加速失敗與長期追蹤聯合模型分析– 肝硬化之實例研究

存活分析中，Cox比例風險模型為最普遍的存活模型，但當資料沒有通過比例風險假設時，可使用其他的風險模型作為代替，常見的為加速失敗模型，在使用加速失敗模型描述長期追蹤資料中共變數與存活時間之間的關係時，存在著測量誤差與測量時間不固定的問題，同時資料缺失(informative missing)也會造成估計發生偏誤。為了解決這些問題，我們引進長期追蹤模型，利用線性隨機效應模型描述長期追蹤資料，使用概似比檢定與AIC值選擇適合的模型，解決這些問題，結合加速失敗模型與長期追蹤資料模型，也就是聯合模型。聯合模型的參數估計方面，由於使用線性隨機效應模型，將隨機效應視為遺失值，因此對聯合模型的概似函數使用EM(expectation maximization algorithm)演算法估計參數，且由於直接估計參數標準差不易，採用拔靴法估計參數標準差。由於近年來發現，少數資料使用Cox模型與加速失敗模型配適會得到不同的結果，本文使用加速失敗風險模型的聯合模型配適哥本哈根(Copenhagen)的研究團隊(Schlichting et al.,1983)肝硬化資料，分析強體松對肝硬化患者之療效，且將結果與使用Cox模型所得的結果進行比較。

關鍵字

聯合模型；長期追蹤資料；比例風險模型；加速失敗模型

並列摘要

In survival analysis, the most common semi-parametric survival model is Cox proportional hazards model, if the proportional hazards assumption fail, we can use other hazards model to be an alternative model. The accelerated failure time model is an attractive alternative model. When we describe the relationship between longitudinal data and survival time, there exist some problems of measurement error and incomplete covariate history that result in biased estimation for partial likelihood function. In order to solve these problems, we introduce the joint model approach. The model parameter estimation of joint model cannot be obtained directly through the joint likelihood function because the integral outside the likelihood function. Therefore, we conduct EM (expectation maximization algorithm) algorithm to estimate the parameters to overcome the difficulty. Since the standard deviation is not easy to estimate the parameters directly, we use the bootstrap procedure to estimate the standard deviation. In recent literature, data fitted by Cox model or accelerated failure model may lead to different results. Therefore, we use the accelerated failure time model to fit the cirrhosis data and compare the results with the ones obtained Cox model.

並列關鍵字

joint model ； longitudinal data ； Cox model ； AFT model

參考文獻

1. Brown, E. R., Ibrahim, J. G. & Degruttola, V. (2005). A Flexible B-spline Model for Multiple Longitudinal.Biomarkers and Survival. Biometrics, 61, 64–73.

2. Cox, D. R. (1975). Partial Likelihood. Biometrika, 62, 269–76.

3. Ding, J. & Wang, J. L. (2008). Modeling Longitudinal Data with Nonparametric Multiplicative Random Effects Jointly with Survival Data. Biometrics, 64, 546–56.

4. Efron, B.(1994). Missing data, imputation and bootstrap (with Discussion). J. Am Statist. Ass. 89, 463-479

5. Henderson, R., Diggle, P. & Dobson, A. (2000). Joint Modelling of Longitudinal Measurements and Event Time Data. Biostatistics, 4, 465–80.

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加速失敗與長期追蹤聯合模型分析– 肝硬化之實例研究

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