在臨床試驗中，實驗者常用多種疾病來衡量不同治療的效用。因此將多個終點(multiple endpoints) 的設計作為一個重要的考量，此設計將從同一位受測者檢測多種疾病，因此資料間產生相關性，使得模型配似資料變得困難。 本文提出使用多元負二項 (multinomial negative binomial) 以及兩種變異數設定不同的常態模型作為實作模型 (working model)，並運用Royall and Tsou (2003) 提出的強韌概似函數方法 (robust adjusted likelihood functions) 使實作模型強韌化。透過此方法可獲得強韌化分數檢定統計量 (robust score statistics) 及強韌化韋德檢定統計量 (robust Wald statistics)，且此模型具可重複性 (reproducibility)，儘管受測者檢測疾病個數與模型假設不同，依然可透過強韌概似函數方法得到正確的統計推論。最後本文利用模擬與實例分析以比較強韌化多元負二項模型與強韌化常態模型的好壞，並驗證強韌化方法的優點。 ;In clinical trials, experimenters often use a variety of diseases to measure the effectiveness of different treatments. Therefore, the design of multiple endpoints is an important consideration. This design will detect multiple diseases from the same subject. Therefore, there is correlation between the data, which makes it difficult for the model to fit the data. This paper proposes the use of multivariate negative binomial and two normal models with different settings of variance as the working model, and uses the robust adjusted likelihood functions proposed by Royall and Tsou (2003) to robust the working model. Through this method, the robust score test statistics and the robust Wald test statistics can be obtained, and the model is reproducibility. Although the number of diseases detected by the subjects is different from the model hypothesis, the correct statistical inference can still be obtained through the adjusted likelihood functions method. Finally, this paper uses simulation and example analysis to compare of the robust multivariate negative binomial model and the robust normal model, and verify the advantages of the method.
