Association analysis

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Association analysis

• Genetics for Computer Scientists
• 15.3.-19.3.2004
• Biomedicum Department of Computer Science,
  Helsinki
• Päivi Onkamo

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Lecture outline

• Genetic association analysis
• Allelic association
• ?2 test
• Linkage disequilibrium (LD) process
• Formulation of the computational problem for LD
  mapping
• Limitations of the LD mapping
• Approaches. For example HPM

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Genetic association analysis

• Search for significant correlations between gene
  variants and phenotype
• For example
• Locus A for
• SLE 100
• cases and 100
• controls
• genotyped

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Allelic association An allele is associated to
a trait

• Allele 1 seems to be associated, based on sheer
  numbers, but how sure can one be about it?

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• The idea is to compare the observed frequencies
  to frequencies expected under hypothesis of no
  association between alleles and the occurrence of
  the disease (independency between variables)
• Test statistic
• Where
• oi is the observed class frequency for class i,
  ei expected (under H0 of no association)
• k is the number of classes in the table
• Degrees of freedom for the test df(r-1)(s-1)

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Expected
df1 pltlt0,001
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Interpretation of the test results

• The p-value is low enough that H0 can be rejected
  the probability that the observed frequencies
  would differ this much (or even more) from
  expected by just coincidence lt 0.001
• ?2 tables (Appendix), internet resources, etc.

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• Genetic association is population level
  correlation with some known genetic variant and a
  trait an allele is over-represented in affected
  individuals ?
• From a genetic point of view, an association does
  not imply causal relationship
• Often, a gene is not a direct cause for the
  disease, but is in LD with a causative gene
• ?

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Linkage disequilibrium (LD)

• Closely located genes often express linkage
  disequilibrium to each other
• Locus 1 with alleles A and a, and locus 2 with
  alleles B and b, at a distance of a few
  centiMorgans from each other
• At equilibrium, the frequency of the AB haplotype
  should equal to the product of the allele
  frequencies of A and B, ?AB ?A?B. If this
  holds, then ?Ab ?A ?b, ?aB ?a?B and ?ab
  ?a?b , as well. Any deviation from these values
  implies LD.

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Linkage disequilibrium (LD)

• LD follows from the fact that closely located
  genes are transmitted as a block which only
  rarely breaks up in meioses
• An example
• Locus 1 marker gene
• Locus 2 disease locus, with allele b as
  dominant susceptibility allele with 100
  penetrance

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An example
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• Association evaluated ?
• Locus 1 also seems associated, even though it
  has nothing to do with the disease association
  observed just due to LD
• LD mapping utilizing founder effect
• A new disease mutation born n generations ago in
  a relatively small, isolated population
• The original ancestral haplotype slowly decays as
  a function of generations
• In the last generation, only small stretches of
  founder haplotype can be observed in the
  disease-associated chromosomes

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LD mapping Utilizing founder effect
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Data Searching for a needle in a haystack
Disease gene
Disease status
S2
...
SNP1
...
a ? 2 1 1 a ? 1
2 1
1 2 2 1 1 2 1 2 1 2 1 1
2 2
1 2 2 1 2 1 1
2
2 1 1 1 1 1 1
1
c 2 1 ? ?c 1 1
? ?
1 2 2 1 1 2 1 1 2 2 2 1
1 1
a 1 1 2 1a 1 1
1 2
1 1 2 1 1 2 2 2 2 2 1 1
2 1
2 2 ? 1 1 1 ?
1

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• Task is to find either an allele or an allele
  string (haplotype) which is overrepresented in
  disease-associated chromosomes
• markers may vary SNPs, microsatellites
• populations vary the strength of
  marker-to-marker LD
• Many approaches
• old-fashioned allele association with some
  simple test (problem multiple testing)
• TDT modelling of LD process Bayesian, EM
  algorithm, integrated linkage LD

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Limitations of the LD mapping

