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系統識別號 U0002-2107201420054300
中文論文名稱 累積加總之模型檢查方法在腎臟癌、食道癌及胰臟癌資料應用
英文論文名稱 Model-Checking Techniques Based on Cumulative Sum with Application to Kidney, Esophageal, and Pancreatic Cancer
校院名稱 淡江大學
系所名稱(中) 統計學系碩士班
系所名稱(英) Department of Statistics
學年度 102
學期 2
出版年 103
研究生中文姓名 林靜儀
研究生英文姓名 Ching-I Lin
學號 601650251
學位類別 碩士
語文別 英文
口試日期 2014-06-26
論文頁數 160頁
口試委員 指導教授-陳蔓樺
委員-林志娟
委員-張慶暉
中文關鍵字 累積加總  卜瓦松迴歸  羅吉斯迴歸 
英文關鍵字 cumulative sum  Poisson regression  logistic regression 
學科別分類
中文摘要 對於模型配適是否恰當,通常作殘差圖來進行判斷,或者利用缺適性檢定(Goodness-of-fit)來檢驗模式。在本篇文章中,考慮採用累積加總的模型檢查方法(Model-checking techniques based on cumulative sum),此方法不僅可以檢驗模型是否假設錯誤或者存在自然變異,同時也可以提供當模型中的解釋變數之函數形式不適當時的解決方向。在取得分析資料方面,則考慮Surveillance Epidemiology and End Result (SEER) (www.seer. cancer.gov)資料庫中腎臟癌、食道癌及胰臟癌的資料,利用羅吉斯迴歸(logistic regression)與卜瓦松迴歸(Poisson regression)進行配適,並針對羅吉斯模型檢驗是否存在假設錯誤再加以修正。最後利用得到的模型探討在不同狀況下之病患死亡率。
英文摘要 Model-checking techniques (Biometrics 2002, Lin et al.) develops a statistical method in order to check misspecification or natural variation of different models. We focus at discussing the cumulative residuals by considering moving sum. We consider kidney, esophageal, and pancreatic cancer which from the Surveillance Epidemiology and End Result (SEER) (www.seer.cancer.gov) database released in 2012. Moreover, we provide the results of the logistic regression, the Poisson regression by this data. Each cancer is compared, both graphically and numerically.
論文目次 Directory
Chapter 1 Introduction 1
1.1 Model-Checking Based on Cumulative Sum 2
1.2 Logistic Regression 6
1.3 Poisson Regression 7
1.4 Outlines 9
Chapter 2 Review the Cancer Data of SEER Database 10
2.1 Introduction to SEER Database 10
2.2 Literature Review of Kidney, Esophageal and Pancreatic Cancer 11
2.3 Descriptive Statistics and Inferences 20
2.4 Discussion among Kidney, Esophageal and Pancreatic Cancer 42
Chapter 3 Model-Checking Based on Cumulative Sum 46
3.1 Modeling 46
3.2 The Estimation of Parameters 71
3.3 Compare 78
3.4 Result 93
Chapter 4 Poisson Regression 95
4.1 Model 95
4.2 Mortality for Kidney, Esophageal and Pancreatic Cancer 107
4.3 Compare the Cancers 131
4.4 Result 134
Chapter 5 Discussion 135
5.1 Conclusions 135
5.2 Recommendation for Future Research 136
Reference 138
Appendix I 145
Appendix II 157


List of Figures
Figure 1.1 The moving sum when the function form of is misspecified 5
Figure 2.1 Schematic diagram of kidney cancer staging 14
Figure 2.2 Structure of normal kidney 14
Figure 2.3 Schematic diagram of esophageal cancer staging 16
Figure 2.4 Schematic diagram of pancreatic cancer staging 19
Figure 2.5 Structure of normal pancreas 19
Figure 2.6 Pie chart of race for kidney cancer 21
Figure 2.7 Pie chart of sex for kidney cancer 22
Figure 2.8 Pie chart of tumor size for kidney cancer 23
Figure 2.9 Pie chart of extent (metastasis) for kidney cancer 24
Figure 2.10 Pie chart of vital status for kidney cancer 25
Figure 2.11 Bar chart of age for kidney cancer 26
Figure 2.12 Pie chart of race for esophageal cancer 28
Figure 2.13 Pie chart of sex for esophageal cancer 29
Figure 2.14 Pie chart of tumor size for esophageal cancer 30
Figure 2.15 Pie chart of extent (metastasis) for esophageal cancer 31
Figure 2.16 Pie chart of vital status for esophageal cancer 32
Figure 2.17 Bar chart of age for esophageal cancer 34
Figure 2.18 Pie chart of race for pancreatic cancer 36
Figure 2.19 Pie chart of sex for pancreatic cancer 37
Figure 2.20 Pie chart of tumor size for pancreatic cancer 38
Figure 2.21 Pie chart of extent (metastasis) for pancreatic cancer 39
Figure 2.22 Pie chart of vital status for pancreatic cancer 40
Figure 2.23 Bar chart of age for pancreatic cancer 41
Figure 3.1 Cumulative sum of the age in the sex for kidney cancer 47
Figure 3.2 Cumulative sum of predicted value in the sex for kidney cancer 48
Figure 3.3 Cumulative sum of the age in the tumor size for kidney cancer 49
Figure 3.4 Moving sum of the age in the tumor size for kidney cancer 49
Figure 3.5 Cumulative sum of the age with the revise form in the tumor size for kidney cancer 50
