Confidence intervals for biomarker-based human immunodeficiency virus incidence estimates and differences using prevalent data

Prevalent biologic specimens can be used to estimate human immunodeficiency virus (HIV) incidence using a two-stage immunologic testing algorithm that hinges on the average time, T, between testing HIV-positive on highly sensitive enzyme immunoassays and testing HIV-positive on less sensitive enzyme immunoassays. Common approaches to confidence interval (CI) estimation for this incidence measure have included 1) ignoring the random error in T or 2) employing a Bonferroni adjustment of the box method. The authors present alternative Monte Carlo-based CIs for this incidence measure, as well as CIs for the biomarker-based incidence difference; standard approaches to CIs are typically appropriate for the incidence ratio. Using American Red Cross blood donor data as an example, the authors found that ignoring the random error in T provides a 95% CI for incidence as much as 0.26 times the width of the Monte Carlo CI, while the Bonferroni-box method provides a 95% CI as much as 1.57 times the width of the Monte Carlo CI. Further research is needed to understand under what circumstances the proposed Monte Carlo methods fail to provide valid CIs. The Monte Carlo-based CI may be preferable to competing methods because of the ease of extension to the incidence difference or to exploration of departures from assumptions.