臺灣博碩士論文加值系統

本篇論文包含兩個研究主題。第一個主題是對於多項分布機率值的區間估計。統計區間在各個領域的應用非常地廣泛。多項分布的參數之聯合信賴區間已經應用於很多領域，包含品質管制和臨床資料分析。由於如此廣泛的應用，多項分布在各個學科領域上扮演著重要的角色。因此，我們提出一個方法建造多項分布機率值的信賴區間並透過模擬分析來呈現各種區間估計的比較。第二個主題是對缺失資料在錯誤的模型下補值之後，進行參數估計並且計算完整資料所需要的樣本數。我們考慮錯誤的模型設定可以是低度擬合。最後，我們應用所提出的方法來分析一筆腦中風資料。對於缺血性腦中風的病患而言，送醫時間是非常關鍵的。因此，我們研究了送醫時間與送醫方式、中風嚴重程度、初始症狀及危險因子之間的關係。

In this dissertation, we focus on two topics. The first topic is the interval estimation for the probability of the multinomial distribution. Statistical intervals are widely-used in many study fields. Simultaneous confidence intervals for the multinomial proportions have been proposed in many applications, including quality control and clinical data analysis. Because of these wide applications, the multinomial distribution plays an important role in many areas of science. Thus, we propose a method for constructing the confidence interval for the probability of the multinomial distribution. A simulation study is conducted to compare the performance of different intervals. The second topic is to derive the parameter estimators after the missing data imputation under the misspecified model and determine the sample size of the complete data. We consider the case that the misspecified model is underfitting. Finally, we apply the proposed methodology to analyze a stroke data. The time interval called the pre-hospital delay is important for thrombolytic therapy. Therefore, our study aimed at exploring the association of prehospital delay and arrival way, stroke severity, initial symptom and sign, and stroke risk factors.

Contents

摘要…………………………………………………………………………………….i
Abstract………………………………………………………………………………..ii
誌謝…………………………………………………………………………………...iii
Contents…………………………………………………………………………….…vi
List of Tables…………………………………………………………………….…...vii
1. Introduction………………………………………………………………………1
2. Literature Review……………………………………………………….….…….5
2.1 Confidence Interval for the Cumulative Probability of the Binomial Distribution………………………………………………………….………5
2.2 Introduction of Stroke………………………………………………………6
2.3 The Behavior and Characteristic of Strokes Patients……………………….8
2.3.1 National Institute of Health Stroke Scale…………………...……8
2.3.2 Arrival Way………………………………………………………9
2.3.3 Risk factors…………………………………………………...…..9
2.4 Imputation Methods………………………………………………………...9
3. Confidence Intervals for ………………………………………………….....11
3.1 Simultaneous Confidence Intervals………………………………………..11
3.2 Main Results……………………………………………………………….12
3.3 Simulation Study…………………………………………………………..18
4. Missing Data Imputation under the Misspecified Model……………………….25
4.1 Parameters Estimation…………………………………………………..…25
4.2 Sample Size Calculation………………………………….……………..…28
5. Data Analysis……………………………………………………………………37
5.1 Database…………………………………………………………………...37
5.2 Analysis before imputation……………………………………………......38
5.3 Analysis after imputation………………………………………………….41
6. Conclusions……………………………………………………………………..43
Appendix..…….……………………………………………………………………...44
References…….……………………………………………………………………...73

