在現今的醫學研究中，每當病人進入實驗都會記錄其共變數數值，
例如: 存活時間、血壓、血型等，我們可將與時間相依的共變數作為
生物指標以衡量疾病的預測能力。在傳統醫學研究上，通常會使用接
受者作業特徵曲線(Receiver Operating Characteristic Curve，或者叫ROC 曲線) 作為衡量疾病預測能力的標準。先前的研究中亦發展了固定共變數下時間相依敏感度與特異度之 Cox 風險迴歸模型。然而
當比例風險假設不符合時，即不適用一般的 Cox 風險迴歸模型，在此
我們建議可使用加速失效模型(Accelerated Failure Time Model)作為替代。接著，我們進一步將其推廣到長期追蹤共變數的資料。並於模擬與實例分析中，比較傳統模型衡量指標𝑅 square與一致性指標𝐶，以評估兩者模型預測能力之表現。

In current medical research, whenever a patient enters an experiment, they will record their covariate values, such as: survival time, blood pressure, blood type, etc.
We can use these time-dependent covariates as biomarkers to measure and predict disease. In traditional medical research, the Receiver Operating Characteristic Curve (or called ROC curve) is often used as a measure of disease
prediction ability. Previous studies have also developed Cox regression models with time-dependent sensitivity and specificity for fixed covariates. However, when the proportional assumption is not fit, the general Cox regression model is not applicable. Here, we suggest that an Accelerated Failure Time Model can be used as an alternative. Then, we further extended it to the longitudinal covariate data. In the simulation and example analysis, the traditional model index 𝑅 square
and the consistency index C were compared to evaluate the performance of the prediction ability of the two models.

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