A comparison of biomarker based incidence estimators

Abstract

Background: Cross-sectional surveys utilizing biomarkers that test for recent infection provide a convenient and cost effective way to estimate HIV incidence. In particular, the BED assay has been developed for this purpose. Controversy surrounding the way in which false positive results from the biomarker should be handled has lead to a number of different estimators that account for imperfect specificity. We compare the estimators proposed by McDougal et al., Hargrove et al. and McWalter & Welte.

Methodology/principal findings: The three estimators are analyzed and compared. An identity showing a relationship between the calibration parameters in the McDougal methodology is shown. When the three estimators are tested under a steady state epidemic, which includes individuals who fail to progress on the biomarker, only the McWalter/Welte method recovers an unbiased result.

Conclusions/significance: Our analysis shows that the McDougal estimator can be reduced to a formula that only requires calibration of a mean window period and a long-term specificity. This allows simpler calibration techniques to be used and shows that all three estimators can be expressed using the same set of parameters. The McWalter/Welte method is applicable under the least restrictive assumptions and is the least prone to bias of the methods reviewed.

Figure 1. The six sector model of McDougal et al.

The top graph shows counts and the bottom graph shows the survival function versus time since infection.

Figure 2. Bias in the McDougal estimator.

Relative difference between the McDougal estimate and the equilibrium incidence plotted as a function of equilibrium incidence.

Figure 3. Bias in the Hargrove estimator.

Relative difference between the Hargrove estimate and the equilibrium incidence plotted as a function of and for an equilibrium incidence of 5% per annum. Black lines indicate contours of equal bias.