Likelihood-based inferences for active-arm trial with counterfactual incidence based on recency assay.

Objectives: The approach of using HIV recency assay to estimate the counterfactual incidence rate is being used as the primary efficacy method in a few ongoing large-scale HIV pre-exposure prophylaxis (PrEP) trials, and the current available approach for the inference is based on the Wald method that leverages the asymptotic distribution of the estimators. One issue with the Wald test is that it does not work well when the number of HIV infections are small in the active arm, and it fails to work when there are zero HIV infections. As future long-acting PrEP products are becoming more efficacious, it is very likely that a small or zero number of infections will be observed in HIV prevention trials, especially for subgroup analyses or interim analyses, hence there is a pressing need to develop inference methods that work under such scenarios. Methods: It is well known that when the sample size is small to moderate, likelihood ratio tests are more reliable than Wald tests in terms of actual error probabilities coming close to matching nominal levels. In this manuscript we derive the likelihood ratio test and the likelihood-based confidence intervals for HIV prevention trials based on recency assays. Results: Compared with the Wald test, the proposed method works when there are zero infections. Additionally, unlike the Wald test, the p-value from the likelihood ratio test is an increasing function with respect to the number of infections, which is a desirable property as otherwise it will cause confusions. Conclusions: For HIV PrEP trials based on recency assay, the likelihood-based p-value and confidence interval can be preferable to the Wald based inference methods when the number of HIV infections is expected to be small.