Abstract

This article examines the zero numerator problem. This problem occurs when the misclassification rates are so low that both forms of misclassification may not both be present in the validation data. For this problem, the article compares two Bayesian methods for analyzing misclassified binary data that has a validation sub-study and three forms of a non-informative prior distribution. It shows that the two methods give similar results. However, the posterior distributions were sensitive to the choice of the prior distribution when misclassification rates are low. The article further presents a simulation study that reveals that the bias is small regardless of the considered prior distribution. However, when the misclassification rates are low, the coverage of credible intervals is markedly better for a Jeffreys’ prior than for either a Haldane’s or a uniform prior. Finally, the article highlights the merit of quantifying expert opinion to form a subjective prior distribution when the posterior distribution is sensitive to the prior.

摘要

本文研究零分子问题。当错误分类率如此之低以至于两种形式的错误分类可能不会同时出现在验证数据中时，就会出现此问题。对于这个问题，本文比较了两种贝叶斯方法，用于分析具有验证子研究的错误分类二进制数据和三种形式的非信息先验分布。它表明这两种方法给出了相似的结果。然而，当错误分类率较低时，后验分布对先验分布的选择很敏感。文章进一步介绍了一项模拟研究，表明无论考虑的先验分布如何，偏差都很小。然而，当错误分类率很低时，Jeffreys 之前的可信区间覆盖率明显好于 Haldane 或制服之前。最后，文章强调了当后验分布对先验敏感时，量化专家意见以形成主观先验分布的优点。