Gene mapping: Linkage and association methods

1
Gene mappingLinkage and association methods

• Disease gene mapping is one of the main purposes
  for genotyping
• Two major approaches linkage and association
  analyses

2
Linkage analysis

• Try to localize genes affecting specific
  phenotypes
• Search for co-segregation of disease and marker
  alleles

3
Basics of Linkage Analysis

1. Idea of Linkage Analysis
2. Types of Linkage Analysis
3. Parametric Linkage Analysis
4. Conclusions

4
Basics of Linkage Analysis

1. Idea of Linkage Analysis
2. Types of Linkage Analysis
3. Parametric Linkage Analysis
4. Conclusions

5
Linkage Analysis

• One of the two main approaches in gene mapping.
• Uses pedigree data.

6
Genetic linkage and linkage analysis

• Two loci are linked if they appear nearby in the
  same chromosome.
• The task of linkage analysis is to find markers
  that are linked to the hypothetical disease locus
• Complex diseases in focus ? usually need to
  search for one gene at a time
• Requires mathematical modelling of meiosis

7
Meiosis and crossover

• Number of crossover sites is thought to follow
  Poisson distribution.
• Their locations are generally random and
  independent of each other.

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The simple idea
Recombination fraction
?
Always 0 ? 0.5

• Task Find ? that maximises L(? data )
• Obtain measure for degree of evidence in favour
  of linkage (LOD score)

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Markers and inheritance

• Polymorphic loci whose locations are known
• Most often SNPs or microsatellites
• Inherited within the chromosomes

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Markers and information

• Two individuals share same allele label ? they
  share the allele IBS (identical by state)
• Two individuals share an allele with same
  (grand)parental origin ? they share an allele IBD
  (identical by descent)
• IBS sharing can easily be deduced from genotypes.
• IBD sharing requires more information. One can
  try to deduce IBD sharing based on family
  structure and inheritance.

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Markers and information
1,2
2,3
The children share allele 1 IBS.
They also share it IBD.
1,2
1,3
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Markers and information
1,2
1,3
The children share allele 1 IBS.
1,2
1,3
They do not share alleles IBD.
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Markers and information
1,1
2,3
The children share allele 1 IBS.
1,2
1,3
They either share or do not share it IBD.
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Building blocks of linkage analysis
Marker maps
Pedigree structures
Genotypes
Phenotypes
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Building blocks of linkage analysis

• Information about disease model (in parametric
  analysis)

? ?(aa), probability of a homozygote being
affected
? ?(Aa), probability of a heterozygote being
affected
? ?(AA), probability of a non-carrier being
affected (phenocopy rate)

• Assumed disease allele frequency
• Marker allele frequencies
• Information about environmental variables

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Basics of Linkage Analysis

1. Idea of Linkage Analysis
2. Types of Linkage Analysis
3. Parametric Linkage Analysis
4. Conclusions

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Types of linkage analysis

• Parametric vs. non-parametric
• Dichotomous vs. continuous phenotypes
• Elston-Stewart vs. Lander-Green vs. heuristic
• Two-point vs. multipoint
• Genome scan vs. candidate gene

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Basics of Linkage Analysis

1. Idea of Linkage Analysis
2. Types of Linkage Analysis
3. Parametric Linkage Analysis
4. Conclusions

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Maximum likelihood estimation

• A common approach in statistical estimation
• Define hypotheses
• Generate likelihood function
• Estimate
• Test hypotheses
• Draw statistical conclusions

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Hypotheses in linkage analysis

• H0
• ? 0.5
• the disease locus is not linked to the marker(s)
• HA
• ? ? 0.5
• the disease locus is linked to the marker(s)

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Likelihood function for a single nuclear family

• Lj ?gF P(gF) P(yF gF)?gM P(gM)P(yM
  gM)?gOi P(gOi gF, gM) P(yOi gO)

G genotype probabilitiesy phenotype
probabilities
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Several independent families

• The likelihood functions of multiple independent
  families are combined
• L ? Lj or logL ? log Lj

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Testing of hypotheses

• Compute values of likelihood function under null
  and alternative hypotheses.
• Their relationship is expressed by LOD score
  (essentially derived from the likelihood ratio
  test statistic.

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On significance levels

• P-value gives a probability that a null
  hypothesis is rejected even though it was true.
• A LOD-score threshold of 3 corresponds to a
  single-test p-value of approximately 0.0001
• Often, the significant areas pointed out are
  quite large, from 10-40 cM (millions of basepairs)

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0.56
0.5
LOD score
0.0
0.0
0.5
0.14
Recombination fraction
LODgt3 taken as evidence of linkage.
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Basics of Linkage Analysis

1. Idea of Linkage Analysis
2. Types of Linkage Analysis
3. Parametric Linkage Analysis
4. Conclusions

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Conclusions

• Linkage analysis is a pedigree-based approach to
  gene mapping.
• Parametric vs. nonparametric methods.
• Hypothesis-driven vs. explorative analysis.
• Meta-analysis (integration of several studies
  into one big study) becoming increasingly
  popular.

