Gibbs in genetics

Tags: Gibbs

Introduction

1. essential feature of genetic studies: involve related individuals.
2. standard analysis methods of epidemiology is inappropriate which assume independence.

Standard methods in genetics

Genetic terminology

1. genes, alleles, diallelic, genotype,
2. homozygous, heterozygous
3. dominant trait, recessive, codominant
4. fully penetrant, locus, partially penetrant
5. polygene
6. Hardy-Weinberg equilibrium

Genetic models

1. $y_i$: phenotype for subject $i=1,\ldots,I$
2. $x_i$: measured risk factors
3. $z_i$: polygene
4. $P$: a probability

a genetic model is specified in terms of two submodels.

1. penetrance model $P(y\mid G, x,\Omega)$
2. genotype model $P(G,z\mid\Theta)$

penetrance model:

1. $y_i$ are conditionally independent given their genotype
2. consider late-onset disease traits, characterized by a dichotomous disease status indicator $d$.
3. an age variable $t$
4. hazard function: $\lambda(t)$
5. the penetrance for an unaffected individual is the probability of surviving to age $t$ free of the disease, $$S(t) = \exp[-\Lambda(t)]\,,$$ where $\Lambda(t)=\int_0^t\lambda(u)du$
6. the penetrance for an affected individuals is the density function $\lambda(t)S(t)$
7. proportional hazards model: $$\lambda(t, G, x, z)=\lambda_0(t)\exp\{\beta x+\gamma\cdot \mathrm{dom}(G)+\eta z+\ldots\}$$
8. genotype model: $$P(G\mid\Theta)=P(G_1\mid\Theta)\prod\limits_{i=2}^IP(G_i\mid G_1,\ldots,G_{i-1};\Theta)$$

segregation analysis.

New words

1. nuisance
2. frailty
3. meiosis
4. sperm
5. pedigree
6. daunting
7. spouse

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