卵巢癌，國人女性十大死因之一。早期症狀不明顯，當病人發現時，往往已經過了初期的黃金治療時間，對於癌症癒後十分不利。醫學上發現，血液中的CA125濃度，與卵巢癌有高度的相關性，因此我們視CA125為卵巢癌的腫瘤標記物。透過一般健檢抽血項目，即可檢驗出CA125濃度是否超標，若病人的CA125濃度超標，極有可能罹患卵巢癌或是卵巢癌復發。由於CA125與卵巢癌病人的存活以及復發呈現高度的相關性，因此可藉由配適CA125的模型，了解CA125的趨勢，在臨床上可以更精準的掌握卵巢癌病人術後的情況。CA125的趨勢，大致上可分為兩種，一種病人在經過治療後CA125急遽下降並且保持穩定；一種病人在經過治療後CA125急遽下降隨後再度上升。一般長期追蹤資料常用混合效應模型配適，並假設隨機效應與殘差為常態分布，但是此假設在我們的資料不一定適用。本研究透過貝氏階層模型逐步建立分段式線性混合效應模型( Piecewise Linearly Mixed Effect Model )，在模型中加入癌症期別作為配適模型重要變數，並比較不同隨機效應與殘差的分布(包含分布是否偏斜、是否厚尾以及異方差(Heteroskedasticity))對模型的影響。期望透過本模型，更加了解CA125的變化與趨勢走向，對醫學有所貢獻。

In ovarian cancer studies, cancer antigen 125 (CA125) is an important tumor marker which is repeatedly measured over time. We aim to model the CA125 trajectories that can help us understand patients’ prognosis. In longitudinal studies, nonlinear mixed-effects (NLME) models are often used to model patients’ trajectories. The random effects and random errors of NLME are often assumed to be normally distributed and in addition, errors are assumed to be homogeneous. However, these assumption may not be satisfied when modeling the CA125 trajectories. In this paper, we propose a general nonlinear mixed-effects model with random effects being skewed and errors being skewed, heteroskedastic and possibly heavy tailed. We applied the proposed model to the CA125 trajectories and compared the fitting of our model to those with other models. Moreover, we conducted a simulation study to study the effects of skewness, heteroskedasticity and heavy tail on the fitting.

論文審定書 i
誌謝 ii
摘要 iii
Abstract iv
List of Tables vii
List of Figures viii
1 Introduction 1
2 Background 4
2.1 Introduction to Ovarian Cancer 4
2.2 The Staging of Ovarian Cancer 4
2.3 Introduction to CA125 5
3 Model & Methodology 6
3.1 The general NLME model 6
3.2 Estimation of posterior distributions 8
3.3 The statistical software - WinBUGS 9
4 Real Data Analysis 10
4.1 Data Description 10
4.2 Model-building of real data 11
4.2.1 Assumption of β 12
4.2.2 Assumption of skewness parameter 13
4.3 Model comparing 15
4.4 MCMC implementation 15
4.5 Comparison of modeling results 17
5 Simulation studies 20
5.1 Simulate data from model SNSN 20
5.2 Simulate data from model SNSN with 5% outliers 22
6 Conclusion 23
Reference 25
Appendix 28
A Multivariate SN distribution 28
B Multivariate ST distribution 29
C WinBUGS code for model SN ST 31
D WinBUGS code for model SN SN 33

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