Bootstrap confidence intervals and bias correction in the estimation of HIV incidence from surveillance data with testing for recent infection

The incidence of new infections is a key measure of the status of the HIV epidemic, but accurate measurement of incidence is often constrained by limited data. Karon et al. (Statist. Med. 2008; 27:4617–4633) developed a model to estimate the incidence of HIV infection from surveillance data with biologic testing for recent infection for newly diagnosed cases. This method has been implemented by public health departments across the United States and is behind the new national incidence estimates, which are about 40 per cent higher than previous estimates. We show that the delta method approximation given for the variance of the estimator is incomplete, leading to an inflated variance estimate. This contributes to the generation of overly conservative confidence intervals, potentially obscuring important differences between populations. We demonstrate via simulation that an innovative model-based bootstrap method using the specified model for the infection and surveillance process improves confidence interval coverage and adjusts for the bias in the point estimate. Confidence interval coverage is about 94–97 per cent after correction, compared with 96–99 per cent before. The simulated bias in the estimate of incidence ranges from ?6.3 to +14.6 per cent under the original model but is consistently under 1 per cent after correction by the model-based bootstrap. In an application to data from King County, Washington in 2007 we observe correction of 7.2 per cent relative bias in the incidence estimate and a 66 per cent reduction in the width of the 95 per cent confidence interval using this method. We provide open-source software to implement the method that can also be extended for alternate models.