標誌歷程之動態存活預測的統計分析

Statistical Analysis for Dynamic Survival Prediction Involving Marker Processes

蘇登煌(Deng-Huang Su)

指導教授 ： 張淑惠

國立臺灣大學/公共衛生學院/流行病學與預防醫學研究所/博士(2016年)

https://doi.org/10.6342/NTU201610254

摘要

以臨床工作而言，診療慢性患者的過程所形成的記錄，為一長期追踨資料型態。在每次患者就診中，臨床醫師會透過一些標誌或事件訊息來了解未來患者的併發症或死亡風險的高低，根據這些風險的高低，醫師需要制定適當的措施來防制或延緩併發症甚至死亡的發生，故如何量化此類風險是臨床上很重要的問題。本論文的目的在於利用患者的動態指標訊息及基本特性來預測未來的存活機率，亦即利用標誌的訊息，不斷地更新對未來存活的預測。時間依賴性Cox模式(time-dependent Cox’s model)是分析存活資料的一種常用的迴歸模式，具有利用長期追蹤資料具時間順序的特色，而明確地架構標誌歷程和基礎共變數跟終止事件間的相關性。但採用以標誌歷程為時間依賴性共變數的Cox模式的問題在於此時間依賴性模式為一即時解釋模式，無法用過去標誌歷程直接預測未來存活機率。因此本論文運用貝氏定理作機率的反轉及條件式機率的運算來處理這個問題，如此便可利用共變數和標誌歷程的條件式分布，在發生終止事件的時間點上給予適當的權重上(Cox模式中的參數及變數值所構成)，而可在不同標誌歷程及共變數的條件下，估計未來存活機率。此方法之優點在於可免於估計時間依賴性Cox模式中的基礎風險函數及標誌時間的邊際分布。本研究將利用模擬以測試所提出方法之表現，並以甲狀腺乳突癌患者為例加以說明所提之方法的運用。

關鍵字

追蹤資料 ； 標誌歷程 ； 雙變數存活 ； 多變數存活 ； 存活預測

並列摘要

In clinical practice, the records of patients with chronic diseases is a form of the longitudinal data. At each patient’s visit, the physician will collect the signs or event information to understand the level of the patient's future risk of complications or death. According to the level of these risks, physicians need to take some appropriate actions to prevent or delay the occurrence of complications or death. So, how to quantify such risks is a clinically important issue. The purpose of this paper is to use the dynamic messages of marker and the patients’ basic characteristics to predict the patients’ survival. Time-dependent Cox’s model is a population regression model which constructs explicit dependence of the hazard of termination time on baseline covariates and marker process by taking the advantage of longitudinal data with chronological features. However, in the time-dependent Cox’s model, the effect of the marker on the immediate survival has no meaning of prediction. That is, it is not straightforward to predict the future survival given the past information of the marker process in the time-dependent Cox’s model. Therefore, we adopt Bayes' theorem and conditional probability to overcome such problems. We estimate the conditional probability of future survival given the different information of marker process by using the conditional distribution of baseline covariates and marker process given surviving at a time point and the Cox modeling information. The advantage of the proposed method is that marginal distribution of marker process and baseline hazard function in the Cox’s model are not required. Simulation studies are conducted to assess the performance of the proposed method. An example of papillary thyroid carcinoma is provided for illustration.

並列關鍵字

longitudinal data ； marker process ； bivariate survival ； multivariate survival ； prediction

參考文獻

Al-Khalidi, H. R., Hong, Y., Fleming, T. R., and Therneau, T. M. (2011). Insights on the robust variance estimator under recurrent-events model. Biometrics 67, 1564-1572.

Anderson, J. R., Cain, K. C., and Gelber, R. D. (1983). Analysis of survival by tumor response. Journal of Clinical Oncology 1, 710-719.

Austin, P. C. (2012). Generating survival times to simulate Cox proportional hazards models with time‐varying covariates. Statistics in Medicine 31, 3946-3958.

Aydin, Z., Altunbasak, Y., and Borodovsky, M. (2006). Protein secondary structure prediction for a single-sequence using hidden semi-Markov models. BMC Bioinformatics 7, 178.

Bartolomeo, N., Trerotoli, P., and Serio, G. (2011). Progression of liver cirrhosis to HCC: an application of hidden Markov model. BMC Medical Research Methodology 11, 38.