Experimental designs with hierarchically-structured errors are pervasive in many biomedical areas; it is important to take into account this hierarchical architecture in order to account for the dispersion and make reliable inferences from the data. This paper addresses the question of estimating a proportion or a ratio from positive or negative count data akin to those generated by droplet digital polymerase chain reaction experiments when the number of biological or technical replicates is limited. We present and discuss a Bayesian framework, for which we provide and implement a Gibbs sampler in R and compare it to a random effect model.

翻译：在众多生物医学领域中，具有层次结构误差的实验设计十分普遍。为了正确考量数据离散性并得出可靠统计推断，必须充分考虑这种层次结构。本文针对微滴式数字聚合酶链式反应实验产生的正负计数数据，在生物学或技术重复次数有限的情况下，探讨了如何估计比例或比率的问题。我们提出并讨论了一种贝叶斯框架，在R语言中实现并提供了相应的吉布斯采样器，同时将其与随机效应模型进行了比较。