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研究生:曾筱容
研究生(外文):Hsiao-Jung Tseng
論文名稱:利用複雜變異模型探討迴歸分析的異質性變異問題─應用於建立年齡特定參考範圍
論文名稱(外文):Modeling variance heterogeneity using the complex variation model─ applying to age-specific reference range construction
指導教授:傅瓊瑤傅瓊瑤引用關係
指導教授(外文):Chong-Yau Fu
學位類別:碩士
校院名稱:國立陽明大學
系所名稱:公共衛生研究所
學門:醫藥衛生學門
學類:公共衛生學類
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:54
中文關鍵詞:異質性變異數複雜變異模型年齡特定參考範圍兩階段估計
外文關鍵詞:heteroscedasticitycomplex variationage-specific reference rangetwo-stage estimation
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在臨床醫學上,常對測量值建立一個正常的參考範圍,提供醫師作為初步診斷之依據。由於某些測量值會隨著年齡(時間)而變化,因此在建構參考範圍時納入年齡因素所建構的範圍稱為年齡特定參考範圍。本研究針對利用迴歸模型在建構年齡特定參考範圍時,探討遇到異質性變異數問題時的處理方方式。在此提出以複雜變異模型(complex variation model)來解決異質性變異數的問題,並與Altman, D.G. (1993) 提出利用絕對值殘差估計變異的應用於兩階段估計的方法做比較。

實例研究是分析用台北榮總婦產部胎兒鼻骨長度的超音波資料,此資料在建模的過程中會有異質性變異數的情形發生,因此我們利用傳統的兩階段估計以及複雜變異模型分別去建構其年齡特定參考範圍。在模擬研究中,則是探討資料變異在不同的變化情境(線性變化與非線性變化)與變化速度下,評估此兩種方法的估計效果。

模擬研究結果顯示,利用複雜變異模型所的估計效果整體而言比兩階段估計的方式佳,但兩者估計效果差異不大;當資料異質性變異的變化速度增加時,係數估計的偏差也會有變大的趨勢;增加樣本數也會使估計的偏差減小、穩定度增加。在建構年齡特定參考範圍時,利用複雜變異模型同時估計平均與變異,雖然此方法的估計方式較為複雜且容易受限於統計軟體,但運用此種模式建構參考範圍不僅可簡化建構的程序,同時解決變異數異質性問題,得到較可靠的參考範圍。
In clinical medicine, some biomedical measurements are often used to construct normal ranges to offer doctors as a tool for early diagnosis. In some situations that measurements may change with age (time). When constructing such reference ranges, the age effect should be taken into account. That is so called “age-specific reference range”.

The main issue of this study is to deal with the heteroscedasticity problem as well as to model variability in application to age-specific reference range construction. Parametric approaches based on regression models were used. A complex variation model was proposed to model variability and to compare with Altman’s approach (1993) of estimating variability by using absolute residuals. In this study, ultrasound data of fetal nasal bone length was used for illustration. Furthermore, simulation study was conducted to investigate the estimating effects of the complex variation modeling and two-stage estimation (modeling men and standard deviation separately) in different scenarios that data are generated with different rates of variability.

Simulation results show that the estimating effect of using the complex variation model is better than the two-stage estimation as a whole. As the changing rate of variation increases, the coefficient estimates for regression obtained by the two methods are going far from the true and become more unstable. Furthermore, both precision and accuracy can be improved as the sample size becomes larger. The idea of using the complex variation model is proposed to apply to reference range construction in this study. The most advantage is that it simplifies the procedure of reference range construction and gets more accurate and reliable estimation as well.
Acknowledgement........................................... i
Abstract................................................. ii
Abstract in Chinese (中文摘要).......................... iii
Contents................................................. iv
List of Tables .......................................... vi
List of Figures ........................................ vii

Chapter 1 Introduction ................................... 1
1.1 Background and motivation ............................ 1
1.2 The objective ........................................ 3
Chapter 2 Methods of modeling heterogeneity of variance... 4
2.1 Using absolute residuals ............................. 5
2.2 Using the complex variation model .................... 6
2.2.1 An introduction to complex variation ............... 6
2.1.2 Complex variation model used for heteroscedasticity
adjustment ......................................... 8
2.3 Illustration of fetal nasal bone data ................ 9
2.3.1 Background and data description .................... 9
2.3.2 Data analyses for constructing Age-specific reference
range ............................................. 10
A. Two-stage estimation using absolute residuals ........ 11
B. Using the complex variation model .................... 12
Chapter 3 Simulation study .............................. 14
3.1 Simulation setting .................................. 15
3.2 Simulation results .................................. 18
3.2.1 Results for scenario 1~ scenario 3 (linear SD
change) ........................................... 18
3.2.2 Results for scenario 4 ~ scenario 6 (exponential SD
change) ........................................... 20
Chapter 4 Discussion and conclusion ..................... 21
4.1 Discussion for analysis results ..................... 21
4.2 Limitation and Suggestion ........................... 24
Reference ............................................... 26
Appendix ................................................ 27
[A] Adaptive quadrature ................................. 28
[B] STATA code for the simulation ....................... 30
Tables .................................................. 32
Figures ................................................. 39
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國立陽明大學公共衛生研究所 碩士論文.
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