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研究生:黃超顯
研究生(外文):Chao-Sian Huang
論文名稱:CUSUM管制圖應用在呼吸道症候群監控上
論文名稱(外文):The CUSUM Control Chart for Respiratory Syndromic Surveillance
指導教授:陳慧芬陳慧芬引用關係
指導教授(外文):Huifen Chen
學位類別:碩士
校院名稱:中原大學
系所名稱:工業與系統工程研究所
學門:工程學門
學類:工業工程學類
論文種類:學術論文
論文出版年:2009
畢業學年度:97
語文別:英文
論文頁數:79
中文關鍵詞:時間序列累積和管制圖症候群偵測呼吸道症候群廻歸分析ARMA 模式
外文關鍵詞:Regression analysisTime SeriesCUSUM ChartSyndromic SurveillanceRespiratory syndromeARMA model.
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本論文目的在應用品管手法中的累積和管制圖來偵測呼吸道症候群的爆
發,傳統的傳染病偵測方法時效性上明顯不足,因此主動式的症候群偵測方式被
提出用來及早發現疾病疫情的異常,例如:CUSUM 管制圖,研究資料為2003
到2007 年健保資料庫之健保申報資料,健保申報資料是以16 萬人為樣本,呼吸
道症候群ICD-9 診斷碼則採用美國疾病管制局之症候群分類標準。2003 至2007
年中,平均一年有六十萬就診人次,高峰期多發生在10 月至隔年4 月。
累積和管制圖常常被應用在疾病監控上,但是基本假設為觀察值必須互相獨
立,然而本研究資料之間卻有相關性,因此先使用廻歸模式來建立統計預測模
式,然後建立其預測誤差的單邊上累積和管制圖,其ARL 為50,來進行呼吸道
症候群就診人次的監控機制。由於資料間具有相關性,假設廻歸模式的誤差項服
從ARMA 模式,而自變數包含星期一、星期日、12 月、國定假日與國定假日隔
天。本研究利用2003 到2004 年的資料建立廻歸模式,並使用2005 年資料來做
驗證及監控2006 年與2007 年的呼吸道症候群流行情形。
本研究建立出呼吸道症候群統計預測模式與偵測症候群爆發的累積和管制
圖,應用在2005 年時,呼吸道症候群流行的高峰期期間,所建立出的累積和管
制圖確實能偵測出疫情異常,但是在低峰的時候可能會受到颱風的影響而產生錯
誤的警訊。經由監控2006 到2007 年的資料中發現每年的1 月到4 月與12 月都
是呼吸道症候群容易爆發的月份,但是呼吸道疾病似乎有漸漸提早在10 月份的
時候爆發的跡象。在模擬驗證上,本研究所建立出的累積和管制圖偵測疾病爆發
的能力不論在呼吸道症候群流行的高峰期、低峰期或是由低峰期進入高峰期都沒
有顯著差異,大體上本研究所建立出的累積和管制圖確實能偵測出爆發。
The purpose of this thesis is to apply the cumulative sum (CUSUM) control chart
of the quality improvement tools to detect the outbreak of the respiratory syndrome.
The timeliness to identify the outbreak is not good for the traditional infection surveillance.
The active detection “Syndromic surveillance” was developed to early detect
the aberration of diseases. Research data are the 2003 to 2007 data on outpatient
and emergency department visits obtained from the National Health Insurance Research
Database (NHIRD) and the samples of the data are 160,000 patients. The
ICD-9-CM codes of the respiratory syndrome are adopted according to the syndromic
classification criteria of CDC, USA. The annual average number of the visits is
600,000. The peak period of the epidemic for respiratory syndrome is from October to
April in the next year.
