statistical genetics - university of colorado boulder
TRANSCRIPT
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Statistical Genetics
Matt McQueenAssistant Professor
Institute for Behavioral GeneticsUniversity of Colorado at Boulder
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Why am I here?
Statistical Genetics - Biodemography
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Perspectives…
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Perspectives…
Epidemiology
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Perspectives…
Biostatistics
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Perspectives…
Health Policy
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Perspectives…
Environmental Health
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Perspectives…
Society, Human Development and Health
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The View from Here…
GENES Outcome
Environment
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OverviewBackground and Introduction
Linkage and Linkage Disequilibrium
Population Genetics
Linkage Analysis
Association Analysis
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OverviewBackground and Introduction
Linkage and Linkage Disequilibrium
Population Genetics
Linkage Analysis
Association Analysis
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Statistical GeneticsOtherwise known as:
- Genetic Epidemiology- Genetic Statistics
By definition, “integrative”- Combines epidemiological, statistical, clinical,
genetic and molecular approaches
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Genetic Discovery
Evidence for genetic effects? Familial aggregation
Mode of inheritance? Segregation Analysis
Where in the region? Fine Mapping
What chromosome / region? Linkage Analysis
What gene? Association Analysis
What is the effect of the gene? Characterization
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Why Hunt for Genes?
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Why Hunt for Genes?Disease etiology
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Why Hunt for Genes?Disease etiology
Refined diagnosis and/or prognosis
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Why Hunt for Genes?Disease etiology
Refined diagnosis and/or prognosis
Drug development
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Why Hunt for Genes?Disease etiology
Refined diagnosis and/or prognosis
Drug development
Disease prediction
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Challenges
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ChallengesField is young and changes rapidly
- Technology drives the science- We test because we can
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ChallengesLiterature can be difficult
- Statisticians writing genetic papers- Geneticists writing statistical papers
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ChallengesSoftware typically not well-tested or supported
- The cost of being “free”- Use at your own risk!
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ChallengesMethods are often oversold
- Consequence of high-pressure field - Rapid development creates sense of urgency
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Some TerminologyLocus
- A location in the genome
Gene- A DNA segment characterized by sequence, transcription or
homology
Allele- Different forms of a gene: A, a; B, b
Polymorphism- Allele present in the population with > 5% freq
Mutation- Allele present in the population with < 5% freq
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Some TerminologyPhenotype
- Any measurable outcomeQuantitative Trait Locus (QTL)
- A region (gene) that contributes to a phenotypePenetrance (binary, disease phenotypes)
- Prob(Phenotype | Genotype)Heritability (quantitative traits)
- Variance explained by genetic factorsMendelian Disorder
- Diseases influenced by a single geneComplex Trait
- Disease influenced by multiple genes and environment
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Pedigree Notation
Male
Female
Founders
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Pedigree Notation
Male
Female
Affected
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Pedigree Notation
Male
Female
Affected
Deceased
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Mendel’s Laws
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Mendel’s LawsMendel’s First Law
- Independent Segregation
ggGgg
GgGGGDad
gG
Mom
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Mendel’s LawsMendel’s Second Law
- Independent Assortment
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Mendel’s LawsWhat do peas have to do with people?
- Underlying principles of statistical genetics!
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OverviewA Brief Introduction
Linkage and Linkage Disequilibrium
Population Genetics
Linkage Analysis
Association Analysis
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Linkage
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LinkageGeneral Idea:
- Describes the relationship between two loci- If two loci are close in proximity
- “linked”
- If two loci are far apart (different chromosomes):- “not linked”
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Recombinant Events
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RecombinationA1
B1
A2
B2
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RecombinationA1
B1
A2
B2
gametes A1
B1
A2
B2
A2
B1
A1
B2
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RecombinationA1
B1
A2
B2
gametes A1
B1
A2
B2
A2
B1
A1
B2
θ = Recombination Rate
1−θ2
1−θ2
θ2
θ2probability
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No LinkageA1
B1
A2
B2
gametes A1
B1
A2
B2
A2
B1
A1
B2
14
14
14
14probability
θ ~ 0.5
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Where have we seen this before?Mendel’s Second Law
- Independent Assortment
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LinkageA1
B1
A2
B2
gametes A1
B1
A2
B2
θ ~ 0
12
12
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Recombination EventsWhat predicts a recombination event?
