Power to detect QTL Association

Lon Cardon, Goncalo AbecasisUniversity of Oxford

Pak Sham, Shaun PurcellInstitute of Psychiatry

F:\lon\2001\Assocpower

In principle, power to detect association involves same mechanics as linkage

Association Power

We are interested in significance thresholds1- the probability of rejecting the null when it is falseN the number of individuals required to do it

Association Power

What are the important variables/parameters?

Linkage:• Study design• QTL effect size• recombination fraction

Association:• Study design• QTL effect size• Linkage disequilibrium• allele frequencies of marker and QTL

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

Effects of Linkage Disequilibrium

• Key question for positional cloning and candidate gene analysis

• LD expected to decay (1-)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

Extent of Disequilibrium

Pair-wise Disequilibrium

Sensitivity to Disequilibrium

0% 25% 50% 75% 100%

480 triads 0 2 20 70 97

240 sib-pairs 0 2 23 73 98

120 sib-quads 0 3 27 76 98

Estimate of a 0 1.1 2.2 3.4 4.5

Amount of Disequilibrium

Power for =0.001, h² = .1, s² = .3, = 0.

Average additive genetic value estimated at the marker.

Influence of Family Size

For ‘robust’ tests (TDT, QTDT) class,

Best design includes parental genotypes, but theyare not mandatory

As sibship size increases, missing parental databecomes less important

Effect of Family Structure

0

8

16

0 500 1000 1500 2000

Total Offspring

-Log

()

parents sib-pair sib-triad sib-quad

350 sib-pair + parents: 1400 genotypes

500 sib-pairs – no parents: 1000 genotypes

260 sib-trios no parents: 780 genotypes

Single Nucleotide PolymorphismsCommon 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

Extent of Disequilibrium

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

Trios For Genome-Wide Scan

Disease AlleleFrequency

Marker Allele Frequency

0.1 0.3 0.5 0.7 0.9

0.1 248 626 1306 2893 10830

0.3 1018 238 466 996 3651

0.5 2874 702 267 556 2002

0.7 9169 2299 925 337 1187

0.9 73783 18908 7933 3229 616

s = 1.5, = 5 x 10-8, Spielman TDT (Müller-Myhsok and Abel, 1997)

Effect of Allele Frequencies

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

Selection Strategies

• Selection based on one tail– Affected Proband, Affected Pairs

• Selection from either tail– Extreme Proband– Concordant Pairs– Discordant Pairs– Discordant and Concordant

Selection Tresholds

• Hard definition– 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

Intensity of a priori selection

1

10

100

1000

10000

Sele

ctio

n R

atio

AP EP ASP CSP DSP EDAC

Selection Strategy

0.50

0.30

0.10

0.05

Selection of Triads 360 x Single Child Families Selection TDT PDT QTDT Ratio

Unselected - 1.0 0.15 0.54 0.55

AP: "Affected Proband" – Top Tail = .05 20.0 0.86 0.02 0.03

10 10.0 0.75 0.03 0.04 30 3.3 0.55 0.06 0.07 50 2.0 0.36 0.11 0.12

EP: "Extreme Proband" – Top or Bottom Tail = .05 10.0 0.85 1.00 1.00

10 5.0 0.70 0.98 0.98 30 1.7 0.31 0.73 0.74 50 1.0 0.13 0.54 0.53

180 x Two Child Families Selection TDT PDT QTDT Ratio

Unselected - 1.0 0.14 0.51 0.56

AP: "Affected Proband" = .05 10.9 0.68 0.73 0.72

10 5.7 0.56 0.67 0.66

EP: "Extreme Proband" = .05 5.5 0.39 0.92 0.93

10 2.9 0.32 0.80 0.85

ASP: "Affected Sib-Pair" = .05 122.1 0.88 0.04 0.05

10 41.5 0.79 0.05 0.06

CSP: "Concordant Sib-Pair" = .05 61.1 0.50 0.90 0.15

10 20.8 0.40 0.83 0.17

DSP: "Discordant Sib-Pair" = .05 1617.9 1.00 1.00 1.00

10 217.9 0.99 1.00 1.00

EDAC: "Extreme Discordant and Concordant Pair" = .05 58.8 0.53 0.94 0.50

10 19.0 0.47 0.85 0.68

Post hoc SelectionSelection Ratio 1 2 4 8 12 16 20

Discrete Trait Analysis after Dichotomization

ASP* .05 .08 .09 .13 .18 .20 .28

Quantitative Trait Analysis

AP* 0.21 0.22 0.28 0.30 0.31 0.34 0.41

EP* .21 .38 .51 .57 .59 .63 .73

CSP* .21 .17 .26 .30 .31 .32 .48

DSP* .21 .24 .38 .47 .57 .59 .75

EDAC* .21 .31 .36 .43 .42 .44 .49

Effect of Allele Frequencies

Effect of Selection

Summary

•Power for association generally greater than linkage

•Power greatly influenced by D, selection strategy,allele frequency

•Optimal linkage strategies not necessarily best forassociation

•Allele frequency of (unobserved) QTL is important,but more important that marker-QTL match