Figure 3.6 Cumulative sum of predicted value with the revise form in the tumor size for kidney cancer 50
Figure 3.7 Cumulative sum of the age in the extent (metastasis) for kidney cancer 51
Figure 3.8 Moving sum of the age in the extent (metastasis) for kidney cancer 52
Figure 3.9 Cumulative sum of the age with the revise form in the extent (metastasis) for kidney cancer 52
Figure 3.10 Cumulative sum of predicted value with the revise form in the extent (metastasis) for kidney cancer 53
Figure 3.11 Residual plots for female esophageal cancer 56
Figure 3.12 Residual plots for male for esophageal cancer 57
Figure 3.13 Residual plots for male for esophageal cancer with the revise form 57
Figure 3.14 Cumulative sum of the age in the tumor size and the extent (metastasis) for esophageal cancer 58

Figure 3.15 Moving sum of the age in the tumor size and the extent (metastasis) for esophageal cancer 59
Figure 3.16 Cumulative sum of the age with the revise form in the tumor size and the extent (metastasis) for esophageal cancer 60
Figure 3.17 Cumulative sum of predicted value with the revise form in the tumor size and the extent (metastasis) for esophageal cancer 61
Figure 3.18 Cumulative sum of the age in the tumor size for pancreatic cancer 64
Figure 3.19 Cumulative sum of predicted value in the tumor size for pancreatic cancer 65
Figure 3.20 Cumulative sum of the age in the sex and the extent (metastasis) for pancreatic cancer 66
Figure 3.21 Moving sum of the age in the sex and the extent (metastasis) for pancreatic cancer 67
Figure 3.22 Cumulative sum of the age with the revise form in the sex and the extent (metastasis) for pancreatic cancer 68
Figure 3.23 Cumulative sum of predicted value with the revise form in the sex and the extent (metastasis) for pancreatic cancer 69
Figure 3.24 The mortality rate of the sex for kidney cancer 79
Figure 3.25 The mortality rate of the tumor size for kidney cancer 79
Figure 3.26 The mortality rate of the extent (metastasis) for kidney cancer 80
Figure 3.27 The mortality rate of the tumor size for kidney cancer 81
Figure 3.28 The mortality rate of the extent (metastasis) for kidney cancer 81
Figure 3.29 The mortality rate of the sex for kidney cancer 82
Figure 3.30 The mortality rate of the sex for kidney cancer 82
Figure 3.31 The mortality rate of the sex for esophageal cancer 83
Figure 3.32 The mortality rate of the tumor size for esophageal cancer 83
Figure 3.33 The mortality rate of the extent (metastasis) for esophageal cancer 84
Figure 3.34 The mortality rate of the tumor size for esophageal cancer 85
Figure 3.35 The mortality rate of the extent (metastasis) for esophageal cancer 85
Figure 3.36 The mortality rate of the sex for esophageal cancer 86
Figure 3.37 The mortality rate of the sex for esophageal cancer 86
Figure 3.38 The mortality rate of the sex for pancreatic cancer 87
Figure 3.39 The mortality rate of the tumor size for pancreatic cancer 87
Figure 3.40 The mortality rate of the extent (metastasis) for pancreatic cancer 88
Figure 3.41 The mortality rate of the tumor size for pancreatic cancer 89
Figure 3.42 The mortality rate of the extent (metastasis) for pancreatic cancer 89
Figure 3.43 The mortality rate of the sex for pancreatic cancer 90
Figure 3.44 The mortality rate of the sex for pancreatic cancer 90
Figure 3.45 The mortality rate of the sex for each cancer 91
Figure 3.46 The mortality rate of the tumor size for each cancer 92
Figure 3.47 The mortality rate of the extent (metastasis) for each cancer 93
Figure 4.1 Mortality of the sex under different ages for kidney cancer 109

Figure 4.2 Mortality of the tumor size under different ages for kidney cancer 109
Figure 4.3 Mortality of the extent (metastasis) under different ages for kidney cancer 110
Figure 4.4 Mortality for female kidney cancer data 111
Figure 4.5 Mortality for male kidney cancer data 112
Figure 4.6 Mortality of sex under different tumor size for kidney cancer 113
Figure 4.7 Mortality of sex under different extent (metastasis) for kidney cancer 114
Figure 4.8 Mortality of the sex under different ages for esophageal cancer 116
Figure 4.9 Mortality of the tumor size under different ages for esophageal cancer 116
