Download e-book for kindle: Analysis of Genetic Association Studies by Gang Zheng

By Gang Zheng

Analysis of Genetic organization reviews is either a graduate point textbook in statistical genetics and genetic epidemiology, and a reference ebook for the research of genetic organization stories. scholars, researchers, and pros will locate the subjects brought in Analysis of Genetic organization Studies relatively proper. The booklet is appropriate to the examine of data, biostatistics, genetics and genetic epidemiology.

In addition to offering derivations, the publication makes use of actual examples and simulations to demonstrate step by step purposes. Introductory chapters on chance and genetic epidemiology terminology give you the reader with useful historical past wisdom. The association of this paintings enables either informal reference and shut research.

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The Wald statistic for H0 : θ = θ0 can be written as WT = (θ − θ0 )T in (θ )(θ − θ0 ) = (θ − θ0 )T {−l (θ )}(θ − θ0 ) ∼ χd2 under H0 . Likelihood Ratio Test To test H0 : θ = θ0 , the likelihood ratio test (LRT) is based on the likelihood ratio and is given by LRT = 2 log L(θ ) = 2l(θ) − 2l(θ0 ) ∼ χd2 L(θ0 ) under H0 . 4 Likelihood-Based Test Statistics: With a Nuisance Parameter In genetic association studies, nuisance parameters are often present. For example, in the analysis of gene-environment interaction, we may be interested in testing only the gene-environment interaction and treat the odds ratios of the main genetic and environmental effects as nuisance parameters.

The mean and variance of Xi are given by E(Xi ) = npi and Var(Xi ) = pi (1 − pi )/n. The covariance of two outcomes Xi and Xj is given by Cov(Xi , Xj ) = −pi pj /n for i = j . Thus, Corr(Xi , Xj ) = − pi pj . (1 − pi )(1 − pj ) The Normal Distribution The normal distribution is the most commonly used distribution in statistics. Let X be a random variable that follows a normal distribution. 3) where μ is the mean (location) of X and σ is the standard deviation (scale) of X. The normal distribution is denoted by X ∼ N(μ, σ 2 ), where σ 2 is the variance of X.

To apply a Bonferroni correction when testing M null hypotheses, each null hypothesis is tested at the level α/M. If one of the M tests is significant at the α/M level, the null hypothesis is rejected, and the overall Type I error would be controlled at the α level. Let Ti be the ith test for the ith null hypothesis with level α/M. Denote its critical value by Ci . Thus, under H0 , Pr(Ti > Ci ) = α/M. Hence, under H0 , the Type I error to incorrectly reject H0 is M Pr(reject H0 ) = Pr M (Ti > Ci ) ≤ i=1 M Pr(Ti > Ci ) = i=1 α/M = α.

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