根據資料統計，癌症在台灣名列十大死因已數十年。近幾年之研究大多在探討有關癌症死亡率、存活率潛在因子之影響情形，然而癌症轉移方面的研究相對甚少。癌症轉移與否，常被視作癌症患者病程嚴重程度以及治療效果的指標。本研究將探討癌症轉移間轉移時間、病患特徵、慢性疾病、治療效果之潛在因子影響情形。
本研究使用台灣健保資料庫癌症檔進行資料之建構與蒐集，台灣健保資料庫涵蓋近二十年就診資料且包含百分之九十九健保制度國民。前段在台灣健保資料庫癌症檔獲取影響癌症轉移之潛在因子後，透過R軟體工具探討多狀態下半馬可夫過程在不同潛在因子影響下癌症轉移情形。
多狀態半馬可夫鏈模型探討在不同潛在因子下癌症轉移情形，其中針對癌症轉移時間隱含指數分配、韋伯分配、指數化韋伯分配。多狀態半馬可夫鏈無記憶性的基本假設:呈現轉移矩陣中本期只與前期有關；在轉移時間機率分配明確設定情況下，多狀態半馬可夫鏈中即符合基本假設且存在離散狀態(癌症)以及連續時間(癌症轉移時間)。本模型結合比例風險模型配適三種模型分別為:基礎模型、單一共變量模型、複合共變量並且分析半馬可夫過程危險函數變化情形以及癌症轉移間不同潛在因子下相對危險性；另一階段為了解癌症轉移之間時間比例，透過半馬可夫過程模型計算各狀態轉移間平均時間的變化。本研究結合半馬可夫過程以及比例風險模型，透過台灣健保資料庫找尋相關潛在因子探討癌症轉移間半馬可夫過程危險函數的變化。最終得到癌症轉移間轉移時間比例、不同潛在因子下半馬可夫鏈過程危險函數、相對危險性之比較。

According to statistics in Taiwan, cancer is the most serious and been in the reason of death many decades. In recent years, most of study discussed on different characteristic effect on cancer mortality or incidence, but seldom investigated on cancer metastasis. The severity of cancer patient and treatment effect treats as the indicator. Our research investigated impact of hidden factor on metastasis time (sojourn time), characteristic, chronic diseases, and treatment effect.
National Health Insurance Research Database which has been launched twenty years and resulting database covers 99% of 23 million populations. After pre-processing the National Health Insurance (NHI) Research Database to obtain the hidden factors, an R software package constructed Multi-State Semi-Markov (MSSM) model provided useful and relevant tool for observing the impact of cancer metastasis under different hidden factors.
Multi-State Semi-Markov (MSSM) model represented the impact on cancer metastasis under different hidden factors (covariates) and the metastasis time (sojourn time) involved exponential distribution, weibull distribution, and exponentiated weibull distribution. The MSSM model assumed that the process is independent from the time spent in the state (memoryless); in MSSM model can be considered with the discrete state (cancer state) and continuous time (sojourn time). The MSSM model incorporated the cox proportional regression model to fit three final model: based-model, single-covariate model, and multi-covariate model. Final model provided to calculate the relative risk (RR) of sojourn time but consider the hazard function of Semi-Markov process (SMP) under different hidden factors.
Our research incorporated the concept of Semi-Markov process and cox proportional regression model. Hidden factors (covariates) built from National Health Insurance research database like chronic diseases, individual characteristic, treatments. Eventually, this study will have the proportion of time from Semi-Markov process (SMP), state transfer relative risk (RR), and the hazards function of Semi-Markov process (SMP) with different covariates.

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