Biostatistics

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By Gang Zheng

Analysis of Genetic organization experiences is either a graduate point textbook in statistical genetics and genetic epidemiology, and a reference e-book for the research of genetic organization reports. scholars, researchers, and pros will locate the subjects brought in Analysis of Genetic organization Studies quite appropriate. The publication is acceptable to the learn of records, biostatistics, genetics and genetic epidemiology.

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

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To find the MLE, the likelihood function is first obtained, which is given by n L(θ |x1 , . . , xn ) = f (xi |θ ), i=1 where f (x|θ ) is the PDF or the distribution function. We often use L(θ ) for the likelihood function. An estimate of θ , denoted by θ , is the MLE for θ if it maximizes the likelihood function. , Θ = (0, 1) for the binomial probability p. Then the MLE θ satisfies L(θ ) = max L(θ ). 6) We may also write θ = arg max L(θ ) = arg max l(θ ), θ∈Θ θ∈Θ where l(θ ) = log L(θ ) is the log-likelihood function.

0 ≤ x ≤ n. Let Xi be the number of ith outcomes of a multinomial random variable. 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.

Penetrance is defined as the probability of having a disease given a specific genotype at the marker, denoted by fi = Pr(case |Gi ) for genotype Gi , i = 0, 1, 2. Here we assume perfect LD. When there is no association, f0 = f1 = f2 = Pr(case). We denote Pr(case) = k as the prevalence of the disease. 1, in which one locus is a marker with alleles A/a and the other is a functional locus with alleles B/b. We will discuss two types of designs: population based and family based. In the population-based design, we focus on the retrospective case-control study.

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