臺灣博碩士論文加值系統

針對多重生物指標在時間相關之ROC曲線分析，研究興趣通常在尋找合適之多重生物指標函
數以增進預測未來存活狀態的準確度。藉由對存活機率所建立之廣義線性模型，我們可導出
最佳生物指標函數為一線性組合函數。在不完整倖存資料結構下，我們利用嵌入條件期望值的方法
估計最佳線性組合中的係數。在此，我們推導所提出參數，$R!O!C_{t}$及$A!U!C_{t}$估計式之一致性。
更進一步，藉助模擬檢視估計式之有限樣本性質，並應用所提出之估計方法在心血管疾病的資料上
來改善預測心血管疾病死亡狀態及非限定因素死亡狀態的準確度。

In the time-dependent receiver operating characteristic (ROC) curve
analysis with several baseline markers, research interest focuses on
seeking an appropriate composition score of these potential markers
to improve the performance of individual markers in early prediction
of vital status. Under the validity of a generalized linear model
for the vital status at each time point within the study period, an
optimal linear composition score is shown to have a best ROC curve
among all functions of the markers. Based on censored survival data,
the inverse probability weighting approach was considered to
estimate the time-varying coefficients in the previous paper.
Without making assumption on the relationship between censoring time
and markers, we propose an imputation estimation method. The
consistency of the parameter estimators and the estimators of ROC
curve and area under ROC curve (AUC) at each time point is also
established in this article. However, the inverse probability
weighting approach will introduce a bias when the selection
probability is incorrectly specified in the estimating equations.
The performance of both estimation procedures are examined through a
class of numerical studies. Applying these methods to an angiography
cohort, our estimation procedures are shown to be useful in
predicting the vital outcomes.

Table of Contents
Table of Contents ii
List of Tables iv
Acknowledgements vi
Abstract vii
摘要viii
1 Introduction 1
2 Optimal Composition Score and Estimation 3
2.1 Model and Optimal Linear Combination Score . . . . . . . . . . . . . 3
2.1.1 Estimation of Time-Varying Coefficients . . . . . . . . . . . . 4
2.1.2 Inverse Probability Weighting Method . . . . . . . . . . . . . 4
2.1.3 Imputation Estimation Method . . . . . . . . . . . . . . . . . 5
2.2 Estimation of Time-Dependent ROC Curves and AUC . . . . . . . . 7
3 Asymptotic Properties 9
3.1 Consistency of bθt . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
3.2 Consistency of dAUCt . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
4 Monte Carlo Simulations 13
4.1 First Scenario . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
4.2 Second Scenario . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
5 Application to an Angiography Cohort 25
6 Discussion 30
Bibliography 31

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