What drives the recombination fraction?
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Genetic DistanceDefinition:
- The expected number of crossover events between two loci
Units:- Morgans- 1 Morgan = 1 crossover event expected
Genetic Map- A linearly arranged set of loci with genetic distances between
them- Human Autosomes ~ 3900 cM
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Linkage Disequilibrium
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Linkage DisequilibriumGeneral Idea:
- Describes the relationship between alleles at two loci
- If the alleles at each loci are close in proximity:- “in linkage disequilibrium”
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Linkage Disequilibrium
x4x3x2x1Frequency
A2B2A2B1A1B2A1B1Gametes
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Linkage Disequilibrium
x4x3x2x1Frequency
A2B2A2B1A1B2A1B1Gametes
pB2=x2+x4pB1=x1+x3pA2=x3+x4pA1=x1+x2Frequency
B2B1A2A1Allele
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Linkage Disequilibrium
x4x3x2x1Frequency
A2B2A2B1A1B2A1B1Gametes
pB2=x2+x4pB1=x1+x3pA2=x3+x4pA1=x1+x2Frequency
B2B1A2A1Allele
D = Observed - Expected
D = x1 − pA1pB1
D = x1 − (x1 + x2)(x1 + x3)D = x1x4 − x2x3
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Another Common LD Metric
r2 =D2
pA1pA 2 pB1pB 2
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Reasons for LDMutation
Population Subdivision
Genetic Drift
Lack of Recombination
Selection
Non-Random Mating
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How does linkage relate to linkage disequilibrium?
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Linkage and LD
Dt = (1−θ)t D0
After t generations of random mating…
LD is a function of recombination and time (generations)
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Linkage and LD
Key Concepts…- Linkage : Location- LD : Alleles- There can be Linkage without LD- There can be LD without Linkage
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OverviewBackground and Introduction
Linkage and Linkage Disequilibrium
Population Genetics
Linkage Analysis
Association Analysis
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DNA VariationDNA
- Adenine (A)- Guanine (G)- Cytosine (C)- Thymine (T)
DNA double helix- A pairs with T and G pairs with C
Codons- Triplets of bases- 64 possible codons
- 20 amino acids
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MutationsPoint
- Substitute one base for another
Deletions- Base removed entirely
Insertions- Base inserted
Duplications- Base and/or sequence duplicated
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MutationsPoint
- Substitute one base for another
Deletions- Base removed entirely
Insertions- Base inserted
Duplications- Base and/or sequence duplicated
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More on Point MutationsPoint Mutations
- Synonymous- No change in amino acid
- Nonsynonymous- Amino acid change
- Creates a new polymorphic site- “Single Nucleotide Polymorphism” (SNP)
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Mutation Becomes PolymorphismInfinite Sites Model
- Each mutation creates a unique polymorphic site- Mutation rate ~ 10-6
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Life After MutationMutation is neutral
- Random Genetic Drift- Eventually, the allele will “drift” out
Mutation is harmful- Selective Pressure
- Allele may quickly disappear
Mutation is beneficial- Selective Pressure
- Allele frequency may increase rapidly
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Human Genetic History
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Human Genetic History
National Geographic: The Genographic Project
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Human Genetic History
National Geographic: The Genographic Project
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Human Genetic History
National Geographic: The Genographic Project
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Human Genetic History
National Geographic: The Genographic Project
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Who Are We?
Tim
e
Sequences
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Who Are We?
Tim
e
Sequences
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Who Are We?
Tim
e
MRCA
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Who Are We?All DNA sequences are derived from others
- Every sample has a genealogy
Eventually, all lineages coalesce- Most Recent Common Ancestor (MRCA)
The “older” the genetic history…- The less observed LD (Africans vs European)
The more isolated genetic history…- The more observed LD (Mayan)
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Who Are We?What does this have to do with gene-mapping?
Balding (2006) Nat Rev Genet.
