Human%20Genetics

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Human Genetics

• Genetic Epidemiology

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• Family trees can have a lot of nuts

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Genetic Epidemiology - Aims

1. Gene detection
2. Gene characterization

mode of inheritance allele frequencies ?
prevalence, attributable risk
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Genetic Epidemiology - Methods

• Aggregation
• Segregation
• Co-segregation
• Association

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Segregation
determined by a dominant or recessive allele

• Can the dichotomy or trichotomy be explained by
  Mendelian segregation?

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Likelihood (parameter(s) data) ?
Probability (data parameter(s))
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Transmission Probabilities
Value if there is Mendelian segregation 1 ½ 0
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Ascertainment

• We examine segregating sibships
• The proportion of sibs affected is larger than
  expected on the basis of Mendelian inheritance
• The likelihood must be conditional on the mode
  of ascertainment
• We need to know the proband sampling frame

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Cosegregation

• Chromosome segments are transmitted
• Cosegregation is caused by linked loci

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Methods of Linkage Analysis

• Trait model-based assume a genetic model
  underlying the trait
• Trait model-free - no assumptions about the
  genetic model underlying the trait

• Ascertainment is often not an issue for locus
  detection by linkage analysis

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Model-based Linkage Analysis

• If founder marker genotypes are known or can
  be inferred exactly,
• ? no increase in Type 1 error
• ? smallest Type 2 error when the model
  is correct

• If founder marker genotypes are unknown, we can
• 1) estimate them
• 2) use a database

• All parameters other than the recombination
  fraction are assumed known

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Model-free Linkage AnalysisIdentity-in-state
versus Identity-by-descent

• Two alleles are identical by descent if they are
  copies of the same parental allele

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Sib pairs share

• 0, 1 or 2 alleles identical by descent at a
  marker locus
• 0, 1 or 2 alleles identical by descent at a
  trait locus

Linkage
The average proportion shared at any particular
locus is 1/2
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Relative Pair Model-Free Linkage Analysis

• We correlate relative-pair similarity
  (dissimilarity) for the trait of interest with
  relative-pair similarity (dissimilarity) for a
  marker

• Linkage between a trait locus and a marker
  locus
• ? positive correlation

• Affected relative pair analysis Do affected
  relative pairs share more
  marker alleles than expected if there is no
  linkage?
• No controls!

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Association

• Causes of association between a marker and a
  disease

• chance
• stratification, population heterogeneity
• very close linkage
• pleiotropy

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Causes of Allelic Association
Heterogeneity/stratification
The best solution to avoid this confounding is to
study only ethnically homogeneous populations
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(Tight) Linkage
This chromosome is passed down through the
generations, and now there are many copies. If
the distance between D and A1 is small,
recombinations are unlikely, so most D
chromosomes carry A1 This is the type of allelic
association we are interested in
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Guarding Against Stratification

• Three solutions

• use a homogenous population
• use family-based controls
• use genomic control

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Matching on Ethnicity

• Close relatives are the best controls, but can
  lead to overmatching
• Cases and control family members must have the
  same family history of disease

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Transmission Disequilibrium Test (TDT)

• A design that uses pseudosibs as controls
• Cases and their parents are typed for markers

Transmitted genotype is A1A2 Untransmitted
genotype is A2A2
Father transmits A1, does not transmit A2 Mother
transmits A2, does not transmit
A2 (uninformative in terms of alleles)
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• Build up a 2 x 2 table

• The counts a and d come from homozygous
  parents
• The counts b and c come from heterozygous
  parents

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Genomic Control

• Calculate an association statistic for
  a candidate locus
• Calculate the same association statistic, from
  the same sample, for a set of unlinked loci
• Determine significance by reference to the
  results for the unlinked loci

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Linkage Between a Marker and a Disease

• Intrafamilial association
• Typically no population association
• Not affected by population stratification
• Population association if very close

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Association versus Linkage

• Association at the population level

Intrafamilial association

• Pinpoints alleles

Pinpoints loci

• More powerful

Less powerful

• More tests required

Fewer tests required

• More sensitive to mistyping

Less sensitive to mistyping

• Sensitive to population stratification

Not sensitive to population stratification

• Which is better?

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What is the Best Design and Analysis?

