在生物醫學研究領域中經常會有成對的資料，例如一個人的雙腳、雙耳等。當成對的器官或身體部位接受治療時，觀察到的結果可以分為治癒或未治癒，因此產生二元資料。若因分層因素而導致相同的治療下產生不同的治療效果，則需進行治療效果的同質性檢定 (homogeneity test) 以及共同性檢定 (common test)。由於成對的資料具有相關性，使得機率模型需要引入更多參數，造成配適變得困難。 在本研究中我們使用強韌化兩個獨立伯努利模型的概似函數來分析分層成對的二元資料。根據Tsou (2018) 提出的方法，我們的模型忽略了數據中的相關性。由於感興趣的參數的最大概似估計量具有一致性，我們仍然可以得出正確的統計推論。此外，在本文的模擬研究與實例分析中，我們將在同質性以及共同性的假設下，呈現我們提出的強韌分數檢定統計量 (robust score test statistics) 與Sun et al. (2022) 提出的Dallal模型的分數檢定統計量 (score test statistics) 之間進行比較。;In the field of biomedical research, paired data are often encountered, such as a person′s feet or ears. When paired organs or body parts undergo treatment, the observed outcomes may be categorized as either healed or not healed, thus producing binary data. If stratification factors lead to different treatment effects under the same treatment, a homogeneity test and a common test are required to assess the treatment effect. Due to the correlation inherent in paired data, probability models need to incorporate additional parameters, making fitting the model more challenging. In this study, we analyze stratified paired binary data using the likelihood functions of robustified two independent Bernoulli models. Following the method proposed by Tsou (2018), our model disregards the correlation therein. Since the maximum likelihood estimation of the parameter of interest exhibits consistency, we can still draw correct inferences. Furthermore, in the simulation studies and case analyses of this paper, we will present comparisons between the score test statistics of the Dallal model proposed by Sun et al. (2022) and the robust score test statistics we propose, under assumptions of homogeneity and commonality.
