Sample size methods for estimating HIV incidence from cross-sectional surveys

Understanding HIV incidence, the rate at which new infections occur in populations, is critical for tracking and surveillance of the epidemic. In this article, we derive methods for determining sample sizes for cross-sectional surveys to estimate incidence with sufficient precision. We further show how to specify sample sizes for two successive cross-sectional surveys to detect changes in incidence with adequate power. In these surveys biomarkers such as CD4 cell count, viral load, and recently developed serological assays are used to determine which individuals are in an early disease stage of infection. The total number of individuals in this stage, divided by the number of people who are uninfected, is used to approximate the incidence rate. Our methods account for uncertainty in the durations of time spent in the biomarker defined early disease stage. We find that failure to account for this uncertainty when designing surveys can lead to imprecise estimates of incidence and underpowered studies. We evaluated our sample size methods in simulations and found that they performed well in a variety of underlying epidemics. Code for implementing our methods in R is available with this article at the Biometrics website on Wiley Online Library.