Figure 4.10 Mortality of the extent (metastasis) under different ages for esophageal cancer 117
Figure 4.11 Mortality for female esophageal cancer data 119
Figure 4.12 Mortality for male esophageal cancer data 120
Figure 4.13 Mortality of sex under different tumor size for esophageal cancer 121
Figure 4.14 Mortality of sex under different extent (metastasis) for esophageal cancer 122
Figure 4.15 Mortality of the sex under different ages for pancreatic cancer 124
Figure 4.16 Mortality of the tumor size under different ages for pancreatic cancer 125
Figure 4.17 Mortality of the extent (metastasis) under different ages for pancreatic cancer 125
Figure 4.18 Mortality for female pancreatic cancer data 127
Figure 4.19 Mortality for male pancreatic cancer data 128
Figure 4.20 Mortality of sex under different tumor size for pancreatic cancer 129
Figure 4.21 Mortality of sex under different extent (metastasis) for pancreatic cancer 130
Figure 4.22 Mortality of the sex for each cancer 132
Figure 4.23 Mortality of the tumor size for each cancer 133
Figure 4.24 Mortality of the extent (metastasis) for each cancer 133
Figure I.1 Residual plots for female small tumor under kidney cancer 145
Figure I.2 Residual plots for female large tumor under kidney cancer 145
Figure I.3 Residual plots for female metastasis not occurring under kidney cancer 145
Figure I.4 Residual plots for female metastasis occurring under kidney cancer 146
Figure I.5 Residual plots for male small tumors under kidney cancer 147
Figure I.6 Residual plots for male large tumor under kidney cancer 147
Figure I.7 Residual plots for male metastasis not occurring under kidney cancer 148
Figure I.8 Residual plots for male metastasis occurring under kidney cancer 149
Figure I.9 Residual plots for female small tumors under esophageal cancer 149

Figure I.10 Residual plots for female large tumors under esophageal cancer 149
Figure I.11 Residual plots for female metastasis not occurring under esophageal cancer 149
Figure I.12 Residual plots for female metastasis occurring under esophageal cancer 150
Figure I.13 Residual plots for male small tumor under esophageal cancer 151
Figure I.14 Residual plots for male large tumor under esophageal cancer 151
Figure I.15 Residual plots for male metastasis not occurring under esophageal cancer 152
Figure I.16 Residual plots for male metastasis occurring under esophageal cancer 153
Figure I.17 Residual plots for female small tumors under pancreatic cancer 153
Figure I.18Residual plots for female large tumors under pancreatic cancer 153
Figure I.19 Residual plots for female metastasis not occurring 154
Figure I.20 Residual plots for female metastasis occurring 155
Figure I.21 Residual plots for male small tumors under pancreatic cancer 155
Figure I.22 Residual plots for male large tumor under pancreatic cancer 155
Figure I.23 Residual plots for male metastasis not occurring under pancreatic cancer 156
Figure I.24 Residual plots for male metastasis occurring under pancreatic cancer 156

List of Tables
Table 2.1 Kidney cancer staging 13
Table 2.2 Esophageal cancer staging 16
Table 2.3 Pancreatic cancer staging 18
Table 2.4 Frequency distribution of race for kidney cancer 21
Table 2.5 Frequency distribution of sex for kidney cancer 22
Table 2.6 Frequency distribution of tumor size for kidney cancer 23
Table 2.7 Frequency distribution of extent (metastasis) for kidney cancer 24
Table 2.8 Frequency distribution of vital status for kidney cancer 25
Table 2.9 Frequency distribution of age for kidney cancer 26
Table 2.10 Test for the proportion between female data and male data 27
Table 2.11 Frequency distribution of race for esophageal cancer 28
Table 2.12 Frequency distribution of sex for esophageal cancer 29
Table 2.13 Frequency distribution of tumor size for esophageal cancer 30
Table 2.14 Frequency distribution of extent (metastasis) for esophageal cancer 31
Table 2.15 Frequency distribution of vital status for esophageal cancer 32
Table 2.16 Frequency distribution of age for esophageal cancer 33
Table 2.17 Test for the proportion in female data and male data 34
Table 2.18 Frequency distribution of race for pancreatic cancer 35