• If heterogeneity / stratification is a
  non-issue,
• unrelated cases and controls for association
  analysis
• (genome scan?)

large extended pedigrees, type all (founders and
non- founders) for 200-400 equi-spaced markers,
for linkage analysis
Note cost, burden of multiple testing
A wise investigator, like a wise investor, would
hedge bets with a judicious mix
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Case-Control Data
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• Consider the probability structure

• Cochran-Armitage trend test the null
  hypothesis
• p2 ½p1 q2 ½q1
• without assuming the two alleles a person has
  are independent

Sasieni (1997) Biometrics 531253-1261
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asymptotically has a ?2 distribution with 1 d.f
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Cochran-Armitage Trend Test

• Does not assume independence of alleles within a
  person
• Does assume independence of genotypes from
  person to person

• Is not valid if there is population
  stratification

• The increased variance due to stratification
  can be estimated from a random set of markers
  that are independent of the disease

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Case-only Studies

• Suggested as
• more powerful (only cases needed)
• more precise (signal decreases faster with
  distance from the causative locus)

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Case - only Studies

• No power in the case of a multiplicative model

• No controls

• there must be a difference in HWD between
  cases and controls

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Weighted average of the Cochran-Armitage trend
test and the HWD trend test statistics
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• To investigate the null distribution of this
  average we simulate many different situations
  sample sizes up to 10,000 cases and 10,000
  controls - and generate

• For all situations considered, the distribution
  is well approximated by a Gamma distribution

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• As the sample size and marker allele frequency
  increase, the largest mean and the smallest
  variance occur for 10,000 cases and 10,000
  controls, and for a marker allele frequency 0.5

• For 10,000 cases and 10,000 controls, and
  marker allele frequency 0.5, the upper tail of
  the distribution is well approximated by a Gamma
  distribution with mean µ 1.78 and variance s2
  3.45

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• We develop a prediction equation to determine
  percentiles of the null distribution for smaller
  sample sizes and marker allele frequencies
• We base goodness of fit on the root mean squared
  error (RMSE) of logea, calculated for various
  sample size combinations, from the variance among
  50 replicate samples

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• With 90 confidence, the true loge a lies in
  the interval logea 1.645(RSME), i.e., a is
  within e1.645(RSME) - fold of the true a

• For total sample size (R S) 200 or larger
  and a 0.0001 or larger, in the very worst case
  (R S 100, a 0.0001) with 90 confidence a
  could differ from the true a by a factor of at
  most 4.8
• The average RMSE is 0.35, corresponding to
  being between 78 and 122 of the true a with
  90 confidence

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POWER Genetic Models Simulated
Probability of being affected given Probability of being affected given Probability of being affected given
A1A1 A1A AA
1 Recessive 1 1.00 0.10 0.10
2 Recessive 2 1.00 0.05 0.05
3 Additive 1.00 0.50 0.00
4Multiplicative 0.81 0.045 0.0025

• Each simulated population contains 500,000
  individuals allowed to randomly mate for 50
  generations after the appearance of a disease
  mutation

• Marker loci placed at distances 0 6 cM from
  the disease susceptibility locus
• For type I error, no association between the
  disease and marker loci

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Tests Performed

• Homogeneous populations
• HWD, cases only
• Allele test
• Allele test x HWD in cases
• HWD trend test
• Cochran-Armitage trend test
• Cochran-Armitage trend test x HWD trend test
• Weighted average

• Population stratification
• Cochran-Armitage trend test with genomic control
• Product of this and the HWD trend test
• Weighted average with genomic control

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Type I error, homogeneous population
? HWD test, cases only ? product of the
allele test and HWD test
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Type I error, population stratification
? allele test ? Cochran-Armitage trend
test ? product of the allele test and HWD
test weighted average test ? product
of the Cochrn-Armitage trend test and the HWD
test
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Power, homogeneous population
weighted average test
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Power, population stratification
? HWD trend test ? CA test with genomic
control weighted average with genomic
control
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Conclusions

• Under recessive inheritance, the weighted
  average has better performance than either the
  Cochran-Armitage trend test or the HWD trend test
• Has good performance for other models as well
• The product of the Cochran-Armitage trend test
  statistic and the HWD test statistic (cases only)
  has better power, but has inflated Type I error
  if there is population stratification
• The weighted average has good overall
  properties, automatically controls for marker
  mistyping

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• With acknowledgment to
• Kijoung Song

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• Can we use evolutionary models, when we have
  large amounts of genetic data on a sample of
  cases and controls, to obtain a more powerful way
  of detecting loci involved in the etiology of
  disease?
• Will these models bear fruit or nuts?