Biomedical Engineering Reference
In-Depth Information
occur when
θ
k/n
. However, because we typically consider
θ
to range between 0 and
0.5, the maximum likelihood estimate for
θ
is taken to be
=
⎧
⎨
⎩
k
n
n
2
if
k
≤
θ
=
1
2
if
k
>
n
2
and the maximum LOD score is then log
10
L( θ)/L(
0
.
5
)
. For more complex data, however,
software is used to evaluate the likelihood functions and compute LOD scores.
The early computer programs for two-point (i.e. single marker) LOD score linkage
analysis, such as LIPED [78], were revelatory in their time and allowed for rapid anal-
ysis of complex pedigrees. User-friendly software packages in popular use today for rapid
multipoint parametric linkage analysis include MERLIN [79] and Genehunter [80]; these
programs also implement non-parametric linkage analysis, discussed next.
4.2.4 Linkage methods: non-parametric methods
Parametric methods have been successful in identifying genes for rare Mendelian disorders
for which the mode of inheritance is typically recognizable. However, multifactorial diseases
such as type II diabetes and psychiatric diseases often do not lend themselves to specification
of an unequivocal disease model. This has led to the popularity of 'non-parametric' methods
that do not require a disease model to specified, including affected sib pair (ASP) analysis,
affected pedigree member (APM) analysis and variance components (VCs) analysis.
Despite the labeling of these methods as 'model-free' or 'non-parametric,' it is important
to be aware that equivalencies between ASP and parametric tests have been demonstrated
in particular cases [81]. Furthermore, implicit model assumptions exist for ASP tests, and
the power of such tests is thus influenced by the appropriateness of these assumptions and
the true underlying model [82].
ASP and APM methods evaluate whether affected relatives share more than the expected
number of marker alleles identical by descent (IBD), where two alleles are IBD if they are
inherited from the same ancestral source. Alleles that appear to have the same value but are
not known to be from the same ancestor are called identical by state (IBS). For a sibling
pair, the expected IBD proportion is 0.5; this is equivalent to one out of the two possible
alleles being shared IBD. At a particular marker or genetic map position, the evidence for
linkage is typically measured by the maximum LOD score (MLS). That is, the LOD score
is maximized over the parameters used to parameterize the single major locus model; for
example, over the IBD sharing probabilities at the putative trait locus.
Modern multipoint relative-pair methods have their roots in an early idea of Penrose
[82]. Penrose proposed tabulating the proportion of sib-pairs that are alike or not alike
for two observable states, or 'phenotypes,' which nowadays are in fact typically a disease
trait and genotype status at a marker. The test for linkage in a more focused ASP design
consists of comparing the phenotypic similarity of each sib pair with its allelic similarity, the
latter measured by IBD status. Because with an ASP design the sib pair members are both
affected with the disease, they are necessarily phenotypically similar and we expect that if a
marker is linked to a disease locus (or is itself the disease locus) then the IBD status at that
marker will be elevated above the 0.5 proportion expected under the null hypothesis of no
linkage. Several formal statistical tests to compare these null and alternative hypotheses are