Table 2.19 Frequency distribution of sex for pancreatic cancer 36
Table 2.20 Frequency distribution of tumor size for pancreatic cancer 37
Table 2.21 Frequency distribution of extent (metastasis) for pancreatic cancer 38
Table 2.22 Frequency distribution of vital status for pancreatic cancer 40
Table 2.23 Frequency distribution of age for pancreatic cancer 41
Table 2.24 Test for the proportion in female data and male data 42
Table 2.25 Test for the average age for three cancers with 43
Table 2.26 Multiple comparisons of the average age between two cancers 44
Table 2.27 Test for the proportion of male in three cancer data 44
Table 2.28 Test for the proportion of dead in three cancer data 45
Table 3.1 The cumulative residuals results under the sex, tumor size, and extent (metastasis) for kidney cancer 53
Table 3.2 The cumulative residuals results under the sex with tumor size and extent (metastasis) for kidney cancer 54
Table 3.3 The cumulative residuals results under the sex, tumor size, and extent (metastasis) for esophageal cancer 61
Table 3.4 The cumulative residuals results under the sex with tumor size and extent (metastasis) for esophageal cancer 62
Table 3.5 The cumulative residuals results under the sex, tumor size, and extent (metastasis) for pancreatic cancer 69
Table 3.6 The cumulative residuals results under the sex with tumor size and extent (metastasis) for pancreatic cancer 70
Table 3.7 The parameter estimation for each level of sex, tumor size and extent (metastasis) for kidney cancer 72



Table 3.8 The parameter estimation for each level of tumor size and extent (metastasis) in female data and male data for kidney cancer 73
Table 3.9 The parameter estimation for each level of sex, tumor size and extent (metastasis) for esophageal cancer 74
Table 3.10 The parameter estimation for each level of tumor size and extent (metastasis) in female data and male data for esophageal cancer 75
Table 3.11 The parameter estimation for each level of sex, tumor size and extent (metastasis) for pancreatic cancer 76
Table 3.12 The parameter estimation for each level of tumor size and extent (metastasis) in female data and male data for pancreatic cancer 77
Table 4.1 Parameter estimation of and for kidney cancer 96
Table 4.2 Parameter estimation of and in female data and male data for kidney cancer 98
Table 4.3 Parameter estimation of and for esophageal cancer 100
Table 4.4 Parameter estimation of and in female data and male data for esophageal cancer 102
Table 4.5 Parameter estimation of and for pancreatic cancer 104
Table 4.6 Parameter estimation of and in female data and male data for pancreatic cancer 106
Table 4.7 Mortality of sex, tumor size, and extent (metastasis) under different ages for kidney cancer 108
Table 4.8 Mortality of tumor size, extent (metastasis) in female data and male data under different ages for kidney cancer 110
Table 4.9 Mortality of sex, tumor size, and extent (metastasis) under different ages for esophageal cancer 115
Table 4.10 Mortality of tumor size, extent (metastasis) in female data and male data under different ages for esophageal cancer 118
Table 4.11 Mortality of sex, tumor size, and extent (metastasis) under different ages for pancreatic cancer 123
Table 4.12 Mortality of tumor size, extent (metastasis) in female data and male data under different ages for pancreatic cancer 126
Table II.1 The number of dead and total for sex, tumor size, extent (metastasis) 157
Table II.2 The number of dead and total for female data for kidney cancer 157
Table II.3 The number of dead and total for male data for kidney cancer 157
Table II.4 The number of dead and total for sex, tumor size, extent (metastasis) 158
Table II.5 The number of dead and total for female data for esophageal cancer 158
Table II.6 The number of dead and total for male data for esophageal cancer 159
Table II.7 The number of dead and total for sex, tumor size, extent (metastasis) 159
Table II.8 The number of dead and total for female data for pancreatic cancer 160
Table II.9 The number of dead and total for male data for pancreatic cancer 160
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