• The relationship between the distance of the
  markers vs. the strength of LD theoretical curve

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Linkage disequilibrium (D) for the African
American (red) and European (blue) populations
binned in 5 kb classes after removing all SNPs
with minor allele frequencies less than 20. 3429
SNPs were included (Source http//www.fhcrc.org/la
bs/kruglyak/PGA/pga.html)
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Limitations LD is random process

• LD is a continuous process, which is created and
  decreased by several factors
• genetic drift
• population structure
• natural selection
• new mutations
• founder effect
• ? limits the accuracy of association mapping

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Research challenges

• Haplotyping methods needed as prerequisite for
  association/LD methods
• or, searching association directly from genotype
  data (without the haplotyping stage)
• Better methods for measurement of the association
  (and/or the effects of the genes)
• Taking disease models into consideration

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A methodological projectHaplotype Pattern
Mining (HPM)AJHG 67133-145, 2000

• Search the haplotype data for recurrent patterns
  with no pre-specified sequence
• Patterns may contain gaps, taking into
  consideration missing and erroneous data
• The patterns are evaluated for their strength of
  association
• Markerwise score of association is calculated

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• Algorithm
• Find a set of associated haplotype patterns
• number of gaps allowed (2)
• maximum gap length (1 marker)
• maximum pattern length (7 markers)
• association threshold (?2 9)
• Score loci based on the patterns
• Evaluate significance by permutation tests
• Extendable to quantitative traits
• Extendable to multiple genes

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Example a set of associated patterns
Marker 01 02 03 04 05 06 07 08 ?2 P1
2 1 2 2 2 9.6 P2 2 1
2 2 2 1 9.2 P3 2 1 2 2
1 1 8.9 P4 2 1 2 1
8.1 P5 1 1 2 2 7.4 P6
1 2 2 1 2 7.1 P7
2 1 2 7.1
P8 2 1 1 2 6.9 P9
2 1 1 6.8

Score 5 6 7 7 6 3 2 0
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Pattern selection

• The set of potential patterns is large.
• Depth-first search for all potential patterns
• Search parameters limit search space
• number of gaps
• maximum gap length
• maximum pattern length
• association threshold

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Score and localization an example
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Permutation tests

• random permutation of the status fields of the
  chromosomes
• 10,000 permutations
• HPM and marker scores recalculated for each
  permuted data set
• proportion of permuted data sets in which score gt
  true score ? empirical p-value.

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Permutation surface (A7.5 ). The solid line is
the observed frequency.
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Localization power with simulated SNP data
(density 3 SNPs per 1 cM). Isolated population
with a 500-year history was simulated. Disease
model was monogenic with disease allele frequency
varying from 2.5-10 in the affecteds. 12.5 of
data was missing. Sample size 100 cases and 100
controls.
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Benefits drawbacks

• Non-parametric, yet efficient approach no
  disease model specification is needed
• Powerful even with weak genetic effects and small
  data sets
• Robust to genotyping errors, mutations, missing
  data
• Allows for gaps in haplotypes

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• Flexible easily extended to different types of
  markers, environmental covariates, and
  quantitative measurements
• optimal pattern search parameters may need to be
  specified case-wise -
• no rigid statistical theory background -
• requires dense enough map to find the area where
  DS gene is in LD with nearby markers.

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• Search of the susceptibility gene
• With good luck - and information from gene banks,
  pick up the correct candidate gene
• Genetic region with positive linkage signal is
  saturated with markers, and this data is now
  searched for a secondary correlation
  correlation of marker allele(s) with the actual
  disease mutation (LD)

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• Improved statistical methods to detect LD
• Terwilliger (1995)
• Devlin, Risch, Roeder (1996)
• McPeek and Strahs (1999)
• Service, Lang et al. (1999)
• Statistical power of association test statistics
• Long, Langley (1999).
• Review on statistical approaches to gene mapping
• Ott, Hoh (2000)