復發間隔時間資料之Cox比例風險模型的診斷

在各種醫學領域中，常利用Cox比例風險模型以探討共變數對風險函數的影響，在固定變數後，比較其相對風險，在所有時間點之下，任兩位個體的風險比必須是與時間無關的常數，稱為比例風險假設。在臨床研究中，個體在研究結束前可能經歷數次相同的事件。以乳腺癌的治療而言，患者可能反覆發生腫瘤復發事件，這種反覆發生相同事件稱為復發事件。本文感興趣的是兩相鄰復發事件的間隔時間，但由於同一個體之間隔時間彼此有相關性存在，會使得第二次以後的間隔時間和對應之設限事件無法彼此獨立。本論文採用兩種相關性來源處理間隔時間彼此的相關性與誘導性相依設限問題去處理這種誘導性相依設限，分別為相關性來自脆弱參數和相關性來自歷史事件。首先，我們利用尺度Schoenfeld殘差檢定應用於復發間隔時間資料，並結合不同的時間轉換型式，接著提出整合式尺度Schoenfeld殘差檢定。最後，將累積平賭殘差檢定納入比較其效果。因此，本論文透過模擬與實際資料比較不同相關來源情境下的檢驗力與圖形判斷力，並將方法實際運用在囊狀纖維化的復發間隔資料。

關鍵字

間隔時間；復發事件；誘導性設限；比例風險；累積殘差；尺度Schoenfeld殘差；分數檢定

並列摘要

In various medical fields, Cox’s regression model is one of the most popular methods. The purpose of the model is to explore the effects of covariates on the hazard function. The key assumption of this model is that the ratio between two hazard functions is independent of time, which is referred to as proportional hazards assumption. In follow-up studies, subjects may experience several events of the same type before the end of study. For example, multiple tumor recurrences are usually observed for investigating the efficiency of the treatment of patients with mammary cancer. Such repeated occurrences of the same event are called recurrent events. In this study, the outcomes of interest are gap times between any two successive events. However, the analysis of the second and later gap times is often subject to the dependent censoring which is induced by the dependence among the recurrent gap times. The aim of this thesis is to test the proportional hazards assumption for the Cox-type hazards models for recurrent gap times. We consider two sources of dependence among the recurrent gap times per subject: subject-specific frailty and the event history to handle such induced dependent censoring. First, we promote the scaled Schoenfeld residuals test to the recurrent gap time data. Then, we propose a combined scaled Schoenfeld residuals test by integrating the commonly used time transformation. Simulation studies are conducted to investigate and compare the performance of the proposed scaled Schoenfeld residuals tests as well as the cumulative sum of martingale residuals test. Finally, the cystic fibrosis data are analyzed for illustration.

並列關鍵字

gap time ； recurrent events ； induced information censoring ； proportional hazards ； cumulative sum of residuals ； scaled Schoenfeld residuals ； Score test

參考文獻

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

Efron, B. (1994). Missing data, imputation, and the bootstrap. Journal of the American Statistical Association 89, 463-475.

Breslow, N. (1974). Covariate analysis of censored survival data. Biometrics 30, 89–99.

Byar, D. (1980). The Veterans Administration study of chemoprophylaxis for recurrent stage I bladder tumors: Comparisons of placebo, pyridoxine, and topical thiotepa. In Bladder Tumors and Other Topics in Urological Oncology. Plenum Publishers, New York: 363–370.

Chang, S-H and Wang, M-C. (1999). Conditional regression analysis for recurrence time data, Journal of the American Statistical Association 448, 1221-1230.

國際替代計量

復發間隔時間資料之Cox比例風險模型的診斷

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