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Fine mapping and association analysis

• After successful linkage analysis, what to do?
• How to refine the linked area where actually
  the disease susceptibility locus is?
• Outline of the rest of the lecture
• Allelic association
• ?2 test
• LD mapping

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Allelic association

• An example A leukaemia study, where a number of
  affected and healthy control persons have been
  contacted for DNA samples
• A candidate gene has been suggested GSTM1, which
  functions in the metabolism of benzene
• GSTM1 has two different alleles, 1 and 2, where
• A person is positive for allele 1 if his
  genotype is 1 1 or 1 2
• A person is null, if having genotype 2 2
• The numbers of leukaemic and control individuals
  either positive or null with respect to allele 1
  are compared by ?2-test in order to find out,
  whether there is statistically significant
  difference

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Allelic assosiation

• Results observed frequencies
• Expected frequencies

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Test statistic

• The observed are compared to expected
  frequencies. (null hypothesis, H0 carrier status
  and disease occurrence are independent of each
  other )
• Test statistic
• where
• oi is the observed frequency for class i, ei the
  expected frequency for class i
• k is the number of classes

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Allelic assosiation

• Now, ?2 111,39.
• Degrees of freedom for the test df(r-1)(s-1),
  where r number of rows, s number of columns
• Here, df (2-1)(2-1) 1
• The ?2 value is then compared to the null
  distribution of critical ?2-test statistic values
  (within the given df class)

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?2-distribution critical values for chosen
significance levels

• df\p 0.10 .05 .025 .01 .005
• 1 2.71 3.84 5.02 6.63 7.88
• 2 4.61 5.99 7.38 9.21 10.60
• 3 6.25 7.81 9.35 11.34 12.84
• 4 7.78 9.49 11.14 13.28 14.86
• 5 9.24 11.07 12.83 15.09 16.75
• 6 10.64 12.59 14.45 16.81 18.55
• 7 12.02 14.07 16.01 18.48 20.28
• 8 13.36 15.51 17.53 20.09 21.96
• 9 14.68 16.92 19.02 21.67 23.59
• 10 15.99 18.31 20.48 23.21 25.19
• 11 17.28 19.68 21.92 24.73 26.76

When the observed value of test statistic is
greater than the critical value (for the chosen
significance levels) given in the table, the null
hypothesis can be rejected.
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Allelic association

• The value we obtained, ?2 111,39 , exceeds all
  critical values with df1 given in the table. We
  conclude, that H0 can be rejected and thus, there
  is statistically significant difference between
  the affected and healthy with respect to GSTM1
  genotypes.
• The relative frequencies of null and positive
  genotypes show the same
• It seems that different GSTM1 genotypes, by
  changing the benzene metabolism, considerably
  affect the probability of getting leukaemia

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• Note compared to linkage analysis, which is
  based on the observed inheritance patterns in
  pedigrees, the association analysis studies
  correlation of allele presence and a disease in
  the level of population
• We find an allele or a haplotype overrepresented
  in affected individuals ?
• BUT the statistical correlation does not
  implicate a causal relationship !!!! ?
• Quite often, the associating allele or haplotype
  is not the cause of the disease itself, but is
  merely correlated with the presence of the actual
  susceptibility gene in the same chromosome. It is
  then said to be in linkage disequilibrium with
  the disease gene. ?

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Original mutation in one chromosome in the
founder population
A
Time
Current generation
C
B
An affected pedigree
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LD mapping

• The marker itself is NOT the reason for the
  disease, but its located nearby the disease
  susceptibility gene, and there is correlation
  between the presence of certain marker allele and
  the disease gene allele (LD)
• The correlation, i.e. LD, is based on founder
  effect the disease allele has been born a long
  time ago on a certain ancestral chromosome, and
  majority of disease alleles existing presently
  predate from that original mutation

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LD-mapping Utilizing the founder effect
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Data
Disease locus
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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Many approaches, several programs

• 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 LD is random process

• The amount of LD is on a continuous but slow
  change, where the natural forces of
• genetic drift
• population structure
• natural selection
• new mutations
• founder effect
• ...affect it even if two pairs of loci are in
  exactly the same distance from each other, their
  amount of LD may vary a lot.
• ? This limits the accuracy of LD mapping, though
  it is much more accurate in pinpointing the
  location of a disease gene compared to linkage