隨著醫療技術的進步，部分患者預後良好，導致在試驗期間內無法觀察到事件的發生因而被視作治癒。到目前為止，許多相關研究皆使用混合治癒模型(Mixture cure model)對具有長期設限存活時間的存活數據進行分析，但臨床上許多疾病同時也兼具重複復發的性質，因此本研究主要探討復發事件的混合模型。將模型分為復發與否之機率以及復發與否之存活函數兩部分進行討論，第一部分，考慮到復發狀態會隨著時間改變，我們引入馬可夫鏈，利用轉移機率矩陣求出不同時段下復發與否之機率；第二部分，分別使用Cox比例風險模型和韋伯分配對復發與未復發之存活函數進行建模，建立4種混合復發模型，依序為單次復發結合Cox比例風險模型、單次復發結合Cox比例風險模型和韋伯分配、多次復發結合Cox比例風險模型和韋伯分配、及多次復發結合受風險因子影響之轉移機率矩陣，並計算患者的存活機率。
接著，透過統計模擬復發資料，利用最大概似估計(Maximum Likelihood Estimation, MLE)估計模型參數，並將每個模型中估計轉移機率的四種方法進行比較，結果顯示在單次復發模型中MLE的估計最為準確。在模型四中因為加入自變數對轉移機率的影響，所以相較於其他方法，MLE能考慮到每位受試者的個別差異，並針對風險因子對轉移機率的影響進行估計。最後，本研究採用R語言內建膀胱癌多腫瘤復發資料進行實例分析，整體而言，接受安慰劑治療之受試者各時段預測存活狀態準確率落在74.39%~89.34%之間；接受吡哆醇治療之受試者各時段預測準確率落在56.19%~69.00%之間；接受噻替哌治療之受試者各時段預測準確率落在76.22%~82.33%之間。

With the advancement of medical technology, some patients have good prognosis, so that the occurrence of events cannot be observed during the trial period and thus they are regarded as cured. So far, many related studies have used the mixture cure model to analyze the survival data with long-term survival time. But many clinical diseases also have the property of repeated recurrence. Therefore, this study mainly focuses on the mixed model of recurrence events. The model is divided into two parts: the probability of recurrence or not and the survival function of recurrence or not. In the first part, considering that the recurrence status will change with time, so we introduce the idea of the Markov chain and use the transition probability matrix to calculate the probability of recurrence at different time periods. In the second part, the Cox proportional hazards model and Weibull distribution were used to model the survival function of recurrence and non-recurrence, respectively. Besides, we establish four mixture recurrence models: single recurrence combined with Cox proportional hazards model, single recurrence combined with Cox proportional hazards model and Weibull distribution, repeatedly recurrence combined with Cox proportional hazards model and Weibull distribution, and repeatedly recurrence combined with transition probability matrix influenced by risk factors model. Then we calculate the survival probability of patients.
Then, through statistical simulation of recurrence data, the Maximum Likelihood Estimation (MLE) is used to estimate model parameters. The four methods for estimating the transition probability matrix in each model are compared. The results show that in the single recurrence model, MLE can obtain the most accurate estimation. The fourth model with the effect of independent variables on the transition probability, so compared to the other methods, MLE considers individual differences and estimates the effect of risk factors on the transition probability. Finally, this study uses the built-in bladder cancer multi-tumor recurrence data in the sample of R language as an example to analysis. Overall, the prediction accuracy of subjects receiving placebo treatment at each time period falls between 74.39%~89.34%; the accuracy falls between 56.19%~69.0% for receiving pyridoxine treatment; and it falls between 76.22%~82.33% for receiving thiotepa treatment.

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