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OverviewBackground and Introduction
Linkage and Linkage Disequilibrium
Population Genetics
Linkage Analysis
Association Analysis
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Linkage AnalysisGene-Mapping
- Manipulate the Properties of Linkage- Using an observed locus (marker) to draw inferences about
an unobserved locus (disease gene)
Family-Based Design- Extended (grandparents, parents and kids)- Nuclear (parents and kids)
- Sibling Pair (no parents and kids)
Goal: Find genomic region “linked” to disease
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Linkage Analysis
0 2010 30 40 50 60 70
cM
M1 M2 M3 M4 M5 M6 M7 M8
Disease Gene (unobserved)
Genetic Markers
Genetic Distance
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Linkage Analysis
0 2010 30 40 50 60 70
cM
M1 M2 M3 M4 M5 M6 M7 M8
Disease Gene
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Linkage Analysis
0 2010 30 40 50 60 70
cM
M1 M2 M3 M4 M5 M6 M7 M8
Disease Gene
Linkage Region
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Linkage AnalysisParametric
- Affected / Unaffected- Observed recombination events
Non-Parametric- Affected / Unaffected- Identity-by-Descent (IBD)
“Semi-Parametric”- Quantitative- IBD
MCMC- Any phenotype- IBD
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Linkage AnalysisParametric
- Affected / Unaffected- Observed recombination events
Non-Parametric- Affected / Unaffected- Identity-by-Descent (IBD)
“Semi-Parametric”- Quantitative- IBD
MCMC- Any phenotype- IBD
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Linkage AnalysisKey Concepts
- Allele Sharing (IBS and IBD)- Linkage Statistics (LOD Score, etc.)
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Allele Sharing
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Identity by State (IBS)
ac bd
IBS = 0
How many alleles are in common?
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Identity by State (IBS)
ac ad
IBS = 1
How many alleles are in common?
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Identity by State (IBS)
ac ac
IBS = 2
How many alleles are in common?
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Identity by Descent (IBD)
ab cd
ac bd
IBD = 0
How many alleles are common by descent?
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Identity by Descent (IBD)
ab cd
ac ad
IBD = 1
How many alleles are common by descent?
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Identity by Descent (IBD)
ab cd
ac ac
IBD = 2
How many alleles are common by descent?
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IBS and IBD
ab cd
ac bd
IBS = 0IBD = 0
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IBS and IBD
ab cd
ac ad
IBS = 1IBD = 1
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IBS and IBD
ab cd
ac ac
IBS = 2IBD = 2
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Ambiguous IBD
ab cb
bc ab
IBS = 1IBD = 0
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IBD Probabilities
00.500.50Avuncular
00.500.50Half-Sibs
00.500.50Grandparent-Grandchild
00.250.75First Cousin
010Parent-Offspring
0.250.500.25Full Sibs
100MZ Twins
π2π1π0Relative PairProbability of Sharing IBD Alleles
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IBD and Sibling Pairs
00.500.50Avuncular
00.500.50Half-Sibs
00.500.50Grandparent-Grandchild
00.250.75First Cousin
010Parent-Offspring
0.250.500.25Full Sibs
100MZ Twins
π2π1π0Relative PairProbability of Sharing IBD Alleles
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IBD and Sibling PairsUse of Sibling Pairs in linkage analysis
- Affected Sibling Pair (ASP) Design- Binary Trait
- Unascertained Sibling Pair Design- Quantitative Traits
- Ascertained Sibling Pair Design- Quantitative Traits
We look for regions that show deviation of IBD from what is expected under the null
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Linkage Analysis of Sibling PairsBasic Idea
- Sibling pairs sharing more alleles IBD than expected at a trait-influencing locus should have more similar phenotypes
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Affected Sibling Pairs
ASP DSP USP
If there is a shared genetic component…
P(IBD=0, IBD=1, IBD=2) = 0.25, 0.50, 0.25
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Affected Sibling Pairs
100255025Expected
100354520Observed
Total210
Number of Alleles Shared IBD
H0: No LinkageH1: Linkage
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Sibling Pairs (Quantitative Traits)
If there is a shared genetic component…
P(IBD=0, IBD=1, IBD=2) = 0.25, 0.50, 0.25
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Quantitative TraitsHaseman-Elston Algorithm
- Calculate number of alleles shared IBD and the squared phenotype difference for each sibpair
- Regress squared differences against IBD sharing
E(∆2) =α + βπ
∆ = trait difference between sibsα = regression interceptβ = slopeπ = IBD sharing
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0
1
2
3
4
5
6
7
8
9
-0.1 0.4 0.9 1.4 1.9
IBD
