ABSTRACT

This paper proposes two new approximate confidence limit methods for the common odds ratio from multiple 2 × 2 tables. The two new procedures, based on the asymptotic distribution of Woolf estimator and Mantel-Haenszel estimator, associate with inverse sinh transformation. We employ three pseudo-frequency methods to calculate confidence intervals in order to avoid the interval failure caused by the presence of zero cells in multiple 2 × 2 tables. We develop the modified inverse sinh intervals for the common odds ratio which add one pseudo-frequency (c₁) to all the cells before computing the point estimate of common odds ratio and another pseudo-frequency (c₂) to all the cells before computing the standard error estimate. The simulation is to evaluate the 22 confidence intervals, including Woolf, Mantel-Haenszel, their inverse sinh intervals, and their pseudo-frequency modified inverse sinh intervals, in terms of their coverage probabilities and average log lengths. Simulation results demonstrate that the adjusted inverse sinh intervals by two different pseudo-frequencies perform quite well when c₂ is slightly greater than c₁ since the coverage probabilities of them are closer to confidence level of 95%. Larger values of c₂ lead to narrow intervals and low coverage probabilities. We also find that inverse sinh intervals are shorter than untransformed intervals based on Woolf estimator and Mantel-Haenszel estimator, respectively. These procedures were illustrated with two clinical trials.

摘要

本文针对来自多个 2 × 2 表的常见优势比提出了两种新的近似置信限方法。这两个基于 Woolf 估计量和 Mantel-Haenszel 估计量的渐近分布的新程序与逆 sinh 变换相关联。我们采用三种伪频率方法来计算置信区间，以避免由于多个 2 × 2 表中存在零单元格而导致区间失败。我们开发的改进逆用于公共比值比的sinh间隔其中添加一个伪频率（Ç ₁）的所有单元格计算的共同比值比的点估计和另一伪频率之前（c ^ ₂) 到所有单元格，然后再计算标准误差估计。模拟是根据覆盖概率和平均对数长度来评估 22 个置信区间，包括 Woolf、Mantel-Haenszel、它们的反 sinh 区间和它们的伪频率修正反 sinh 区间。仿真结果表明，当c ₂略大于c ₁时，由两种不同伪频率调整的反sinh 间隔表现相当好，因为它们的覆盖概率更接近95%的置信水平。c _{2 的}较大值导致间隔窄和覆盖概率低。我们还发现，inverse sinh 区间分别比基于 Woolf 估计量和 Mantel-Haenszel 估计量的未变换区间短。这些程序通过两个临床试验进行了说明。