Introduction to Quantitative Trait Loci

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Introduction to Quantitative Trait Loci Linkage
and Association Studies
Lon Cardon Wellcome Trust Centre for Human
Genetics University of Oxford Pak Sham Institute
of Psychiatry Kings College London Stacey
Cherny Both, and then some
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QTL Mapping Morning Schedule
09.00 10.00 Linkage Theory (overview) Sham 10.00
10.30 Illustrative application Cardon 11.00
11.30 Association/Linkage Disequilibrium Theory
Sham 11.30 12.15 Application Cherny 12.15
12.30 Interpreting the results Cardon

• F\lon\fulker_paper99.pdf
• Fourteenth International Twin Course (Advanced)
  
• Boulder, Colorado, March 2000

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Positional Cloning of Complex Traits
Genetics
Chromosome Region
Association Study
Sib pairs
Genomics
Candidate Gene Selection/ Polymorphism Detection
Mutation Characterization/ Functional Annotation
Physical Mapping/ Sequencing
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Genome Screens for Linkage in Sib-pairs
In 1997/98, gt 20 genome screens published using
sib-pairs
- Diabetes (IDDM NIDDM) - Asthma -
Osteoporosis - Obesity - Multiple Sclerosis -
Epilepsy - Inflammatory Bowel Disease - Celiac
Disease - Psychiatric Disorders - Behavioral
Traits - others...
Many more studies of specific loci, candidate
gene regions
Scan Rate at least 2-fold greater in 1998/1999
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Disequilibrium Mapping

• 100s candidate gene studies every year
• Replications rare
• Genome-wide SNP maps expected in late 2001
  (300,000 SNPs 1 SNP/10 kb)
• Applications in epidemiology, drug design,
  functional assessment,

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Likelihood for Variance Components Applications
where yi is the vector of phenotypes for the ith
family, Ei is a function of polygenic effects,
environmental effects, major loci, interactions,
etc., and m may be used to incorporate a wide
range of covariates, including
association/disequilibrium parameters. Lange,
Westlake Spence, AJHG, 1976
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Linear Model of Association (Fulker et al, AJHG,
1999)
Biometrical basis
Variance model (linkage)
pijk proportion of alleles shared ibd at
marker s2a additive genetic variance
parameter s2g polygenic (residual) variance
parameter s2e environmental (residual) variance
parameter
Means model (association)
Population association is parameterized
independent of linkage (unlike TDT)
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Application ACE

• British population
• Circulating ACE levels
• Normalized separately for males / females
• 10 di-allelic polymorphisms
• 26 kb
• Common
• In strong Linkage disequilibrium
• Keavney et al, HMG, 1998

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Angiotensin-1 Converting Enzyme
Keavney et al. (1999) Hum Mol Gen, 71745-1751
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Angiotensin-1 Converting Enzyme Keavney et al.
(1999) Families
83 extended families 4 - 18 members/family age
19-90 years Families ascertained for study of
blood pressure Phenotype Plasma ACE activity,
standardized within gender No correlation
between ACE and SBP or DBP
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ACE Markers and Disequilibrium
Data from Keavney et al. (1999) Hum Mol Gen,
71745-1751
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Angiotensin Converting Enzyme Marker/IBD Files

• F\lon\2000\linkage.mx
• F\lon\2000\marker.mx

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Between Pairs Model of Association (Fulker et al,
AJHG, 1999)
Biometrical Model
Between Pair Expectations
G1 G2 A1 A2 Mean BB BB a a a BB Bb a 0
a/2 BB bb a -a 0 Bb BB 0 a a/2 Bb Bb
0 0 0 Bb bb 0 -a -a/2 bb BB -a a
0 bb Bb -a 0 -a/2 bb bb -a -a -a

• Genotype-phenotype associations between pairs
  may result from allelic
• association or from population substructure

