and deriving maximum likelihood estimators of incidence. The performance of the proposed method is evaluated through a simulation study, and its use is illustrated using data from the Botswana AIDS Impact (BAIS) III survey of 2008.