When testing for a rare disease, prevalence estimates can be highly sensitive to uncertainty in the specificity and sensitivity of the test. Bayesian inference is a natural way to propagate these uncertainties, with hierarchical modelling capturing variation in these parameters across experiments. Another concern is the people in the sample not being representative of the general population. Statistical adjustment cannot without strong assumptions correct for selection bias in an opt‐in sample, but multilevel regression and post‐stratification can at least adjust for known differences between the sample and the population. We demonstrate hierarchical regression and post‐stratification models with code in Stan and discuss their application to a controversial recent study of SARS‐CoV‐2 antibodies in a sample of people from the Stanford University area. Wide posterior intervals make it impossible to evaluate the quantitative claims of that study regarding the number of unreported infections. For future studies, the methods described here should facilitate more accurate estimates of disease prevalence from imperfect tests performed on non‐representative samples.

中文翻译：

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具有未知特异性和敏感性的测试的贝叶斯分析

在检测罕见病时，患病率估计值可能对检测的特异性和敏感性的不确定性高度敏感。贝叶斯推理是传播这些不确定性的自然方式，分层建模捕获这些参数在实验中的变化。另一个问题是样本中的人不能代表一般人群。如果没有强有力的假设，统计调整就不能纠正选择加入样本中的选择偏差，但多层次回归和后分层至少可以调整样本和总体之间的已知差异。我们用 Stan 中的代码展示了层次回归和后分层模型，并讨论了它们在最近一项有争议的研究中的应用，该研究是在斯坦福大学地区的人群样本中进行的 SARS-CoV-2 抗体研究。较宽的后验区间使得无法评估该研究关于未报告感染数量的定量声明。对于未来的研究，这里描述的方法应该有助于通过对非代表性样本进行的不完美测试更准确地估计疾病流行率。