臺灣博碩士論文加值系統

本文針對有興趣的數量性狀受到單一主效基因、以及單一主效基因以外的其他遺傳效應和環境因素的控制，利用變異數組成模式來分析數量性狀的變異數成份，進而推測主效基因的存在性。過去對於主效基因與標識基因的連鎖分析，一般會以概似函數為基礎，求最大概似估計值及概似比檢定；本文從另一個角度思考，利用貝氏分析的觀點，採用MCMC方法中常用的Gibbs 抽樣方法，並藉助統計軟體WinBUGS1.3來獲得事後機率樣本以進行統計推論。為了比較貝氏方法和最大概似法，以核心家庭有兩位子女的情況作模擬，經由結果顯示，對於主效基因的變異數估計，貝氏方法確實比最大概似法估計較穩定且較精確。此外，透過貝氏因子的檢定可以知道連鎖對應不連鎖的強度為何，本文在最後一章會說明如何進行貝氏因子。

The variance-component model is considered in this thesis for the quantitative trait. Specifically, the model is comprised of a polymorphic single major gene, polygenic effect, and random environmental effect. It is worth noticing that the asymptotic distribution of MLE may not follow the standard normality assumptions, and the estimate itself sometimes falls in the negative region. In contrast to the conventional maximum likelihood estimation, the Bayesian approach is used for statistical analysis. The inference based on the posterior distribution and posterior samples of the parameters of interest, particularly the additive variance of the single major gene, is derived via Markov Chain Monte Carlo method using WinBUGS1.3. Simulations conducted to compare the MLE and Bayesian estimation show that the Bayesian estimate, the posterior mode, is more accurate than MLE. The posterior variance is also smaller than that of MLE. The procedure for testing the linkage using Bayesian approach will be outlined and discussed.

第一章 背景與大綱…………………………………………….…….. 1
第二章 變異數成份分析法應用在混合模式………………….…….. 4
第一節 變異數成份分析法……………………………………….. 4
一 、只存在微效基因………………………………………….. 5
二 、主效基因和微效基因同時存在………………………….. 7
第二節 數量性狀模式………………………………………..…… 8
第三節 變異數組成模式…………………………………...……... 10
第四節 統計推論…………………………………………...……... 12
一 、貝氏方法的參數估計………………………………..…… 12
二 、貝氏檢定…………………………………………...……... 16
三 、最大概似法……………………………………………….. 17
四 、概似比檢定…………………………………………..…… 19
第三章 模擬……………………………………………….………….. 23
第一節 資料模擬…………………………..…………………….... 23
第二節 參數估計……………………………………………...…... 28
第四章 討論…………………………………………..……………… 37

楊玉齡譯 (1994) 基因聖戰，天下文化出版，台北，台灣。
譯自Bishop JE, Waldholz M (1990) Genome
戴政 (2002) 遺傳流行病學，藝軒圖書出版社，台北，台灣。
Abney M, McPeek MS, Ober C (2000) Estimation of variance components of quantitative traits in inbred populations. Am J Hum Genet 66: 629-650.
Almasy L, Blangero J (1998) Multipoint quantitative-trait linkage analysis in general pedigrees. Am J Hum Genet 62:1198-1211.
Amos CI (1994) Robust variance-components approach for assessing genetic linkage in pedigrees. Am J Hum Genet 54:535-543.
Beaty TH, Self SG, Liang KY, Connolly MA, Chase GA, Kwiterovich PO (1985) Use of robust variance components models to analyse triglyceride data in families. Ann Hum Genet 49:315-328.
Blangero J, Williams JT, Almasy L (2000) Robust lod scores for variance component-based linkage analysis. Genet Epidemiol 19(suppl 1):S8-S14.
Brooker RJ (1999) Genetics: analysis & principles. Calif.: Addison-Wesley.
Burton PR, Tiller KJ, Gurrin LC, Cookson WOCM, Musk AW, Palmer LJ (1999) Genetic variance components analysis for binary phenotypes using generalized linear mixed models (GLMMs) and Gibbs sampling. Genet Epidemiol 17:118-140.
Coon H, Leppert MF, Kronenberg F, Province MA, Myers RH, Arnett DK, Eckfeldt JH, Heiss G, Williams RR, Hunt SC (1999) Ann Hum Genet 63:401-412.
Crow JF, Kimura M (1970) An introduction to population genetics theory. Harper and Row, New York.
Falconer DS, Mackay TFC (1996) Introduction to quantitative genetics, 4th edition. Longman, England.
Ferguson TS (1996) A course in large sample theory. London: Chapman and Hall.
Festing MFW (1979) Animal models of obesity. MacMillan Press,London.
Fisher RA (1918) The correlation between relatives on the supposition of Mendelian inheritance. Trans. Roy. Soc. Edinb. 52:399-433.
Haseman JK, Elston RC (1972) The investigation of linkage between a quantitative trait and a marker locus. Behav Genet 2:3-19.
Jeffreys H (1961) Theory of probability, 3rd edition. Oxford University Press.
Kass RE, Raftery AE (1995) Bayes fators. J Am Stat Assoc 90:773-795.
Kass RE, Wasserman L (1996) The selection of prior distributions by formal rules’. J Am Stat Assoc 91:1343-1370.
Lange K (1997) Mathematical and statistical methods for genetic analysis. Springer.
Lee PM (1989) Bayesian statistics. Oxford University Press.
Ludwig EH, Hopkins PN, Allen A, Wu LL, Williams RR, Anderson RR, Ward RH, Lalouel JM, Innerarity TL (1997) Association of genetic variations in apolipoprotein B with hypercholesterolemia, coronary artery disease, and receptor binding of low density lipoproteins. J Lipid Res 38:1361-1373.
Pomp D (1997) Genetic dissection of obesity in polygenic animal models. Behav Genet 27:285-306.
Searle SR, Casella G, McCulloch CE (1992) Variance components. John Wiley and Sons, New York.
Self SG, Liang KY (1987) Asymptotic properties of maximum likelihood estimators and likelihood ratio tests under nonstandard conditions. J Am Stat Assoc 82:605-610.
Spiegelhalter D, Thomas A, Best N (2000) WinBUGS: windows version of BUGS-bayesian inference using Gibbs sampling, version 1.3. MRC biostatistics unit, Cambridge.
Tierney L, Kadane JB (1986) Accurate approximation for posterior moments and marginal densities. J Am Stat Assoc 81:82-86.
Zeger SL, Karim MR (1991) Generalized linear models with random effects; a Gibbs sampling approach. J Am Stat Assoc 86:79-86.