1. Power to detect QTL Association
Lon Cardon, Goncalo Abecasis
University of Oxford
Pak Sham, Shaun Purcell
Institute of Psychiatry
F:\lon\2001\Assocpower

2. Association Power
In principle, power to detect association involves same mechanics as linkage
We are interested in
a significance thresholds
1-b the probability of rejecting the null when it is false
N the number of individuals required to do it

3. Association Power What are the important variables/parameters?
Linkage:
Study design
QTL effect size
recombination fraction
Association:
Linkage disequilibrium
allele frequencies of marker and QTL

4. Association Power In general,
power is greater for association than for linkage
ie., fewer individuals required,
can detect smaller effects (h2 ~ 5% vs. 20%)
But,
more markers may be tested,
false positives are (or may be) more relevant

5. Effects of Linkage Disequilibrium
Key question for positional cloning and candidate gene analysis
LD expected to decay  (1-q)G
How far does it extend?
Debates: 3 kb – 100 kb (Kruglyak : rest of world).
Population-specific (depends on ancestral demographics)
Genomic region-specific (ie., depends on sequence features)
Marker-specific (ie., depends on markers considered)
Variation dominates data

6. Extent of Disequilibrium

7. Pair-wise Disequilibrium

8. Sensitivity to Disequilibrium
Power for =0.001, h² = .1, s² = .3,  = 0.
Average additive genetic value estimated at the marker.

9. Influence of Family Size
For ‘robust’ tests (TDT, QTDT) class,
Best design includes parental genotypes, but they
are not mandatory
As sibship size increases, missing parental data
becomes less important

10. Effect of Family Structure
350 sib-pair + parents:
1400 genotypes
500 sib-pairs – no parents:
1000 genotypes
260 sib-trios no parents:
780 genotypes

11. Single Nucleotide Polymorphisms
Common disease-common variant hypothesis: Common diseases have been around for a long time. Alleles require a long time to become common (frequent) in the population. Common diseases are influenced by frequent alleles.
The SNP Consortium (TSC):
Collection of 10 pharmaceutical companies & Wellcome Trust
Identified > 1 million SNPs across the genome
public databases now have ~ 1.5 million non-redundant SNPs (relatively few verified)
SNPs detected on basis of common disease common variant hypothesis (caucasian, african american, asian)
…Should be preponderance of common alleles

12. Extent of Disequilibrium

13. Effects of Allele Frequency
Key question is not just frequency of QTL, but frequency of marker in LD with it
More important that marker-QTL allele frequencies are the same than that QTL is common;
i.e., CD-CV hypothesis not as relevant as SNP map

14. Trios For Genome-Wide Scan
ls = 1.5, a = 5 x 10-8, Spielman TDT
(Müller-Myhsok and Abel, 1997)

15. Effect of Allele Frequencies

16. Phenotypic Selection Efficiency gains for genotyping
Well characterized for linkage mapping ...
... Association mapping gaining prominence
Selection tresholds
A priori versus Post hoc
Common variant hypothesis
Effect of allele frequency

17. Selection Strategies Selection based on one tail
Affected Proband, Affected Pairs
Selection from either tail
Extreme Proband
Concordant Pairs
Discordant Pairs
Discordant and Concordant

18. Selection Tresholds Hard definition Adaptable selection A priori
Treshold defined before sample collection
Eg, pairs with both sibs in top decile
Adaptable selection
Post hoc
Tresholds defined after sample collection
Eg, subselection from large twin registries

19. Intensity of a priori selection

20. Selection of Triads

22. Post hoc Selection

23. Effect of Allele Frequencies

24. Effect of Selection

25. Summary Power for association generally greater than linkage
Power greatly influenced by D, selection strategy,
allele frequency
Optimal linkage strategies not necessarily best for
association
Allele frequency of (unobserved) QTL is important,
but more important that marker-QTL match