Brick, J. M., & Kalton, G. (1996). Handling missing data in survey research. Statistical methods in medical research, 5(3), 215-238.
Brott, T., Adams Jr, H. P., Olinger, C. P., Marler, J. R., Barsan, W. G., Biller, J., ... & Hertzberg, V. (1989). Measurements of acute cerebral infarction: a clinical examination scale. Stroke, 20(7), 864-870.
Brown, L. D., Cai, T. T., & Dasgupta, A. (2002). Confidence intervals for a binomial proportion and asymptotic expansions. The Annals of Statistics, 30(1), 160-201.
Chang, K. C., Tseng, M. C., & Tan, T. Y. (2004). Prehospital delay after acute stroke in Kaohsiung, Taiwan. Stroke, 35(3), 700-704.
Fang, J., Yan, W., Jiang, G.-X., et al. (2011), Time interval between stroke onset and hospital arrival in acute ischemic stroke patients in Shanghai, China, Clinical Neurology and Neurosurgery, 113:85-88.
Faraway, J. J. (2016). Linear models with R. Chapman and Hall/CRC.
Fitzpatrick, S., & Scott, A. (1987). Quick simultaneous confidence intervals for multinomial proportions. Journal of the American Statistical Association, 82(399), 875-878.
Gold, R. Z. (1963). Tests auxiliary to χ 2 tests in a Markov chain. The Annals of Mathematical Statistics, 34(1), 56-74.
Goodman, L. A. (1965). On simultaneous confidence intervals for multinomial proportions. Technometrics, 7(2), 247-254.
Hahn, G. J., & Meeker, W. Q. (2011). Statistical intervals: a guide for practitioners (Vol. 92). John Wiley & Sons.
Hastie, T., Tibshirani, R., & Friedman, J. (2009). The elements of statistical learning: data mining, inference, and prediction, Springer Series in Statistics.
Jin, S. (2013). Computing Exact Confidence Coefficients of Simultaneous Confidence Intervals for Multinomial Proportions and their Functions. Department of Statistics, Uppsala University.
Keener, R. W. (2011). Theoretical statistics: Topics for a core course. Springer.
Kleindorfer, D., Kissela, B., Schneider, A., Woo, D., Khoury, J., Miller, R., ... & Jauch, E. (2004). Eligibility for recombinant tissue plasminogen activator in acute ischemic stroke: a population-based study. Stroke, 35(2), e27-e29.
Little, R. J., & Rubin, D. B. (2014). Statistical analysis with missing data (Vol. 333). John Wiley & Sons.
Mozaffarian, D., Benjamin, E. J., Go, A. S., Arnett, D. K., Blaha, M. J., Cushman, M., ... & Howard, V. J. (2016). Heart disease and stroke statistics-2016 update a report from the American Heart Association. Circulation, 133(4), e38-e48.
National Institute of Neurological Disorders and Stroke rt-PA Stroke Study Group. (1995). Tissue plasminogen activator for acute ischemic stroke. New England Journal of Medicine, 333(24), 1581-1588.
Perkins-Porras, L., Whitehead, D. L., Strike, P. C., & Steptoe, A. (2009). Pre-hospital delay in patients with acute coronary syndrome: factors associated with patient decision time and home-to-hospital delay. European Journal of Cardiovascular Nursing, 8(1), 26-33.
Quesenberry, C. P., & Hurst, D. C. (1964). Large sample simultaneous confidence intervals for multinomial proportions. Technometrics, 6(2), 191-195.
Rubin, D. B. (1996). Multiple imputation after 18+ years. Journal of the American statistical Association, 91(434), 473-489.
Rupert Jr, G. (2012). Simultaneous statistical inference. Springer Science & Business Media.
Sison, C. P., & Glaz, J. (1995). Simultaneous confidence intervals and sample size determination for multinomial proportions. Journal of the American Statistical Association, 90(429), 366-369.
Tanaka, Y., Nakajima, M., Hirano, T., & Uchino, M. (2009). Factors influencing pre-hospital delay after ischemic stroke and transient ischemic attack. Internal Medicine, 48(19), 1739-1744.
Wang, H. (2008). Exact confidence coefficients of simultaneous confidence intervals for multinomial proportions. Journal of Multivariate Analysis, 99(5), 896-911.
Wang, H. (2009). Exact average coverage probabilities and confidence coefficients of confidence intervals for discrete distributions. Statistics and Computing, 19(2), 139-148.
Wardlaw, J. M., & Warlow, C. P. (1992). Thrombolysis in acute ischemic stroke: does it work? Stroke, 23(12), 1826-1839.
Xie, L., Huang, S. F., & Hu, Y. Z. (2015). Factors influencing pre-hospital patient delay in patients with acute myocardial infarction. Chinese Nursing Research, 2(2-3), 75-79.
Zhou, Y., Yang, T., Gong, Y., Li, W., Chen, Y., Li, J., ... & Lu, Z. (2017). Pre-hospital delay after acute ischemic stroke in Central Urban China: prevalence and risk factors. Molecular neurobiology, 54(4), 3007-3016.