Advances in Populationbased Studies of Complex Genetic Disorders

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Advances in Population-based Studies of Complex
Genetic Disorders

• n i h e s Programme
• March 31 April 4, 2003
• Erasmus MC
• Rotterdam

Faculty Yurri Aulchenko, David Clayton, Cornelia
van Duijn, Susan Service
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Programme Overview

• Day 1 Basic Principles of Association
• Day 2 Population-based Studies
• Day 3 Family-based Studies
• Day 4 Linkage Disequilibrium and
  Haplotyping
• Day 5 Isolated Populations

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Day 1 Basic Principles of Association

• Hardy-Weinberg Equilibrium
• Measures of Association
• Study Designs Case Control

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Hardy-Weinberg Equilibrium

• In a population, allele and genotype frequencies
  will remain constant over generations

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HWE

• Can compare allele frequencies between cases and
  controls under HWE only
• If not in HWE, then parental allele transmissions
  have not been independent / uncorrelated
• Therefore, classical statistics cant be applied

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Measures of Association

• In epidemiology, associations between disease and
  aetiological factors are usually expressed in
  terms of relative risk measures
• In the simplest case
• measure of disease risk in exposed subjects /
  same measure of risk in unexposed subjects
• Relative risks may be defined for genotypes,
  alleles or haplotypes

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Genotype Relative Risks

• For a biallelic locus with alleles A, a, there
  are three genotypes AA, Aa, aa
• We usually take one of these, e.g. aa, as
  reference GRRAA Risk for AA / Risk for aa
• GRRAa Risk for Aa/ Risk for aa
• No standard in which should be taken as
  reference, but usually the commonest
• CI easier to interpret when the reference is
  common

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Allelic Relative Risks

• Allelic relative risks, fA and fa are defined by
  the multiplicative model
• One allele, e.g. a, is taken as reference so that
  fa1
• GRRAA(fA)2 and GRRAafA
• Assume HWE each subjects 2 chromosomes are
  sampled independently from the population

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Study Designs Case Control

• Healthy controls vs. Population controls
• Healthy controls matched for age, gender etc
• more power
• Population controls randomly drawn
• cost-effective
• Usefulness of controls drops after 4 controls to
  1 case (max)

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Testing H0 against alternative models

• Multiplicative model allele-wise comparison
• Dominant model carriers vs. non-carriers
• Recessive model homozygotes vs. rest
• Must have reason to think the effect is dominant
  / recessive
• If we dont know the best compromise is the
  multiplicative model
• If all 3 tests are carried out, must correct for
  multiple, non-independent testing randomise cc
  status and repeat permutations on 3 tests

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Day 2 Population-based Studies

• Multiple Comparison Problems
• Confounding and Stratification
• Study Design Matching

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Possible Outcomes of a Statistical Test
aprobability of false ve, bprobability of
false ve 1-bpower of the test
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Correcting for Multiple Testing

• Traditional solution the Bonferroni Method
• for k tests, reject H0 at a/k level for each
  test
• Controls the probability to falsely reject at
  least 1 H0
• Overly conservative for large k and / or
  dependent tests diminished power
• Appropriate when expecting 0 or 1 H0 to be false

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New Paradigm the False Discovery Rate

• Controls the rate of false positives
• More appropriate when expecting several H0 to be
  false / when tests are correlated
• More liberal than traditional methods
• Greatly increases power
• Order p values from n tests smallest to largest
• FDR threshold is stringent for 1st test, but gets
  less stringent as number of tests is reduced

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Confounding and Stratification

• Spurious associations can be due to confounding
  by population stratification
• Can avoid difficulties by analysing within strata
• Stratified analysis
• - loss of power due to little data in each
  stratum
• - useful when different strata are associated
  with different alleles / inverse effect
  of same allele

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Different approach

• Assume that the same effect exists across strata
• Sum contributions from each stratum
• Can use logistic regression

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Study Design Matching

• Matching maintain the same ratio of controls to
  cases in every stratum
• Also better sampling of controls
• Individually matched studies each case has
  his/her own set of controls, defining a stratum
  conditional logistic regression must be used
• Overmatching matching for a variable which,
  while not a confounder, is related to the factor
  of interest reduction of effective sample size

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Unobserved Stratification

• Random differences in allele frequencies between
  strata
• Two ways of tackling this have been proposed
• Estimate unobserved stratification empirically
  Devlin and Roeders genome-wide control
• Unobserved stratification generates deviation
  from HWE and apparent LD between distant markers.
  Thus latent stratification can be modelled