The CUSUM charts are widely used in disease surveillance, but the basic assumption
is that the observations are mutually independent. However, the data in this
research are correlated. We use the regression model to establish the statistical forecasting
model. We construct the one-sided upper CUSUM chart based on forecasting
errors in which ARL is set 50 and then undertake the surveillance mechanism of the
number of visits for respiratory syndrome. As a result of the correlated data, we assume
that the error term of the regression model follows autoregressive moving average
(ARMA) model. The independent variables are Monday, Sunday, December, the
national holiday and the next day of the national holiday. In this study, we use the data
in 2003 and 2004 to establish the regression model. The data in 2005 are used to validate
and then we apply it to monitor the epidemic of the respiratory syndrome from
2006 to 2007.
In this research, we establish the statistical forecasting model for respiratory syndrome
and construct a CUSUM chart that detects the outbreak of respiratory syndrome.
When the CUSUM chart is applied in 2005, it is indeed able to detect the aberration
of respiratory syndrome during the peak period of the epidemic for respiratory
syndrome in 2005. However, in the low peak period of the epidemic, the control
chart could be affected by typhoons to have the false alarms. By monitoring the data
in 2006 and 2007, January, February, March, April and December are the months that
the respiratory syndrome would outbreak easily. The respiratory diseases seem to outbreak
in October, which time is earlier than past year. In the verification with simulation,
the detecting ability is non-significant for the epidemic peak period, the epidemic
low peak period and the period from the epidemic low peak to the epidemic peak. The
CUSUM chart we construct certainly can detect the outbreak in substance.
TABLE OF CONTENTS
ABSTRACT (Chinese) .................................................................................................. I
ABSTRACT.................................................................................................................. II
TABLE OF CONTENTS..............................................................................................V
LIST OF TABLE........................................................................................................ VII
LIST OF FIGURES ..................................................................................................VIII
LIST OF FIGURES ..................................................................................................VIII
I. INTRODUCTION...................................................................................................1
1.1 Motivation.....................................................................................................1
1.2 Problem Definition........................................................................................1
1.3 Thesis Results ...............................................................................................2
II. LITERATURE REVIEW.......................................................................................5
2.1 Research and Study of Respiratory Syndromes Surveillance in Taiwan......5
2.2 Time Series Analysis for Modeling ..............................................................5
2.2.1 Non-seasonal Models.........................................................................6
2.2.2 Seasonal Models ................................................................................8
2.2.3 The Three Stages of Model Building...............................................11
2.3 The Methods of Diseases Surveillance .......................................................12
2.3.1 The Standardized CUSUM Chart ....................................................12
2.3.2 The Poisson CUSUM Chart.............................................................14
2.3.3 The CUSUM Chart Based on Residuals..........................................15
III. METHODS .........................................................................................................17
3.1 Data Source.................................................................................................17
3.2 Data Summary ............................................................................................18
3.3 Time Series Model ......................................................................................21
3.4 Forecasting of The Daily Count for Respiratory Syndrome .......................29
3.5 The CUSUM Control Chart for The Residuals...........................................30
IV. EXPERIMENTAL RESULTS ...........................................................................34
4.1 The Validation of The CUSUM Chart ........................................................34
4.2 Monitoring The Respiratory Syndrome in 2006 and 2007 .........................39
4.3 The Verification with Simulation................................................................46
V. CONCLUSIONS AND FUTHER RESEARCH ..................................................52
5.1 Summary of the Results and Conclusions ..................................................52
5.2 Future Research ..........................................................................................53
LIST OF REFEREBCES .............................................................................................54
Appendix A: The Early Aberration Reporting System (EARS)...............................58
Appendix B: Autocovariances for Simulation..........................................................60
B.1 Computations of Lag-0 to Lag-8 Autocovariances for   t
 .....................60
B.2 The Verification of Simulation Data ..........................................................66
Appendix C: Respiratory syndrome ICD-9-CM codes of USA—CDC ...................67
LIST OF TABLE
Table 3.1 The descriptive statistics of the daily count for respiratory syndrome each
year.....................................................................................................................19