Quantitative Traits
β=0
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Quantitative Traits
0
1
2
3
4
5
6
7
8
9
-0.1 0.4 0.9 1.4 1.9
IBD
β<0
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Linkage Analysis Statistics
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The LOD ScoreMorton (1955)Log10 of the ODds for linkageEssentially a Likelihood Ratio
- Likelihood of observed- Likelihood of expected (no linkage, theta=0.5)
Developed in the context of parametric linkage
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Common Nonparametric StatisticsMaximum LOD Score
- “MLS” (or MLOD)- ASP design only- GENEHUNTER, ASPEX
Nonparametric Linkage Score- “NPL Score”- Any family design- GENEHUNTER
Kong and Cox LOD Score- “K&C LOD Score”- Derived from the NPL- MERLIN, ALLEGRO
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Interpreting Linkage StatisticsTraditional View…
- LOD > 3.0 for genome-wide significance
More Contemporary View…- Simulate for empirically derived significance
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Examples from the LiteratureLinkage Analysis
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Alcoholism
Reich et al (1998) Am J Med Genet (Neuropsychiatric Genetics)
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Antisocial Drug Dependence
Stallings et al (2005) Archives of Gen Psychiatry
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Bipolar Disorder
McQueen et al (2005) Am J Hum Genet
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OverviewBackground and Introduction
Linkage and Linkage Disequilibrium
Population Genetics
Linkage Analysis
Association Analysis
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Association Analysis
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Association AnalysisGene-Mapping
- Manipulate the Properties of Linkage Disequilibrium- Using an observed locus (marker) to draw inferences about
an unobserved locus (disease gene)
Fine-Mapping- Refine a linkage region
Candidate-Gene- Evaluate the genetic variation as it relates to an outcome
Goal: Find genomic region and/or genes “associated”with disease
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Association AnalysisFamily-Based
- Parent/Offspring Trios- Sibling Pairs- Nuclear Families- Extended Pedigrees
Population-Based- Case-Control- Cohort
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Association AnalysisKey Concepts
- Genotype Coding- Population Stratification- Transmission Disequilibrium Test (TDT)- Whole Genome Association
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Coding GenotypesAssume a biallelic marker (SNP)There are three possible genotypes
- AA- Aa- aa
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Coding Genotypes
Genotype
100Recessive
(A)
110Dominant
(A)
1,0,00,1,00,0,1Genotype
(A)
210Additive
(A)
AAaAaa
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Genotype Coding
Marker Score = XAdditive : X = (0, 1 or 2)Dominant : X = (0 or 1)Recessive : X = (0 or 1)
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Additive Model
X0 1 2
Y
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Dominant Model
X0 1 2
Y
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Recessive Model
X0 1 2
Y
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Population Stratification
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Genetic AssociationsTruth
- Causal locus (direct)- In LD with causal locus (indirect)
Chance- If you test 100 times, you’ll see ~ 5 tests < 0.05- No causal underpinning
Bias- Association is not causal- e.g. Population stratification
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StratificationEssentially a confounder!
How does it happen?
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Common Cause
G P
A
Ancestry (A) predicts Genotype (G)
Ancestry (A) predicts Phenotype (P)
a.k.a.… Population Stratification
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Poor Epidemiologic DesignSource Population?
Two Necessary Components:- Different prevalence (mean) of disease- Different allele frequency
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Famous Example
Knowler et al (1988) Am J Hum Genet.
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DRD2
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Stratification HappensStrategies to deal with it
- Self-Reported Ancestry- Match (design) or Adjust (analysis)
- Use other genetic markers (ancestry informative)- Genomic Control (Devlin – U of Pittsburgh)- STRUCTURE (Pritchard – U of Chicago)- Eigenstrat (Reich – Broad Institute/Harvard)
- Use a family-based design
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The TDT
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Transmission Disequilibrium Test (TDT)
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Transmission Disequilibrium Test (TDT)
AB AB
ABBBAABA
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Transmission Disequilibrium Test (TDT)
AB AB
ABBBAABA
Under the null:Equally probable!
