Abstract

This paper develops a method to calculate the moments of statistical ratios as functionals of Bernoulli random variables via inverse moments of binomial distributions. We derive exact expressions for the mean, bias and variance formulas of several statistics, including the “modified” versions of the odds ratio and relative risk as well as the (positive) false discovery proportion (FDP), in which the case of zero cells is handled via indicator functions. Similar to the “positive” FDP, we introduce the “positive” odds ratio and relative risk statistics. We provide numerical examples to illustrate the biases and variances of these statistical ratios.

中文翻译：

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关于优势比、相对风险和错误发现比例的偏差和方差

摘要

本文开发了一种通过二项分布的反矩来计算作为伯努利随机变量泛函的统计比率矩的方法。我们推导出几个统计数据的均值、偏差和方差公式的精确表达式，包括优势比和相对风险的“修改”版本以及（阳性）错误发现比例（FDP），其中零细胞的情况通过指标函数处理。与“正”FDP 类似，我们引入“正”优势比和相对风险统计。我们提供了数值示例来说明这些统计比率的偏差和方差。