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Power Calculation for QTL Association
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Power Calculation for QTL Association Pak Sham, Shaun Purcell Twin Workshop 2001
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Power Calculation for QTL Association. Pak Sham, Shaun Purcell Twin Workshop 2001. Biometrical model. GenotypeAAAaaa Frequency(1-p) 2 2p(1-p)p 2 Trait mean-ada Trait variance 2 2 2 Overall meana(2p-1)+2dp(1-p). P ( X ) = G P ( X | G ) P ( G ). - PowerPoint PPT Presentation
Transcript of Power Calculation for QTL Association
Power Calculation for QTL Association
Pak Sham, Shaun Purcell
Twin Workshop 2001
Biometrical model
Genotype AA Aa aa
Frequency (1-p) 2 2p(1-p) p2
Trait mean -a d a
Trait variance 2 2 2
Overall mean a(2p-1)+2dp(1-p)
P(X) = GP(X|G)P(G)
P(X)
X
AA
Aa
aa
Equal allele frequencies
A
0
0.2
0.4
0.6
0.8
1
-5 -3 -1 1 3 5
Rare increaser allele
A
0
0.2
0.4
0.6
0.8
1
-5 -3 -1 1 3 5
Linear regression analysis
-2
-1
0
1
2
3
4
aa Aa AA
Power of QTL association - regression analysis
N = [z - z1-] 2 / A2
z : standard normal deviate for significance z1- : standard normal deviate for power 1-A
2 : proportion of variance due to additive QTL
Required Sample Sizes
QTLvariance10%
0
50
100
150
200
250
300
0 0.05 0.1
Significance level
Sa
mp
le s
ize
80% power
95% power
50% power
Power of likelihood ratio testsFor chi-squared tests on large samples, power is
determined by non-centrality parameter () and degrees of freedom (df)
= E(2lnL1 - 2lnL0)
= E(2lnL1 ) - E(2lnL0)
where expectations are taken at asymptotic values of maximum likelihood estimates (MLE) under an assumed true model
Between and within sibships components of means
Variance/Covariance explained
The better the fit of a means model:
- the greater the explained variances and covariances
- the smaller the residual variances and covariances
Variance of b- component
Variance of w- component
Covariance between b- and w- components
Null model
Between model
Within model
Full model
NCPs for component tests
Determinant of a uniform covariance matrix
])1([)( 1 bsabaA sS
Determinants of residual covariance matrices
NCPs of b- and w- tests
Definitions of LD parametersB1 B2
A1 pr + D ps - D p
A2 qr - D qs + D q
r s
pr + D < min(p, r)
D < min(p, r) - pr DMAX = min(ps, rq)
= min(p-pr, r-pr) D’ = D / DMAX
= min(ps, rq) R2 = D2 / pqrs
Apparent variance components at marker locus
N/22 where
Exercise: Genetic Power CalculatorUse Genetic Power Calculator, Association Analysis option
Investigate the sample size requirement for the between and within sibship tests under a range of assumptions
Vary
sibship size
additive QTL variance
sibling correlation
QTL allele frequencies
marker allele frequencies
D’
N for 90% powerIndividuals
0 - 10% QTL variance
QTL, Marker allele freqs = 0.50
D-prime = 1
No dominance
Type I error rate = 0.05
Test for total association
QTL variance
0
200
400
600
800
1000
1200
0 0.02 0.04 0.06 0.08 0.1
QTL variance
N
QTL variance
0
20
40
60
80
100
120
0 0.02 0.04 0.06 0.08 0.1
QTL variance
NC
P p
er
ind
ivid
ua
l
Effect of sibship size
Sibship size 1 - 5
Sib correlation = 0.25 , 0.75
5% QTL variance
QTL, Marker allele freqs = 0.50
D-prime = 1
No dominance
Type I error rate = 0.05
Total
0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
0.1
1 2 3 4 5
Sibship size
NC
P p
er
ind
ivid
ua
l
T r = 0.25
T r = 0.75
Within
0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
1 2 3 4 5
Sibship size
NC
P p
er
ind
ivid
ua
l
W r = 0.25
W r = 0.75
Between
0
0.01
0.02
0.03
0.04
0.05
0.06
1 2 3 4 5
Sibship size
NC
P p
er
ind
ivid
ua
l
B r = 0.25
B r = 0.75
Exercises1. What effect does the QTL allele frequency have
on power if the test is at the QTL ?
2. What effect does D’ have?
3. What is the effect of differences between QTL and marker allele frequency?
Allele frequency & LDQTL allele freq = 0.05, no dominance
Sample sizes for 90% power :
Marker allele freq 0.1 0.25 0.5
D’ 1 1 1
N 205 625 1886
Marker allele freq 0.1 0.25 0.5
D’ 0.5 0.5 0.5
N 835 2517 7560