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Transmission Disequilibrium Test (TDT)
AB AB
AB
Father - “A” was transmitted and “B” wasn’tMother - “B” was transmitted and “A” wasn’t
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Transmission Disequilibrium Test (TDT)
AB AB
AB
Offspring
BBxBB
ABxBB
010ABxAB
AAxBB
AAxAB
AAxAA
BBABAAParent
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Transmission Disequilibrium Test (TDT)
AB AB
AB
Offspring
BBxBB
ABxBB
010ABxAB
AAxBB
AAxAB
AAxAA
BBABAAParent
nBA
nAA
A
nBBB
nABA
B
Not Transmitted
�Tra
nsm
itted
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Transmission Disequilibrium Test (TDT)
AB AB
AB
Offspring
BBxBB
ABxBB
010ABxAB
AAxBB
AAxAB
AAxAA
BBABAAParent
1
0
A
0B
1A
B
Not Transmitted
�Tra
nsm
itted
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TDT
nBA
nAA
A
nBBBnABAB
Not Transmitted
�Tra
nsm
itted
TDT =(nBA − nAB )2
nBA + nAB
~ χ12
McNemar Test for Matched-Pair Data
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Generalized ExtensionsMultiple OffspringMissing ParentsNon-Binary Phenotypes
- Quantitative, time-to-onset, ordinal…
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Generalized ExtensionsFBAT/PBAT (Laird/Lange - Harvard)
QTDT (Abecasis/Cardon - Michigan)
PDT (Monks/Kaplan - Duke)
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Population StratificationWhy are Family-Based Designs etc. robust to
population stratification?
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Family-Based Data
G P
A
GP1 GP2
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Family-Based Data
G P
A
GP1 GP2
Condition on parental genotypes
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Family-Based Data
G P
A
GP1 GP2
Condition on parental genotypes
P(G|GP1,GP2,A) = P(G| GP1,GP2)
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Paradigm ShiftFrom Linkage to Association
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Gene-MappingMonogenic ‘Mendelian’ Diseases
- Rare disease- Rare variants
- Highly penetrant
Complex Disease- Rare/Common disease- Rare/Common variants
- Variable penetrance
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Gene-MappingMonogenic ‘Mendelian’ Diseases
- Rare disease- Rare variants
- Highly penetrant
Complex Disease- Rare/Common disease- Rare/Common variants
- Variable penetrance
Linkage!
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Gene-MappingMonogenic ‘Mendelian’ Diseases
- Rare disease- Rare variants
- Highly penetrant
Complex Disease- Rare/Common disease- Rare/Common variants
- Variable penetrance Association
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Genetic Discovery
Evidence for genetic effects? Familial aggregation
Mode of inheritance? Segregation Analysis
Where in the region? Fine Mapping
What chromosome / region? Linkage Analysis
What gene? Association Analysis
What is the effect of the gene? Characterization
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Genetic Discovery
Evidence for genetic effects? Familial aggregation
Mode of inheritance? Segregation Analysis
Where in the region? Fine Mapping
What chromosome / region? Linkage Analysis
What gene? Association Analysis
What is the effect of the gene? Characterization
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Gene-MappingWhere in the genome (1980s - 2005)?
- Linkage
Where in the genome (2006 - )?- Association
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Foreshadowing the Paradigm Shiftc. 1996
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Linkage and Complex Disease
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Linkage of Complex TraitsDismal and controversial picture
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The Power of Linkage vs Association
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Relative Power*
70022,3850.200.20
6598,0670.010.20
2,448207,6350.200.05
2,27867,2190.010.05
ASSOCIATION(NA)
LINKAGE(NL)PrevalenceMAF
MAF = Minor allele frequencyNL = Number of affected sibling pairsNA = Number of case-control pairsOdds Ratio = 1.5
*Adapted from Roeder et al, Am J Hum Genet (2006)
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Rare Disease - Rare Variant
70022,3850.200.20
6598,0670.010.20
2,448207,6350.200.05
2,27867,2190.010.05
ASSOCIATION(NA)
LINKAGE(NL)PrevalenceMAF
MAF = Minor allele frequencyNL = Number of affected sibling pairsNA = Number of case-control pairsOdds Ratio = 1.5
*Adapted from Roeder et al, Am J Hum Genet (2006)
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Common Disease - Rare Variant
70022,3850.200.20
6598,0670.010.20
2,448207,6350.200.05
2,27867,2190.010.05
ASSOCIATION(NA)
LINKAGE(NL)PrevalenceMAF
MAF = Minor allele frequencyNL = Number of affected sibling pairsNA = Number of case-control pairsOdds Ratio = 1.5
*Adapted from Roeder et al, Am J Hum Genet (2006)
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Common Variant - Rare Disease
70022,3850.200.20
6598,0670.010.20
2,448207,6350.200.05
2,27867,2190.010.05
ASSOCIATION(NA)
LINKAGE(NL)PrevalenceMAF
MAF = Minor allele frequencyNL = Number of affected sibling pairsNA = Number of case-control pairsOdds Ratio = 1.5
*Adapted from Roeder et al, Am J Hum Genet (2006)
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Common Disease - Common Variant
70022,3850.200.20
6598,0670.010.20
2,448207,6350.200.05
2,27867,2190.010.05
ASSOCIATION(NA)
LINKAGE(NL)PrevalenceMAF
MAF = Minor allele frequencyNL = Number of affected sibling pairsNA = Number of case-control pairsOdds Ratio = 1.5
*Adapted from Roeder et al, Am J Hum Genet (2006)
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Why Now?
