Download Basics of Linkage Analysis

Gene mapping:
Linkage and association methods
• Disease gene mapping is one of the main
purposes for genotyping
• Two major approaches: linkage and association
analyses
Linkage analysis
 Try to localize
genes
affecting
specific
phenotypes
 Search for: cosegregation
of disease and
marker alleles
Basics of Linkage Analysis
1.
2.
3.
4.
Idea of Linkage Analysis
Types of Linkage Analysis
Parametric Linkage Analysis
Conclusions
Basics of Linkage Analysis
1.
2.
3.
4.
Idea of Linkage Analysis
Types of Linkage Analysis
Parametric Linkage Analysis
Conclusions
Linkage Analysis
• One of the two main approaches in gene mapping.
• Uses pedigree data.
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
Meiosis and crossover
• Number of crossover sites is thought to follow Poisson
distribution.
• Their locations are generally random and independent
of each other.
The simple idea
DIS
Recombination
fraction
Marker

Always: 0 ≤  ≤ 0.5
• Task: Find  that maximises L( |data )
• Obtain measure for degree of evidence in
favour of linkage (LOD score)
Markers and inheritance
1
2
4
3
2
2
1
3
3
1
4
2
Father
2
3
1
3
4
1
Mother
Child
• Polymorphic loci whose locations are known
• Most often SNPs or microsatellites
• Inherited within the chromosomes
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.
Markers and information
1,2
2,3
The children share allele 1 IBS.
1,2
1,3
They also share it IBD.
Markers and information
1,2
1,3
The children share allele 1 IBS.
1,2
1,3
They do not share alleles IBD.
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.
Marker maps
Building blocks of linkage analysis
Pedigree structures
Chr. 1
1
1
2
5
1 12 1
2 14 1
2
3
1
2
1 2
1 2
1
2
Chr. 2
1 3
3 4
4 5
4 7
1
1
2 3 2
4 3 4
4 2 1
4 2 3
Genotypes
Phenotypes
Chr. 22
2 1 1 3 2
2 2 3 3 4
Building blocks of linkage analysis
•
Information about disease model (in parametric analysis)
 0.99   (aa), probability of a homozygote being affected


   0.8   (Aa), probability of a heterozygote being affected
 0.001  (AA), probability of a non-carrier being affected


(phenocopy rate)
Assumed disease allele frequency
•
•
Marker allele frequencies
Information about environmental variables
Basics of Linkage Analysis
1.
2.
3.
4.
Idea of Linkage Analysis
Types of Linkage Analysis
Parametric Linkage Analysis
Conclusions
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
Basics of Linkage Analysis
1.
2.
3.
4.
Idea of Linkage Analysis
Types of Linkage Analysis
Parametric Linkage Analysis
Conclusions
Maximum likelihood estimation
•
•
•
•
•
•
A common approach in statistical estimation
Define hypotheses
Generate likelihood function
Estimate
Test hypotheses
Draw statistical conclusions
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)
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)
The parameter  is
incorporated here
G = genotype probabilities
y = phenotype probabilities
Several independent families
• The likelihood functions of multiple independent
families are combined:
• L =  Lj
or
logL =  log Lj
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.
LOD ( ' )  log 10
L(   ' )
 log 10 L(   ' )  log 10 L(  0.5)
L(  0.5)
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)
0.56
0.5
LOD
score
0.0
0.0
0.14
Recombination fraction
LOD>3 taken as evidence of linkage.
0.5
Basics of Linkage Analysis
1.
2.
3.
4.
Idea of Linkage Analysis
Types of Linkage Analysis
Parametric Linkage Analysis
Conclusions
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.
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
• χ2 –test
• LD mapping
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 χ2-test in order to find
out, whether there is statistically significant difference
Allelic assosiation
Results: observed frequencies
Expected frequencies
Test statistic
• The observed are compared to expected frequencies.
(null hypothesis, H0: carrier status and disease
occurrence are independent of each other )
• Test statistic
(oi  ei )
 
i1 ei
k
2
2
where
• oi is the observed frequency for class i, ei the
expected frequency for class i
• k is the number of classes
Allelic assosiation
• Now, χ2 = 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 χ2 value is then compared to the null distribution of
critical χ2-test statistic values (within the given df class)
χ2-distribution: critical values
for chosen significance levels
df\p
1
2
3
4
5
6
7
8
9
10
11
0.10
2.71
4.61
6.25
7.78
9.24
10.64
12.02
13.36
14.68
15.99
17.28
.05
3.84
5.99
7.81
9.49
11.07
12.59
14.07
15.51
16.92
18.31
19.68
.025
5.02
7.38
9.35
11.14
12.83
14.45
16.01
17.53
19.02
20.48
21.92
.01
6.63
9.21
11.34
13.28
15.09
16.81
18.48
20.09
21.67
23.21
24.73
.005
7.88
10.60
12.84
14.86
16.75
18.55
20.28
21.96
23.59
25.19
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.
Allelic association
•
•
•
The value we obtained, χ2 = 111,39 , exceeds all critical values with df=1
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
•
•
•
•
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. →
Time
A
Original mutation
in one chromosome
in the founder
population
Current
generation
B
An affected
pedigree
C
6
2
1
3
1
2
5
3
LD mapping
• The marker itself is NOT the reason for the disease,
but it’s 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
LD-mapping: Utilizing the founder effect
Data
Disease locus
Disease
status SNP1
S2 ...
...
a
a
?
?
2 1
1 2
1
1
1 2 2 11 2
2 1 2 11 2
1
2
1 2
2 1
2 1
1 2
c
c
2
1
1 ?
1 ?
?
?
1 2 2 11 2
1 2 2 21 1
1
1
2 1
1 1
1 1
1 1
a
a
1
1
1 2
1 1
1
2
1 1 2 11 2
2 2 2 11 2
2
1
2 2
1 1
?
?
…………
1
1
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
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