在過去文獻中，布賴爾分數（Brier Score）多半被應用於固定共變數情境下的預測評估。然而在生物醫學研究中，個體的生物標記或臨床指標常隨追蹤時間反覆測量，形成時間相依共變數，此類資料若直接採用固定共變數評估框架，將無法全面反映模型的動態預測效能。有鑑於此，聯合模型（Joint Model）提供了一個自然的統計架構，能夠同時處理時間相依共變數與存活時間之間的關聯，並以此為基礎，進一步探討動態預測準確度的評估問題。 本研究以聯合模型為工具，核心貢獻在於將布賴爾分數的應用推廣至此一動態預測情境，以動態布賴爾分數（Dynamic Brier Score）作為預測誤差的主要衡量指標。我們同時考慮參數模型（基於指數、韋伯、對數常態及對數羅吉斯分佈）與半母數模型，分別在比例風險（Proportional Hazards）模型、加速失效時間（Accelerated Failure Time）模型與比例勝算（Proportional odds）模型三類存活架構下，藉由動態布賴爾分數比較不同模型的預測準確度，以探討各存活假設下模型的預測穩健性。針對右設限資料，引入逆設限機率加權法（Inverse Probability of Censoring Weighting， IPCW）對動態布賴爾分數進行修正，以確保評估結果的正確性。 透過模擬研究，針對於不同設限率及模型錯誤配適情境下，以動態布賴爾分數與整合布賴爾分數（Integrated Brier Score， IBS）作為跨模型比較的主要指標，系統性評估各模型的預測表現。此外，本研究亦以 PBC 真實臨床資料進行實例分析，以驗證模擬結論在真實資料情境下的適用性。;In the existing literature， the Brier Score has predominantly been applied to static prediction evaluation under fixed covariate settings. However， in biomedical research， individuals’ clinical indicators are often measured repeatedly over follow-up， giving rise to time-dependent covariates for which static evaluation frameworks are inadequate. The Joint Model provides a natural framework for handling such data， serving as the basis for this study. The core contribution of this study is to extend the Brier Score to this dynamic prediction setting via the Dynamic Brier Score. We consider both parametric and semi-parametric models under three survival frameworks—Proportional Hazards (PH)， Accelerated Failure Time (AFT)， and Proportional Odds (PO)—with IPCW correction for right-censoring to ensure unbiased evaluation. Simulation studies systematically evaluate predictive performance under varying censoring rates and model misspecification， using the Integrated Brier Score (IBS) as the primary summary measure. A real data analysis based on the PBC dataset is further conducted to verify the simulation findings.
