1. Statistical methods for genetic association studies

2. A tutorial on statistical methods for population association studies
David Balding
Nature Reviews Genetics (2006) 7:
This talk is based on a review by David Balding from Imperial College London. It covers only one kind of association study, a population based

3. ? Genetics G×E interaction Environment Health outcome or
We want to know why two people with the same environmental exposure differ in their susceptibility to disease. Partic common complex diseases, heart disease, diabetes, etc. California Cholesterol levels 50-90%, Scandinavia Mortality due to heart disease 50-60%. So we look at the DNA. We might be able to genotype subjects for one strong candidate mutation, but usually we will have little or no idea what’s going on. This is the approach I’m going to talk about today.

4. Recombination X/x: unobserved causative mutation A/a: distant marker
B/b: linked marker A X a x
Gametophytes
(gamete-producing cells)
Gametes
Recombination B b
To understand assoc crucial to understand the process of recombination. If you look in any almost cell of your body you’ll find two sets of chromosomes, 23 from each parent. When we produce our own germ cells, sperm or eggs, each cell has just one copy. Process involves recomb. Crucial because it breaks down statistical association between markers.

5. Approaches to finding disease genes
Population-based association study
“unrelated” subjects
Family-based association study
nuclear families
Admixture mapping
recently admixed population
Linkage mapping
large pedigrees
Darvasi & Shifman (2005) Nature Genetics

6. Types of population association study
Candidate causative polymorphism
SNP (single nucleotide polymorphism), deletion, duplication
Candidate causative gene (5-50 marker SNPs)
evidence from linkage study or function
Candidate causative region (100s of marker SNPs)
evidence from linkage study
Genome-wide (>300,000 marker SNPs)
no prior evidence required

7. Common disease common variant (CDCV) hypothesis

8. Preliminary analysis: data quality
Assuming mating is random and the population is large, HWE genotype frequencies will apply
Allele frequencies:
P(X) = p
P(x) = q
HWE genotype frequencies:
P(XX) = p2
P(Xx) = 2pq
P(xx) = q2
Useful data quality check:
chi-squared or exact test
log QQ plot
But can discard causative mutations p q p2 pq q2

9. Log QQ plot

10. Preliminary analysis: dealing with missing data
Imputation
various methods: maximum likelihood; probalistic; ‘hot-deck’; regression modelling
test for independence of ‘missingness’ and case-control status

11. Choice of inheritance model
Snapdragons
Antirrhinum majus

12. Choice of inheritance model
Snapdragons
Antirrhinum majus

13. Choice of inheritance model
Snapdragons
Antirrhinum majus

14. Tests of association: single SNP
Case-control
Treat genotype as factor with 3 levels, perform 2x3 goodness-of-fit test. Loses power if effect is additive
Count alleles rather than individuals, perform 2x2 goodness-of-fit test. Out of favour because
sensitive to deviation from HWE
risk estimates not interpretable
Major allele homozygote (0)
Heterozygote (1)
Minor allele homozygote (2)
Case
Control

15. Tests of association: single SNP
Case-control
Cochran-Armitage test
loses power if additivity assumption wrong
For complex traits additivity often thought to be a good model
Cochran-Armitage test

16. Tests of association: single SNP
Case-control
Armitage or goodness-of-fit? Depends on:
Prior knowledge of inheritance (additive, dominant, etc)
Genotype frequencies, e.g. use Armitage test when minor allele is rare, goodness-of-fit test otherwise
For complex traits additivity often thought to be a good model

17. Tests of association: single SNP
Case-control
Logistic regression
Easily incorporates inheritance model (additive, dominant, etc)
But assumes phenotype is outcome variable not genotype, so easier to justify for prospective studies
For complex traits additivity often thought to be a good model

18. Tests of association: single SNP
Continuous outcome
Linear regression
Ordered categorical outcomes
Multinomial regression
But must be normal and equal variance

19. Problems: population stratification
Cases

20. Correcting for population stratification
Genomic control
Genotype null SNPs and use to calculate background inflation in test statistic due to population stratification
Limited to simple single-SNP analyses
Can over- or under-correct
Other approaches using null SNPs
Regression, principal components analysis, model underlying demography

21. Problems: multiple testing
Bonferroni correction
conservative when SNPs are linked
Permutation
computationally demanding
False discovery rate
Bayesian approaches

22. Tests of association: multiple SNPs
Advantages
Many SNPs may be linked to a gene, but individually may not have a significant effect
Interactions between SNPs can be modelled
‘Tag’ SNPs can reduce testing of redundant linked SNPs
Methods
Linear regression, logistic regression
Armitage test
Haplotype-based methods
Natural interpretation
But power reduced due to multiple alleles

23. Haplotypes
Nature Genetics  37, (2005)

24. Crucially, any stretch of recombining DNA can be divided into regions of high LD (haplotypes), and the history of this haplotype can be represented as a tree.
Tag SNPs times fewer loci.

25. Inferring haplotype phase

26. Inferring haplotype phase?

27. Inferring haplotype phase

28. Inferring haplotype phase

29. Inferring haplotype phase
Methods & software
PHASE, FASTPHASE
EH+
FBAT
HAPLOTYPER
EM-DECODER
PLEM
HAP
HAPLORE
Haplo.stat
SNPEM
PEDPHASE
SNPHAP
TDTHAP

30. Inferring haplotype phase
Phase cases and controls separately or pooled?
Separating can give inflated type I error
Pooling can reduce power