The standard unadjusted cross-sectional estimator of HIV incidence should be used when all infected individuals would eventually become reactive to the less sensitive test. When a subset of individuals would indefinitely remain nonreactive to the less sensitive test, the maximum likelihood estimator for this setting should be used. Characterizing the proportion of individuals who would indefinitely remain nonreactive is crucial for accurate estimation of HIV incidence.
To elucidate when and how cross-sectional estimators of HIV incidence rates based on a sensitive and less sensitive diagnostic test should be adjusted.
When every infected subject would eventually become reactive to the less sensitive test, the McDougal adjusted estimator is uniformly less precise than the unadjusted estimator and more susceptible to bias. When a subset of the infected population would indefinitely remain nonreactive to the less sensitive test, the McDougal adjusted estimator is less precise than the maximum likelihood estimator, which coincides with an estimator developed by McWalter and Welte using a mathematical modeling approach. When the assumed model is incorrect, the unadjusted estimator overestimates incidence, whereas the maximum likelihood estimator can be biased in either direction.
Evaluate the statistical properties of unadjusted and adjusted cross-sectional estimators of HIV incidence, including the adjusted estimators considered by McDougal et al, for the 2 settings where (a) all infected subjects eventually become reactive to the less sensitive test, and (b) a subset of infected subjects indefinitely remain nonreactive to the less sensitive test. Derive the maximum likelihood estimator of incidence for the latter setting and use analytical results and simulation studies to compare the performance of the various estimators.