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The “-omics” Agec. 1996
-Pre-genomic era-100’s of Markers
- STRs
c. 2007-Post-genomic era-100,000’s of markers
- SNPs
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c. 2007
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Available TechnologyPlatforms available (or coming soon)
- 1 SNP- Hundreds of SNPs- Thousands of SNPs- Hundreds of thousands of SNPs- Millions of SNPs
Flexibility for Association- Single Marker- Candidate Gene- Whole-Genome
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Examples from the LiteratureWhole Genome Association
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What if we discover that genes have nothing to do with complex phenotypes?
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What if we discover that genes have nothing to do with complex phenotypes?
Good News: We may not have to cross that bridge
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Replicated AssociationsType II DiabetesBMI / ObesityCrohn’s DiseaseAge-Related Macular Degeneration (AMD)Prostate CancerBreast CancerHeart Disease
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Framingham Heart Study and BMI
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Framingham Heart Study and BMI
The SNP is close (in LD) with INSIG2- A plausible candidate for obesity- Responds to insulin- Involved in trigylceride synthesis
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Framingham Heart Study and BMI
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Framingham Heart Study and BMIReplicated in 4 out 5 studies
- Childhood sample- African American Sample- Europe and North America
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Hot off the press…
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Hot off the press…
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In Summary…WGA is starting off successful
- More replicated associations in one year…
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Statistical GeneticsThe Challenges We Face
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Analytic Challenges
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Wealth of InformationWhole Genome Association using SNPs
- Potentially use all of the data- Covariates, interactions, effect size, etc.- Statistical issues abound…
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Multiple Comparisons
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Multiple Comparisons
The 500K People Chip
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Multiple ComparisonsWhich SNPs are “real”?
- 500K Chip- 25,000 SNPs with p < 0.05
Multiple Phenotypes- 10 Phenotypes, 500K chip
- 5,000,000 comparisons!!!!
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The P-Value Epidemic
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“My name is Matt McQueen and I have a P-value problem”
The smallest p-values- Most addictive- We’ve been trained to focus on them- What do they mean?
- Truth- Chance- Bias
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Replicated Associations…
Scott et al (2007) Science
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The Phenotype Question
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What is a phenotype?Depends on who you ask…
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What is a phenotype?If we asked a gene…
GENE
Trait 1
Trait 2
Trait 3
Trait 4
Trait 5
Trait 6
5%
55%
4%
20%
1%
15%
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What is a phenotype?If we asked an environmental factor…
Trait 1
Trait 2
Trait 3
Trait 4
Trait 5
Trait 6
10%
10%
30%
5%
5%
40%
ENV
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What is a phenotype?
GENE
Trait 1
Trait 2
Trait 3
Trait 4
Trait 5
Trait 6
5%
55%
4%
20%
1%
15%
10%
10%
30%
5%
5%
40%
ENV
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The Genotype Question
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What is a Genotype?
We test SNPs for association because we can
What about epigenetic factors?- Methylation- Copy Number Variation
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The Not-So Distant Future
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The $1000 GenomeNHGRIRFA Number
- RFA-HG-06-020Title
- “The $1000 Genome”Goal
- Develop technology to enable investigators to sequence an entire human genome for $1000 within 10 years
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June 2017Biodemography Short Course
Complete Genome Sequence Analysis