Subjects in clinical studies that investigate paired body parts can carry a disease on either both sides (bilateral) or a single side (unilateral) of the organs. Data in such studies may consist of both bilateral and unilateral records. However, the correlation between the paired organs is often ignored, which may lead to biased interpretations. Recent literatures have taken the correlation into account. For example, Ma and Wang (2021) proposed three asymptotic procedures for testing the homogeneity of proportions of multiple groups using combined bilateral and unilateral data and recommended the score test. It is of importance to notice that the asymptotic behavior is not guaranteed if the sample size is small, resulting in uncontrolled type I error rates. In this paper, we extend their work by considering exact approaches and compare these methods with the score test proposed by Ma and Wang (2021) in terms of type I errors and statistical powers. Additionally, two real-world examples are used to illustrate the application of the proposed approaches.

翻译：临床研究中涉及配对身体部位的研究对象可能在器官双侧（双边）或单侧（单边）携带疾病。此类研究数据可能同时包含双边和单侧记录。然而，配对器官之间的相关性常被忽略，可能导致有偏的解释。近期文献已考虑该相关性。例如，Ma 和 Wang (2021) 提出三种渐近方法，用于检验利用组合双边和单侧数据的多组比例同质性，并推荐了分数检验。值得注意的是，当样本量较小时，渐近行为无法保证，导致I类错误率失控。本文通过考虑精确方法扩展他们的工作，并在I类错误率和统计功效方面将这些方法与 Ma 和 Wang (2021) 提出的分数检验进行比较。此外，使用两个真实世界示例来说明所提方法的应用。