# Gibbs in genetics

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The note is for Gilks, W. R., Richardson, S., & Spiegelhalter, D. (Eds.). (1995). Markov chain Monte Carlo in practice. CRC press..

## Introduction

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

## Standard methods in genetics

### Genetic terminology

- genes, alleles, diallelic, genotype,
- homozygous, heterozygous
- dominant trait, recessive, codominant
- fully penetrant, locus, partially penetrant
- polygene
- Hardy-Weinberg equilibrium
- Linkage analysis

### Genetic models

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

比较表型和性状：

性状是指生物体所有特征的总和，由基因决定，必须是可以遗传的。而表型则是这些基因决定的性状在环境作用下的具体表现，与性状的概念有着本质区别，表型是不可遗传的。所以说表型又称性状的观点是不符合遗传学概念的。

a genetic model is specified in terms of two submodels.

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

penetrance model:

- $y_i$ are conditionally independent given their genotype
- consider late-onset disease traits, characterized by a dichotomous disease status indicator $d$.
- an age variable $t$
- hazard function: $\lambda(t)$
- the penetrance for an unaffected individual is the probability of surviving to age $t$ free of the disease, where $\Lambda(t)=\int_0^t\lambda(u)du$
- the penetrance for an affected individuals is the density function $\lambda(t)S(t)$
- proportional hazards model:
- genotype model:

segregation analysis.

## New words

- nuisance
- frailty
- meiosis
- sperm
- pedigree
- daunting
- spouse