由於疾病發生率(incidence rate)具備明確的意義和容易解釋的特質，疾病發生率已被廣泛應用於醫學研究領域中。在本論文中，針對右設限資料，在無法取得大量的資料下，如何利用外部資料所提供的疾病發生率，精準地估計出Cox比例風險模型參數的研究問題。我們提出了一種有效的估計方法，將次群疾病發生率的輔助資訊納入Cox比例風險模型的估計中。與未結合輔助資訊的傳統模型估計方法相比，本研究利用外部資訊，所提出的最大經驗概似法提高了模型參數估計量的效率。此外，模擬研究顯示，本研究提出的估計量，相較於傳統方法，有更高的效率。

Incidence rate for a disease have been wildly used in the field of medical research because of its clear physical and simple clinical interpretation. In this thesis, we propose an efficient estimation to incorporate with the auxiliary subgroup information of incidence rate information into the estimation of the Cox proportional hazard model. Comparing to the conventional models without incorporation of the available auxiliary information, utilizing the external information shows that the proposed method improves efficiency for the estimation of the regression parameters based on the maximum empirical likelihood method. In addition, simulation studies demonstrate that the proposed method gain in efficiency over the conventional approach.

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