在生物醫學領域中，每當新藥物出現時，爲了比較新藥物與其他藥物是否存在差異會 考慮使用配對設計。例如 Yao(2012)使用高頻熱療治療三叉神經痛患者面部，且左右臉頰使 用不同治療溫度以做對比。根據病患疼痛部位不同可以分為兩組群體（上頜神經痛及下頜 神經痛）。在引入配對設計下，可以排除異質性。但配對設計會引入相關性，這導致更多相 關性參數的出現以及更爲複雜的分配比較。 本文提出了一種強韌概似函數的方法來推論配對設計下兩個伯努利分配的異同。此方 法是將兩個獨立的伯努利概似函數強韌化，得到強韌 Wald 統計量、強韌 Score 統計量以及 強韌性 likelihood ratio 統計量來檢驗分配是否存在相同。文中將提供理論以及推導，並利用 模擬以及實例分析展示強韌化方法的優勢。;In the field of biomedicine, whenever a new drug is introduced, a paired design is considered in order to compare the new drug with other drugs. For example, Yao (2012) used radiofrequency thermocoagulation therapy to treat the face of a patient with trigeminal neuralgia and used different treatment temperatures for the left and right cheeks for comparison. Patients can be divided into two groups (maxillary division of trigeminal nerve and mandibular division of trigeminal nerve) depending on the location of the pain. With the introduction of a paired design, homogeneity can be excluded. However, the paired design will result in the introduction of correlation, which leads to more correlated parameters and more complex comparisons of assignments. In this thesis, a robust likelihood function approach is proposed to infer the similarities and differences between two Bernoulli distributions under a paired design. The method is based on the robustness of two independent Bernoulli likelihood functions to obtain the robust Wald statistic, the robust Score statistic and the robust likelihood ratio statistic to examine whether the distributions are identical. The thesis will provide the theory and derivations, and demonstrate the advantages of the robust likelihood function method using simulations and examples.
