疾病發生率用以描述風險族群罹患疾病的風險，其涵蓋的概念在許多醫學研究題材上得以廣泛應用。本論文主要研究問題有二，當利用Cox比例風險模型配適內部存活資料時，除了如何同時結合外部資料提供之子群疾病發生率，使得模型參數估計更有效之外，本研究進一步推導參數估計的變異數矩陣。因此，提供參數估計的理論變異數亦為探討重點。我們使用經驗概似估計法適當地納入外部輔助資訊，相較於未納入外部輔助資訊的傳統估計方法，模型參數估計的變異更小，並且利用理論變異數佐證本論文的方法確實能使得參數估計地更精確。

By knowing the incidence rate, an investigator can realize how quickly people are getting the disease. Because the concept of incidence rate for a disease is simple, it can be used to interpret the clinical meaning clearly in the field of medical research. In this thesis, we not only propose an efficient estimation of the Cox proportional hazard model incorporated with the auxiliary subgroup incidence rate information but also make inference about the theoretical covariance matrix for the estimation of the regression parameters. Comparing to the conventional models without incorporating the available auxiliary information, making use of the incidence rate from external sources indicates that the proposed method improves efficiency for the estimation of the regression parameters based on the proposed maximum empirical likelihood method.

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