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Day 3 Family-based Studies

• The Transmission Disequilibrium Test
• Parental Origin
• Quantitative Traits

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Transmission Disequilibrium Test

• The use of family-based controls overcomes the
  effects of unmeasured population stratification
• Case-parent trios conditioning on parental
  genotypes the TDT

i/j 1/3 each with probability 0.25
1/4 2/3 2/4
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Reconstructing Missing Parental Genotypes
1/2
?/?
1/2
?/?
1/3
1/2
1/2
?/?
1/1
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Two Unlinked Loci

• For 2 unlinked loci, there are 16 transmission
  patterns, which are equiprobable in the
  population
• Can compare each case with 15 pseudocontrols
• Can look for GxG interactions using conditional
  logistic regression
• Less efficient than the case-only method, but
  resistant to population stratification

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Parental Origin

• An important aspect of the TDT is the ability to
  differentiate allelic effects based on parental
  origin
• The following intercross triads excluded from
  analysis
• Several methods TAT, PAT, CPG, CEPG

1/2
1/2
1/2
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Quantitative Traits

• The weighted TDT (implemented in FBAT) a
  conditional logistic model
• Genotype effects appear as interactions with
  (y-m), where ytrait value of offspring and
  mpopulation mean for trait
• QTDT robust to stratification / admixture
• Regression of trait value y on genotype score g
• Parent-of-origin effect also implemented in
  software

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Day 4 LD and Haplotyping

• Measures of LD
• LD Problems the Bias
• Estimating Haplotype Frequencies
• Haplotype Blocks

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Measures of LD

• p11frequency of 11 haplotype, etc
• Most LD measures are based on the covariance
  D p11 p22 - p21 p12

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Lewontins D

• D D / Dmax, where
• Dmax min(p1.p.1, p2.p.2) if Dlt0
• Dmax min(p1.p.2 , p2.p.1) if D0

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LD Correlation Coefficient r2

• D / vp1.p2.p.1p.2 is a measure of correlation
• r2 D2 / p1.p2.p.1p.2
• the square of the correlation between marker
  alleles
• c2 for the 2x2 table is c2 ND2 / p1.p2.p.1p.2
• with 1 df, where N sample size
• p value for the significance of LD between the
  markers
• r2 is well-related with p value from c2

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LD Problems the Bias

• D is biased upwards with smaller sample size
• Correct the problem by
• - using different measures of LD, e.g. r2
• - use bootstrap Dboo
• - use permutation Dadj

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Estimating Haplotype Frequencies

• In the absence of family data
• Expectation-Maximization algorithm
• Markov chain Monte Carlo algorithm

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EM algorithm

• Maximum likelihood technique
• Goal find haplotype frequency that maximises
  probability of observed genotypes
• Assumption HWE at all loci
• Limitation EM estimate may not be global optimum
• - use different starting conditions to avoid
  convergence to local maximum

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Markov chain Monte Carlo algorithm

• Another approximation method
• Uses sampling to estimate expectations
• Operates on one persons haplotype resolution at
  a time
• MCMC can handle larger problems than EM
• MCMC provides estimates of uncertainty on
  phase-unknown calls
• Monitoring convergence on MCMC can be hard

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Haplotype Blocks

• n SNPs 2n possible haplotypes
• Regions of extended haplotype conservation
• Definition by minimising haplotype diversity
• by identifying regions with low recombination
  rate (D)
• using common SNPs?
• excluding low frequency haplotypes?

Different methods/ thresholds result in different
block structure
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HB use in Association Mapping Possible Strategy

• Genotype a subset of samples for all SNPs
• Define HBs and htSNPs
• Genotype entire sample for htSNPs
• Investigate association
• Will reduce cost
• Will facilitate haplotype approaches
• May not be common to different populations
• Is information lost? Simulation studies

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Day 5 Isolated Populations

• Advantages of Population Isolates
• Disadvantages of Population Isolates
• Ancestral Haplotype Reconstruction

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Advantages of Population Isolates

• Higher prevalence of some diseases
• More inbreeding
• More uniform genetic, environmental and cultural
  background
• Good genealogical records
• Easier to standardise phenotype definitions
• Wider intervals of LD
• Closer to HWE

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Disadvantages of Population Isolates

• Possibly fewer affected individuals
• Difficult to replicate studies
• Markers not polymorphic
• Genes mapped less important to rest of humanity

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Ancestral Haplotype Reconstruction

• A LD mapping method for samples from population
  isolates
• Quantifies chromosome sharing among individuals
  affected with a common phenotype
• Equipped to deal with aetiologic heterogeneity