Table 3.2 The parameter estimates of linear regression with dummy variables ..........23
Table 3.3 The parameter estimates of linear regression with ARMA errors................27
Table 3.4 The test of the normality for the residuals....................................................28
Table 3.5 The parameter estimates of the fitted model ................................................29
Table 3.6 The test of the normality for the residuals....................................................32
Table 4.1 The proportion of false alarms and the average time to signal for in-control
data in ARL0=50, 90, 180 (with the standard error listed in parentheses).........49
Table 4.2 The fraction of times a method missed detecting an outbreak and the
average time to first outbreak signal for one standard deviation in ARL0=50, 90,
180 (with the standard error listed in parentheses) ............................................50
Table 4.3 The fraction of times a method missed detecting an outbreak and the
average time to first outbreak signal for two standard deviation in ARL0=50, 90,
180 (with the standard error listed in parentheses) ............................................50
Table 4.4 The fraction of times a method missed detecting an outbreak and the
average time to first outbreak signal for three standard deviation in ARL0=50,
90, 180 (with the standard error listed in parentheses) ......................................51
Table B.1 Sample and theoretical autocovsriances of   t
 from lag 0 to lag 8 (with
the standard error listed in parentheses).............................................................66
Table C.1 Respiratory ICD-9-CM Code List...............................................................67
Table C.2 Respiratory ICD-9-CM Code List, Cont’d..................................................68
Table C.3 Respiratory ICD-9-CM Code List, Cont’d..................................................69
Table C.4 Respiratory ICD-9-CM Code List, Cont’d..................................................70
LIST OF FIGURES
Figure 2.1 The procedure of model building ...............................................................12
Figure 3.1 The daily counts for the respiratory syndrome form 2003 to 2007 ............19
Figure 3.2 The daily counts of the respiratory syndrome from January to February in
2003....................................................................................................................20
Figure 3.3 The autocorrelation function of the daily counts of the respiratory
syndrome ............................................................................................................21
Figure 3.4 The autocorrelation function of residuals calculated from the multiple
linear regression .................................................................................................24
Figure 3.5 The partial autocorrelation function of residuals calculated from the
multiple linear regression...................................................................................25
Figure 3.6 The Q-Q plot for residuals before deleting outliers....................................28
Figure 3.7 The autocorrelation function for residuals calculated from the appropriate
model..................................................................................................................31
Figure 3.8 The Q-Q plot for the residuals after deleting the outliers...........................31
Figure 4.1 The CUSUM chart from January to April in 2005 .....................................36
Figure 4.2 The CUSUM chart from May to August in 2005 .......................................36
Figure 4.3 The CUSUM chart from September to December in 2005 ........................37
Figure 4.4 The actual and forecasting daily counts for respiratory syndrome from
January to April in 2005.....................................................................................37
Figure 4.5 The actual and forecasting daily counts for respiratory syndrome from May
to August in 2005 ...............................................................................................38
Figure 4.6 The actual and forecasting daily counts for respiratory syndrome from
September to December in 2005........................................................................38
Figure 4.7 The CUSUM chart from January to April in 2006 .....................................40
Figure 4.8 The CUSUM chart from May to August in 2006 .......................................40
Figure 4.9 The CUSUM chart from September to December in 2006 ........................41
Figure 4.10 The actual and forecasting daily counts for respiratory syndrome from
January to April in 2006.....................................................................................41
Figure 4.11 The actual and forecasting daily counts for respiratory syndrome from
May to August in 2006.......................................................................................42
Figure 4.12 The actual and forecasting daily counts for respiratory syndrome from
September to December in 2006........................................................................42
Figure 4.13 The CUSUM chart from January to April in 2007 ...................................43
Figure 4.14 The CUSUM chart from May to August in 2007 .....................................44
Figure 4.15 The CUSUM chart from September to December in 2007 ......................44
Figure 4.16 The actual and forecasting daily counts for respiratory syndrome from
January to April in 2007.....................................................................................45
Figure 4.17 The actual and forecasting daily counts for respiratory syndrome from
May to August in 2007.......................................................................................45
Figure 4.18 The actual and forecasting daily counts for respiratory syndrome from
September to December in 2007 ........................................................................46
Figure 4.19 The flow chart for simulating the in-control data in 2005........................48
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