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.

中文翻译：

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配对连续有限稀释测定

连续有限稀释 (SLD) 测定是公共卫生研究许多领域中广泛使用的工具，用于测量目标实体的浓度。该浓度可以通过最大似然估计。已经提出了渐近推理方法和精确推理方法，用于这一单样本问题的假设检验和置信区间构建。然而，在许多科学应用中，比较一对样品之间目标实体的浓度并为浓度差异构建有效的置信区间可能是有意义的。本文提出了一种精确、计算高效的推理程序，用于两样本 SLD 分析问题中的假设检验和置信区间构建。将所提出的精确方法与模拟研究中基于渐近近似的方法进行比较。这些方法使用北卡罗来纳大学艾滋病毒治疗中心的数据进行说明。