Paired binary data naturally arises when paired body parts are investigated in clinical trials. In this paper, we will further study whether the response rates of $g (g \geq 2)$ groups are equal under Dallal’s model and propose eight test statistics ($T^a_L$, $T^a_W$, $T^a_{SC}$, $T^a_R$, $T^b_L$, $T^b_W$, $T^b_{SC}$ and $T^b_R$). Some expressions of these tests are derived. The simulation results show that likelihood ratio and Wald-type tests are not robust with respect to empirical type I error rates (TIEs). The score and Ronser-type tests can produce satisfactory TIEs and power, and therefore are recommended. A real example is given to illustrate the proposed methods.

中文翻译：

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Dallal模型下响应率相等性检验的进一步研究

当在临床试验中研究成对的身体部位时，自然会出现成对的二进制数据。在本文中，我们将进一步研究 $g (g \geq 2)$ 组在 Dallal 模型下的响应率是否相等，并提出八个检验统计量（$T^a_L$、$T^a_W$、$T^a_ {SC}$、$T^a_R$、$T^b_L$、$T^b_W$、$T^b_{SC}$ 和 $T^b_R$）。推导出这些测试的一些表达式。模拟结果表明似然比和 Wald 型检验在经验 I 类错误率 (TIE) 方面并不稳健。分数和 Ronser 类型的测试可以产生令人满意的 TIE 和力量，因此被推荐。给出了一个真实的例子来说明所提出的方法。