在許多國家，末期腎臟疾病為相當普遍的慢性疾病，尤其在台灣，根據美國腎臟資料系統(USRDS)統計報告顯示，2008年台灣地區末期腎臟疾病的發病率相當高，普及率更居世界之冠，並且隨著末期腎臟疾病人口逐漸增加，所有與末期腎臟疾病相關的醫療花費都成為政府以及社會相當大的負擔。因此，為了有效遏止慢性腎臟疾病病患病情的惡化，政府提出了許多獎勵計畫，希望慢性腎臟病患以及末期腎臟疾病患者能夠得到更好的醫療品質，以達成減少末期腎臟疾病的發生率以及普及率之目的。
在本論文中，我們利用連續時間馬可夫鏈模型來描述腎臟病患的疾病演進，將病患的特徵以及屬性列入考慮，以求出病患各自的期望壽命，並進一步提出一個數學規劃模型，將有限的醫療資源最佳地分配在這些獎勵計畫上，使得腎臟病患能夠獲得最大化的期望壽命。此論文的結果能夠幫助決策者評估患者的特徵以及屬性對於他們生存表現的影響，另外，還可以提供建議給政府，使分配醫療資源時能夠更具理論依據，並進一步促進腎臟病患得到最大的獲益。

End-stage renal disease (ESRD) has been a widespread disease in many countries, especially in Taiwan. According to the statistics of United States Renal Data System (USRDS), Taiwan had high rates of incident ESRD and the greatest rates of prevalent ESRD in 2008. Moreover, with the increasing ESRD patients appear, the huge expense becomes a heavy burden in the society. To avoid deterioration, the government proposed many incentive programs to stimulate better medical quality and the ultimate goal is to reduce the incident and prevalent rates of ESRD.
In this study, we develop a continuous-time Markov chain model to estimate the patients’ life expectancy and their disease progression of ESRD individually under different scenarios. Besides, we propose a mathematical model which is constructed to allocate resources to incentive programs to maximize patients’ life expectancy under the limited funds. The results can help decision makers realize the impact of patients’ attributes on their life expectancies before and after these incentive programs and provide suggestions to the government for allocating resources to achieve optimal patients’ effectiveness.

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