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。

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.

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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