時間相依一致性指標之估計-聯合模型補值法與無母數方法之比較

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姓名

洪誠彣(Cheng-Wen Hong) 查詢紙本館藏

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統計研究所

論文名稱

時間相依一致性指標之估計-聯合模型補值法與無母數方法之比較
(Estimation of Time-dependent C-index: Comparison of Joint Model Imputation Method with Nonparametric Approach)

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至系統瀏覽論文 (2027-7-1以後開放)

摘要(中)

在醫學分析研究的存活資料中，存活時間常包含長期追蹤共變數，而此類型資料通常會伴隨著測量誤差，且當事件發生時，可能導致病患從長期研究中有信息性的退出試驗。針對此種數據，現存的無母數方法僅考慮到時間獨立右設限資料，且不允許有測量誤差存在，而時間相依共變數資料則會因為患者退出試驗，使得估計出現偏誤，為了克服這兩點困難，我們採用聯合模型補值法，並導入時間相依共變數，可以得到有效且一致性的估計。這裡分為兩類方法進行比較，其中之一為補值法，其中包含鄰近點補值法及聯合模型補值法，而我們在聯合模型中進一步探討三種模型，包括Cox模型、AFT模型及PO模型；另一個為無母數方法，包含了逆設限機率加權法。再來我們想了解利用以上三種方法所得到共變數的預測準確性。因此，使用時間相依一致性指標來作為衡量預測模型的標準。本研究目的在於比較以上方法所估計的時間相依一致性指標，在各種不同樣本數、設限率、測量誤差及錯誤模型配適下的影響，最後以實際愛滋病的資料做分析，展示不同方法下的結果。

摘要(英)

In the analysis of survival data in medical research, the survival time often includes long-term follow-up covariates, and such data typically come with measurement errors. When an event occurs, it may lead to informative drop-out of patients from the long-term study. Existing nonparametric methods only consider time-independent right-censored data and do not account for measurement errors, while time-dependent covariate data can result in biased estimates due to patient drop-out. To overcome these challenges, we employ joint modeling imputation methods and incorporate time-dependent covariates to achieve efficient and consistent estimates. We compare two categories of methods: the first category is imputation methods, which include the Nearest Neighbor Imputation and Joint Modeling Imputation, and within the joint model, we further explore three models: the Cox model, the Accelerated Failure Time (AFT) model, and the Proportional Odds (PO) model. The second category is nonparametric methods, which include the Inverse Probability of Censoring Weighted (IPCW) method. We aim to evaluate the prediction accuracy of the covariates obtained by these three methods. Therefore, we use the Time-dependent Concordance Index as a standard to measure the predictive performance of the models. This study aims to compare the estimated Time-dependent Concordance Index across various sample sizes, censoring rates, measurement errors, and model misspecifications. Finally, we apply these methods to real AIDS data to illustrate the results under different approaches.

關鍵字(中)

★ 聯合模型
★ 時間相依一致性指標
★ Cox模型
★ AFT模型
★ PO模型
★ 鄰近點估計法
★ 逆設限機率加權法

關鍵字(英)

★ Joint model
★ time-dependent concordance index
★ Cox model
★ AFT model
★ PO model
★ Nearest Neighbor Estimate
★ IPCW approach

論文目次

摘要 i
Abstract ii
誌謝 iii
目錄 iv
圖目錄 vii
表目錄 x
1.序論 1
1.1 半母數模型 3
1.1.1 Cox迴歸模型 3
1.1.2 AFT迴歸模型 4
1.1.3 PO迴歸模型 5
1.2 ROC、AUC及一致性指標 8
1.3 ROC曲線推廣 10
1.3.1 時間獨立共變數 11
1.3.2 時間相依共變數 14
1.4 補值法 17
1.4.1 鄰近點補值法 17
1.4.2 聯合模型補值法 18
1.5 無母數方法 18
1.5.1 逆設限機率加權法 18
1.6 文獻回顧 20
2.統計方法 22
2.1 聯合模型補值法 23
2.1.1 半母數模型風險函數 24
2.1.2 聯合模型蓋四函數與估計 26
2.1.3 程式套件 31
2.1.4 半母數模型時間相依一致性指標推導 32
3.模擬研究 36
3.1 Cox模型模擬 37
3.1.1 不同樣本數 38
3.1.2 不同設限率 42
3.1.3 不同測量誤差 44
3.1.4 模型錯誤配適 48
3.2 AFT模型模擬 49
3.2.1 不同樣本數 50
3.2.2 不同設限率 54
3.2.3 不同測量誤差 56
3.2.4 模型錯誤配適 60
3.3 PO模型模擬 61
3.3.1 不同樣本數 62
3.3.2 不同設限率 66
3.3.3 不同測量誤差 68
3.3.4 模型錯誤配適 71
4.資料分析 72
4.1 愛滋病資料 72
4.2 時間相依一致性指標 73
5.結論 79
參考文獻 80
附錄 83
A.1 時間獨立共變數在I/D下AUC與concordance推導 83
A.2 時間相依共變數在I/D下AUC與concordance推導 86
A.3 半母數Cox模型推導 88
A.4 參數Weibull AFT模型推導 89
A.5 半母數PO模型推導 90

參考文獻

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指導教授

曾議寬(Yi-Kuan Tseng)

審核日期

2024-7-9

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