Linkage in human families is determined by LOD score analysis

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Linkage in human families is determined by LOD
score analysis

• A LOD score is defined as the logarithm of the
  ratio of the odds (Z) that the observed markers
  are linked at a particular q, as compared to the
  odds of the observed outcome if there is no
  linkage (q 0.5)
• Zq odds of observed result if q x
  
  odds of observed
  result if q - 0.5
• This calculation is then repeated using different
  values of q, and the value of q when LOD is
  maximum is called the MLS or Zmax.

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Scoring recombinants

• A1,A2 A3,A4
• B1,B2 B3,B4
• A1,A3 A2,A3 A1,A4 A2,A4 A2,A3 A1,A4
• B2,B3 B1,B3 B2,B4 B2,B4 B1,B4 B2,B4
• Each parent makes 6 germ cells of which 1 is
  recombinant what is the map distance?
• 1/6 .167 16.7 cm apart

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• To go back to the example we had before
• For each parent 1/6 gametes is recombinant
• The overall likelihood, given linkage, is (1-
  q?r?qnr
• The overall odds of nonlinkage (q 0.5) is (0.5)6
  0.015625
• At q 0.1, (1- q?5?q 0.95????????????
• Zq0.1 0.59/ 0.015625 3.77
• LODq0.1 0.577
• At q 0.15, Z 4.26 and LOD 0.629
• At q 0.20, Z 4.19 and LOD 0.623
• At q 0.25, Z 3.80 and LOD 0.579
• If there are 3 similar families with this trait,
  and the same pattern of segregation, then
  LODq0.15 0.629 0.629 0.629 1.887

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Parameters which must be specified

• Mode of inheritance
• Population frequency of trait
• Population frequency of alleles at tested loci
• Population frequency of phenocopies

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Mode of inheritance
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Great! You have a map result!
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Narrowing down the region
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Narrowing down the region
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The Huntingtons disease example
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The flow of gene discovery
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Homozygosity mapping

• For rare recessive traits, it is sometimes
  possible to map a gene simply by looking at
  regions of homozygosity in affected persons
• In cases of consanguinity, these persons
  presumably inherited both disease and surrounding
  alleles from a common ancestor
• In genetic isolates (or even in relatively small
  gene pools), the same principle applies, though
  the extent to which the region has recombined
  will be a function of q and of the number of
  generations which have elapsed since the putative
  mutation arose

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Non-parametric Linkage

• Non-parametric linkage methods can be used when
  there is some uncertainty about the correct
  genetic model, or when extended kindreds are not
  available for linkage analysis
•  Most of these methods are based on the analysis
  of allele sharing between affected sibling pairs
• The principle underlying this is simply that, if
  two first-degree relatives share a trait in
  common (eg., diabetes), then it follows that they
  will likely share allelotypes of other genetic
  markers in close proximity to the gene which
  confers the risk for diabetes

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NPL, continued

• If these are markers which are readily scored
  (eg., STR, SNP), then it may be possible to map
  the trait for further genetic analysis
• This method can also be extended to other classes
  of 1 or 2 relatives, but it then becomes
  imperative to distinguish IBD from IBS
• A disadvantage of NPL is that statistical power
  of the method is severely reduced, as compared to
  the LOD score method

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Terminology reminder

• Identity by descent a pair of sibs (or other
  relatives) inherit a given allele from the same
  parent
• Identity by state a pair of relatives have the
  same allele, but you cant tell whether it came
  from the same parent

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Allele sharing

• Consider a mating which is fully informative
• A1/A2 x A3/A4 
• There are three possible outcomes for two
  offspring with respect to alleles in common
• 2 alleles shared 1 allele shared 0
  alleles shared
• Eg A1/A3 A1/A3 A1/A3 A1/A4 A1/A3A2/A4
• The probability of these outcomes in the
  illustrated pedigree are 1/4 (2 shared), 1/2 (one
  shared), 1/4 (no shared alleles), respectively

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Allele sharing

• The situation becomes more complex if the mating
  is not fully informative
• A1/A2 x A3p/A3m 
• There are now only two outcomes for a given
  individual A1/A3 A2/A3 so that all
  offspring will share the A3 allele, but it is not
  possible (without further genotyping information)
  to tell whether siblings have or have not
  inherited the same A3 chromosome
• If both siblings are A1/A3, the A1 is shared IBD,
  but the A3 is only shared IBS

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Identity by descent
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Identity by descent or state?
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As was the case for parametric linkage, part of
this problem can be solved with additional
genotyping

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• This mating is fully informative for all markers
  except the shaded marker, but because the
  surrounding markers are all informative, we can
  say with reasonable certainty that offspring 1
  and 4 share this allele IBD, as do offspring 2
  and 3

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But, haplotype information cant resolve all
questions..

