| 姓名 |
侯昰宇(Shi-Yu Hou)
查詢紙本館藏 |
畢業系所 |
統計研究所 |
| 論文名稱 |
時間相依ROC曲線的修正
(Modification of Time-dependent ROC Curves)
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| 相關論文 | |
| 檔案 |
 [Endnote RIS 格式]
[Bibtex 格式]
 [相關文章]  [文章引用]  [完整記錄]  [館藏目錄]  至系統瀏覽論文 (2025-7-1以後開放)
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| 摘要(中) |
醫學研究中，常以受試者特徵曲線(Receiver Operating Characteristic curve，簡稱ROC曲線)評估生物指標對疾病預測能力。其中以Heagerty.& Zheng.(2005)提出的時間相依ROC曲線最為常見，透過分析並提高預測效率，辨別各個生物指標的預測能力，進而找出適合的模型。過去文獻使用比例風險模型(Proportional hazard model,簡稱PH或Cox模型)，或使用AFT模型(Accelerated failure time model)、PO模型(Proportional odds model)，建構時間相依ROC曲線，並獲得曲線下面積(the area under the ROC curves,簡稱AUC)，透過對各個時間下的AUC加權平均，取得一致性指標(Concordance)，並可將其推導為風險迴歸的函數，當使用不同模型時，只需代入對應的風險函數，此一致性指標在先前已被證明對預測精準度有一致性。本研究針對AUC的計算方式提出修正，透過原先的定義，將面積計算方式作調整，進而獲得更貼近真實值的結果。後續再使用過去文獻提出的各個模型，將其應用在同一筆模擬資料中，比較其中的差異與優劣，觀察一致性指標的準確性，最後以實際愛滋病資料分析，展示不同模型下的結果。 |
| 摘要(英) |
In medical research, the receiver operating characteristic curve (ROC curve) is often used to evaluate the predictive ability of biological indicators for diseases. Among them, the time-dependent ROC curve proposed by Heagerty. & Zheng.(2005) is the most common. By analyzing and improving the prediction efficiency, it can identify the predictive ability of each biological indicator, and then find a suitable model. In the past, the literature used proportional hazards model (referred to as PH or Cox model), or used AFT model (Accelerated failure time model), PO model (Proportional odds model) to construct time-dependent ROC curves, and obtained the area under the ROC curves(AUC), through the weighted average of AUC at each time, the consistency index (Concordance) can be obtained, and it can be derived as a function of risk regression. When using different models, just substitute the corresponding hazard function, this consistency metric has previously been shown to be consistent with forecast accuracy. This study proposes a revision to the calculation method of AUC. Through the original definition, the area calculation method is adjusted to obtain results that are closer to the true value. Subsequently, each model proposed in the past literature will be used, applied to the same simulation data, the differences and pros and cons will be compared, and the accuracy of the consistency indicators will be observed. Finally, the actual AIDS data will be analyzed to show the results under different models. |
| 關鍵字(中) |
★ 比例風險模型
★ 加速失敗模型
★ 比例勝算模型
★ 一致性指標
★ ROC曲線計算修正
★ 模型比較 |
關鍵字(英) |
|
| 論文目次 |
摘要{i}
Abstract{ii}
致謝{iii}
目錄{iv}
圖目錄{vi}
表目錄{vii}
第一章 緒論{1}
1.1 ROC 曲線{2}
1.2 時間相依ROC曲線{5}
1.3 累積敏感度與動態特異度{9}
1.4 事件敏感度與靜態特異度{12}
1.5 事件敏感度與動態特異度{13}
第二章 統計方法{15}
2.1 Cox比例風險模型{15}
2.2 AFT模型{17}
2.3 PO模型{19}
2.4 修正計算方式{22}
第三章 模擬研究{25}
3.1 Cox~模型模擬{26}
3.2 AFT~模型模擬{31}
3.3 PO~模型模擬
3.4 修正計算方式結論{41}
3.5 Bivariate normal模擬{43}
第四章 資料分析{46}
4.1 愛滋病資料{46}
4.2 時間獨立共變數存活模型{47}
第五章 結論{49}
參考文獻{50}
附錄A.1 時間相依AUC與一致性指標推導{52}
附錄A.2 不同模型下的模擬結果MSE{54} |
| 參考文獻 |
Bennett,S.(1983). Analysis of Survival Data by the Proportional Odds Model.{Statistics in Medicine}
Box,G. , and Cox,D.(1964). An Analysis of Transformations. {Journal of the Royal Statistical Society Series B}
Chiou, S. H., Kang, S. and Yan, J. (2014). Fitting Accelerated Failure Time Models in Routine Survival Analysis with R Package aftgee.{Journal of Statistical Software}
Cox, D. R. (1975). Partial likelihood.{Biometrics}
Heagerty, P. J., Saha-Chaudhuri, P. and Saha-Chaudhuri, M. P. (2012). Package ‘risksetROC’: riskset ROC curve estimation from censored survival data.
Heagerty, P.J. and Zheng, Y. (2005). Survival Model Predictive Accuracy and ROC Curves.{Biometrika}
Jones, M. C. (1990). The performance of kernel density functions in kernel distribution function estimation. {Statistics and Probability Letter}
Jones, M. C. and Sheather, S. J. (1991). Using non-statistic terms to advantage in kernel-based estimation of integrated squared density derivatives.{Statistics and Probability Letter}
Kamarudin, A. N., Cox, T. and Kolamunnage-Dona, R. (2017). Time-dependent ROC curve analysis in medical research: current methods and applications.{BMC Medical Research Methodology}
Lin, Y. H. (2017). Model-base Time dependent AUC and Predictive Accuracy.{Graduate Institute of Statistics, National Central University.}
Wei, L. J. (1992). The accelerated failure time model: A useful alternative to the cox regression model in survival analysis.{Statistics in Medicine}
林威廷(2021)。風險回歸模型下時間相依~ROC~曲線。國立中央大學統計研究所碩士論文。 |
| 指導教授 |
曾議寬
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審核日期 |
2022-7-15 |
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