Estimating HIV cross-sectional incidence using recency tests from a non-representative sample

Cross-sectional incidence estimation based on recency testing is a widely used tool in HIV research. This method has been used to estimate "placebo" incidence in active-control HIV prevention trials by applying the cross-sectional estimator to the screening population data. The application of this approach faces challenges due to non-representative sampling, as individuals aware of their HIV-positive status may be less likely to participate in screening for an HIV prevention trial. To address this, recent phase 3 trials introduced a test-based criterion, excluding individuals who had recently taken an HIV test. To date, the theoretical and empirical validity of this criterion has yet been studied. We develop a statistical framework incorporating non-representative sampling and the testing-based criterion. We quantify the limiting estimation error in recency-based incidence estimates, and investigate the performance of cross-sectional HIV incidence estimation through simulations emulating realworld trial designs. We find that under non-representative sampling, the incidence estimator is unreliable unless all recently tested individuals are excluded. Additionally, we highlight a bias-variance trade-off: excluding more individuals may reduce estimation bias from non-representative sampling but increases the variability. Our findings emphasize careful application of the testing-based criterion and the importance of improved methods in future HIV prevention trials.