在醫學領域研究中，常見具有群體結構的資料，例如來自同一間醫院或相同醫師治療的受試者等。由於這類資料存在相關性，使得建立分析模型時往往需引入更多參數，進而增加模型的複雜度。 本研究我們使用強韌化多項分配的概似函數來分析存在群內相關的資料。根據Royall與Tsou (2003) 所提出的方法，我們的模型無須考慮資料的相關性，利用感興趣參數的最大概似估計量具有一致性的可強韌化性質，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，我們呈現了強韌華德檢定統計量 (robust wald statistics)、強韌概似比檢定統計量 (robust likelihood ratio statistics)，並且與Landsman et al. (2019) 使用的狄利克雷多項分配 (Dirichlet-multinomial distribution) 的參數估計表現進行比較。 ;In medical research, data with inherent group structures are commonly encountered—for instance, patients treated at the same hospital or by the same physician. Such data often exhibit intra-group correlation, which typically necessitates the inclusion of additional parameters in statistical models, thereby increasing their complexity. In this study, we employ a robustified likelihood function derived from the multinomial distribution to analyze data exhibiting intra-cluster correlation. Following the approach proposed by Royall and Tsou (2003), our model does not explicitly account for the correlation structure. Nevertheless, the maximum likelihood estimator of the parameter of interest remains consistent and robust, allowing for valid statistical inference despite the presence of correlation. Furthermore, through simulation studies and real-world data analyses, we assess the performance of the robust Wald and robust likelihood ratio statistics. These results are then compared with those obtained using the Dirichlet-multinomial distribution model proposed by Landsman et al. (2018), particularly in terms of parameter estimation accuracy.
