Paired serial limiting dilution assays

Serial limiting dilution (SLD) assays are a widely used tool in many areas of public health research to measure the concentration of target entities. This concentration can be estimated via maximum likelihood. Asymptotic as well as exact inference methods have been proposed for hypothesis testing and confidence interval construction in this one-sample problem. However, in many scientific applications, it may be of interest to compare the concentration of target entities between a pair of samples and construct valid confidence intervals for the difference in concentrations. In this paper, an exact, computationally efficient inferential procedure is proposed for hypothesis testing and confidence interval construction in the two-sample SLD assay problem. The proposed exact method is compared to an approach based on asymptotic approximations in simulation studies. The methods are illustrated using data from the University of North Carolina HIV Cure Center.