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• In this pedigree, there are 3 copies of the same
  allele at the distal end of the haplotype
• Offspring 2 and 3 dont share this allele, but
  you cant be certain that individuals 1 and 4
  share the same maternal allele IBD, because only
  one flanking marker is typed

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More about allele sharing

• This method can be (and commonly is) used when
  parents are not available for genotyping, but
  unless enough siblings are available to know that
  the mating was fully informative, one can only
  conclude that shared alleles are IBS
• Eg., if A1/A3, A1/A2, A3/A4 are siblings, then
  you could be certain that A1 for the first pair,
  and A3 for the second pair, are shared IBD
• When using the method for 2 relatives, you must
  typically be able to genotype the entire kindred
  in order to claim IBD
• Caution IBS reduces information by a factor of
  2

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Sib Pair analysis (Haseman-Elston)

• Underlying principle if a genetically
  influenced trait is present in two siblings or 1
  relatives, then it is likely that they will also
  share genetic markers which are physically close
  to the disease allele more frequently than
  expected by chance
• On average, chance sharing of 1 allele IBD is
  50, so what you are looking for is gt50 sharing
  of the trait and marker alleles. For most
  traits, this requires a sample of 100-300 sibling
  pairs, in order to provide statistical power
• The classical Elston/Stewart method is a
  hypothesis-testing method, in which the H0 is
  0.5. The number of cases necessary to achieve
  power to reject this hypothesis is proportional
  to the genetic relative risk or risk ratio.

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Sib pair analysis is the basis of NPL

• A simple computerized method of non-parametric
  linkage analysis is readily available, as are
  multipoint modifications and more statistically
  sophisticated methods which take into account
  additional sources of variance
• Statistical evaluation of the results
• Maximum likelihood, vs simulated p values
• Significant linkage MLS 3.6, p 2 x 10-5.
  Would occur by chance in 1/20 linkage studies
• Highly significant MLS 5.4, p 3 x 10-7.
  Would occur by chance 1/1000 genome scans
• Confirmed linkage independent replication

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An example of NPL analysis
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What is the genetic relative risk (l)?

• l is an estimate of familial resemblance, not
  unlike heritability, but much easier to compute
• l trait in relatives of proband/ trait in
  the population
• For Mendelian traits, l is very large
• Eg., for CF ls 1/4 1/25000 25000/4 625
• For complex traits, l is much smaller (typically,
  2 - 100)
• One can define a range of l values
• For siblings ls
• For 1 relatives l1
• For 2 relatives l2 etc

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Dont confuse genetic RR with epidemiological RR

• Relative risk is actually a term which derives
  from epidemiology, and refers principally to the
  association between a particular risk factor and
  the expression of a disease
• RR ( risk in trait)( controls without risk)
• ( trait without risk)( risk in controls)
• Eg 95 of persons with ankylosing spondylitis
  are HLA-B27, but only 20 of persons with B27
  develop AS
• RR (0.95.93)/(.05.2) 88

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Another use of the Haseman-Elston algorithm is to
map quantitative traits
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Quantitative trait analysis

• The foregoing example uses a quantitative measure
  of the trait under investigation (eg., IQ,
  height, BP, etc). This trait is measured for
  each sibling, then the difference is squared (to
  avoid negative numbers) and regressed against the
  number of alleles shared at a locus IBD.
• A negative regression line is indicative of
  linkage between the locus and trait, while a
  positive regression line would indicate the
  reverse. How about a straight line?

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Association studies

• A standard epidemiological design in which cases
  are compared to controls
• An important assumption is that cases and
  controls are drawn from the same population
• Tested by standard statistical methods (eg., c2)
• Explanations for an observed association
• Population stratification
• Linkage disequilibrium
• The tested allele actually contributes to the risk

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Transmission disequilibrium test (TDT)

• This is a family-based method of evaluating the
  strength of association between a trait and a
  polymorphic marker or markers
• Consider a family in which an affected parent has
  the genotype AB, the unaffected parent is
  homozygous for either allele, and there are 2
  affected offspring.
• The affected parent has an equal probability of
  transmitting allele A or allele B to the affected
  offspring.
• The basic statistical comparison is between the
  alleles which ARE transmitted to affected
  offspring and those which are NOT.

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TDT, continued

• The H0 is that equal s of A and B will be
  transmitted to affected offspring.
• Disequilibrium between the trait and either
  allele (significantly more than 50 of either
  allele) is indicative of genetic association, and
  possibly of linkage.
• NPL is a locus-based method, but TDT is a
  sensitive to the specific alleles being tested.
  It may indicate association between a trait and a
  specific allele (eg., AD and ApoE4), but further
  testing is required to confirm linkage.
• Eg., this particular allele might modify the
  expression of a trait, but not be physically
  close to the trait gene.

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cases required for analysis
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Linkage disequilibrium mapping

• LD occurs when a haplotype occurs more (or less)
  often than would be predicted from the
  frequencies of the separate alleles
• The source of LD is typically a mutation in a
  founder, which is gradually eroded at the rate of
  1-q per generation.
• Conceptually, LD is used as a means of mapping
  which treats affected individuals as members of
  giant pedigrees which extend over many
  generations
• Not surprisingly, genetically isolated or
  homogeneous populations are favorites for this
  type of mapping

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The principle of LD mapping
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LD maps-1
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LD maps-2
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An example
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