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Within Model of Association (Fulker et al, AJHG,
1999)
Biometrical Model
Within Expectations
G1 G2 A1 A2 Diff1 Diff2 BB BB a a 0 0 BB Bb
a 0 a/2 -a/2 BB bb a -a a -a Bb BB 0
a -a/2 a/2 Bb Bb 0 0 0 0 Bb bb 0 -a
a/2 -a/2 bb BB -a a -a a bb Bb -a 0 -a/2
a/2 bb bb -a -a 0 0

• Genotype-phenotype associations within pairs
  unaffected by sampling artifacts
• Difference 0 unless ? 1 parent heterozygous
  (cf. TDT)

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Parameter Expectations
Let a additive genetic value D disequilibrium
coef between q1, m1 alleles P(m1q1)-P(m1)P(q1) r
frequency m1 allele (s 1 r) p frequency
q1 allele (q 1 p) R correlation between
numbered alleles at marker and QTL k population
strata counter
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Variance Components Association Model - Obvious
Uses -
Test of linkage only (typical VC) s2a 0 Test
of substructure bb bw Powerful test in
absence of stratification ba bbw 0 Test of
linkage in presence of association s2a 0 (ba
free)
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Variance Components Test for Linkage
Disequilibrium - Power of Testing Linkage vs LD -
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Evidence for Linkage Full Sample
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Evidence Against Complete LD Full Sample
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Evidence for Association Full Sample
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Drawing Conclusions Full Sample
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ACE Example Summary

• Agrees with haplotype analysis
• Distinguishes complete and incomplete
  disequilibrium
• Measure of distance for incomplete LD
• Indicator of trait allele frequencies
• Typical or fairy-tale?

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Useful diagnostics

• Fit association and linkage models separately
• Provide indicator of distance
• Minimum D (Dmin)
• Select next markers
• Range for QTL alleles
• (pmin, pmax)

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Haplotype Analysis

• 3 clades
• All common haplotypes
• gt90 of all haplotypes
• B C
• Equal phenotypic effect
• Functional variant on right
• Keavney et al (1998)

A
B
C
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The Spielman TDT

• Traditional case-control
• Compare allele frequencies in two samples
• Cases and controls must be one population
• Heterozygous parents
• Parental alleles are the study population
• Population allele frequencies fixed
• 5050, independent of original
• Test for excess among affected offspring

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Transmission/Disequilibrium Test
TDT based on (T - NT)2/(TNT)

• TDT uses only heterozygous parents
• Consequence at different markers with variable
  allele frequencies,
• analyses are based on different subsets of
  overall sample gt
• difficulties for localization
• TDT evaluates linkage in presence of
  association ie., joint test
• Consequence given positive evidence, cannot
  distinguish between
• strong linkage or strong association
• Several sibling-based extensions developed

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Family-based Association Methods for
Quantitative Traits
Primary aim association test free of pop.
sub-structure effects
Allison, D.B., AJHG, 1997 Selected
parent-offspring trios Rabinowitz, D. Hum Hered,
1997 Nuclear families Fulker, D. W. et al.
AJHG, 1999 Sib-pairs without parents Elston,
R. C. et al. AJHG, 1999 General pedigrees
(linkage) Allison, D. B. et al. AJHG, 1999
Sibships with/without parents (linkage) Abecasis,
G. et al. AJHG 2000 General pedigrees
with/without parents Cardon, L.R. Hum Hered 2000
Sib-pairs with GxE, epistatic
interactions Monks, S. et al. abstract 1999
Nuclear families
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Quantitative Genetic Model
d
bb
BB
Bb
midpoint
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Simple Association Model

• Fit by linear regression
• Phenotype (yij)
• Mean (?)
• Number of B alleles at marker (gij)
• Evidence for association when a ? 0

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Linear Model of Association in Sib-pairs
bi and wij are defined on the basis of the marker
genotype i.e., bb and bw are f(genotype(QTL),
genotype(marker),Dmq)
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ACE Dmin, pmin and pmax
Expected Actual Actual Actual
T-5991C G2215A I/D G2350A
D gt 0.78 0.78 0.82 0.85
Minor allele .15 .48 .45 - .50 .45 - .50 .45 - .50