Variance Components for Statistical Genetics: Applications
in Medical Research to Characteristics Related to Human
Diseases and Health
Hopper JL
Faculty of Medicine Epidemiology Unit, University of Melbourne, Carlton, Victoria,
Australia.
Statistical Methods in Medical Research, 2(3):199-223 (1993)
Abstract
RA Fisher introduced variance components in 1918. He synthesized Mendelian
inheritance with Darwin's theory of evolution by showing that the genetic variance of a
continuous trait could be decomposed into additive and non-additive components. The
model can be extended to include environmental factors, interactions, covariation, and
non-random mating. Identifiability depends critically on design. Methods of analysis
include modelling the mean squares from a fixed effects analysis of variance, and
covariance structure modelling, which can be extended to multivariate traits and has
been used to study ordinal traits by reference to postulated, unmeasured, latent
'liabilities'. These methods operate on dependent observations within independent
groups of the same size and structure, and therefore require balanced designs ('regular'
pedigrees). A multivariate normal model handles data in its generic form, utilizes data
efficiently from all members of pedigrees of unequal size or varying structure,
accommodates individuals missing at random, and allows flexible modelling with tests of
distributional assumptions and fit. Most analytical methods use least squares or
maximum likelihood under normal theory. Robust methods, scale transformation,
ascertainment, path diagrams and correlational path models (popular in behavioural
genetics through addressing nonrandom mating and social interactions), 'heritability',
and the contribution and limitations of statistical modelling to the 'nature-nurture'
debate, are discussed.
Variance component linkage analysis