Performance of a two-sample test with Mann-Whitney statistics under dependent censoring with copula models

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許竣瑝(Jiun-Huang Hsu) 查詢紙本館藏

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(Performance of a two-sample test with Mann-Whitney statistics under dependent censoring with copula models)

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摘要(中)

曼-惠特尼檢定是一種用來比較兩組平均數是否一樣的無母數方法。對於右設限(Right censored)存活資料，曼-惠特尼影響(Mann-Whitney effect)是一種有效比較兩組存活時間是否相同的無母數方法。然而，在Efron (1967)、Koziol 及 Jia (2009)和Dobler 及 Pauly (2018)中提到曼-惠特尼影響的估計量會有不一致性，在存活時間跟設限時間不獨立的情況。在這篇論文中，我們推導出在存活時間跟設限時間相依下，曼-惠特尼影響的估計理論值。在給定存活時間跟設限時間相依為一個關聯結構(Copula)模型時，我們也推導出了曼-惠特尼影響估計量的漸進誤差。在假設的關聯結構(Copula)模型下，我們運用關聯結構構圖像法(Copula-graphic)去提供了一個新的曼-惠特尼影響估計量。我們運用了鞅論(Martingale)去證明這個新的估計量具有一致性以及大樣本常態漸進的性質。此外，當遇到假設的關聯結構(Copula)模型不符合實際的資料時，我們額外提供一個新的方法可以有效的鑑定兩個群體的存活時間是否一樣。最後，我們用模擬的方式去驗證我們的方法，然後套用到真實資料上並且說明結論。

摘要(英)

The Mann-Whitney test is a nonparametric test for comparing two groups. For analysis of right-censored survival data, the Mann-Whitney effect is a measure for comparing the two survival times from the two groups. However, the two-sample test based on the estimator of the Mann-Whitney effect (Efron 1967; Koziol and Jia 2009; Dobler and Pauly 2018) can be inconsistent when the independent censoring assumption fails to hold. In this thesis, we derive the theoretical properties of the estimator of the Mann-Whitney effect under dependent censoring. We derive the asymptotic bias of the Mann-Whitney effect estimator when dependence between survival time and censoring time is modeled by a copula. We also propose a new estimator of the Mann-Whitney effect by applying the copula-graphic estimator under assumed copula models. We prove the consistency and asymptotic normality of the proposed estimator by a martingale theory. We propose a new test that is asymptotically valid under a possibly misspecified copula model. Simulations are conducted to verify the proposed method, and a real data example is given for illustration.

關鍵字(中)

★ 曼-惠特尼檢定
★ 關聯結構
★ 關聯結構構圖像估計量
★ 鞅論
★ 相依設限資料
★ 兩樣本問題

關鍵字(英)

★ Mann-Whitney test
★ Copula
★ Copula-graphic estimator
★ Martingale
★ Dependent censoring
★ Two-sample problem

論文目次

Contents
摘要 I
Abstract II
誌謝辭 III
Contents IV
Chapter 1: Introduction 1
Chapter 2: Background 3
2.1 Two-sample comparison 3
2.2 Mann-Whitney effect 5
Chapter 3: Dependent censoring 7
3.1 Bias under dependent censoring 7
3.2 Copula-graphic (CG) estimator 12
3.3 Consistent estimation of under dependent censoring 14
3.4 Bias of under a misspecified copulas 16
Chapter 4: Simulation 23
4.1 Simulation design 23
4.2 Simulation result 25
Chapter 5: Data analysis 29
Chapter 6: Concluding remarks 33
Appendix 35
Appendix A: Asymptotic bias 35
Appendix B: Data generation under copula models 40
Appendix C: Simulation for comparing the KM estimator and CG estimator 42
Appendix D: The Mann-Whitney effect 50
Appendix E: The code for Data Analysis 51
REFERENCES 60

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指導教授

江村剛志(Takeshi Emura)

審核日期

2019-7-10

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