隨著醫學技術的不斷進步，許多疾病已經可以被控制，使得患者的狀況得到改善，在足夠長的時間內沒有觀察到因疾病導致的死亡事件發生。但是，部份疾病可能隨著時間的推進反覆復發，因此混合治癒模型並不能全面描述此種疾病的狀態。本研究使用連續時間馬可夫鏈建立隨時間改變的復發機率，進一步結合未復發群體和復發群體的存活函數，採用以韋伯分配為基礎風險函數的Cox比例風險模型。透過概似函數和牛頓法，分別找出影響復發機率和存活時間的解釋變數，並估計其相對應的參數。接著，我們使用模擬數據和實例，以評估參數估計的好壞。在實例中，我們採用R語言內建的膀胱癌多腫瘤復發資料進行實例分析，透過參數的估計和檢定，找出對轉移機率和存活時間具有影響的解釋變數，並利用該模型估計平均轉移時間和平均存活時間。

With the advancement of medical technology, many diseases are now well studied to provide disease management to patients to improve their quality of life, and death events caused by diseases may not be observed for an extended period of time. However, some diseases may be recurrent over time, and therefore, the mixed cure model cannot fully describe the state of such diseases. In this study, we used a continuous-time Markov chain to establish recurrence probabilities that change with time, further combining the survival functions of non-recurrence and recurrence groups. We adopted a Cox proportional hazards model with a Weibull distribution as the baseline hazard function. Through the use of likelihood function and Newton's method, we identified the explanatory variables affecting the recurrence probability and survival time. We also estimated their corresponding parameters.
Subsequently, we employed simulated data and case studies to evaluate the quality of parameter estimation. In the case study, we used the built-in bladder cancer data with multiple tumor recurrence in the R program for analysis. Through parameter estimation and hypothesis testing, we identified explanatory variables that influence recurrence probability and survival time, and used this model to calculate average transition time and average survival time.

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