Sample size calculation in biomedical practice is typically based on the problematic Wald method for a binomial proportion, with potentially dangerous consequences. This work highlights the need of incorporating the concept of conditional probability in sample size determination to avoid reduced sample sizes that lead to inadequate confidence intervals. Therefore, new definitions are proposed for coverage probability and expected length of confidence intervals for conditional probabilities, like sensitivity and specificity. The new definitions were used to assess seven confidence interval estimation methods. In order to determine the sample size, two procedures—an optimal one, based on the new definitions, and an approximation—were developed for each estimation method. Our findings confirm the similarity of the approximated sample sizes to the optimal ones. R code is provided to disseminate these methodological advances and translate them into biomedical practice.

中文翻译：

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常见的医学和统计问题：敏感性和特异性估计的样本量计算难题

生物医学实践中的样本量计算通常基于有问题的Wald方法的二项式比例，具有潜在的危险后果。这项工作强调了在样本量确定中纳入条件概率概念的必要性，以避免减少导致不足的置信区间的样本量。因此，针对覆盖率和条件概率（如敏感性和特异性）的置信区间的预期长度提出了新的定义。新定义用于评估七种置信区间估计方法。为了确定样本量，针对每种估计方法，开发了两种方法（基于新定义的最佳方法和近似方法）。我们的发现证实了近似样本量与最佳样本量的相似性。提供了R代码来传播这些方法学上的进步并将其转化为生物医学实践。