Supplemental Data
On individual genome-wide association studies
and their meta-analysis
Yu-Fang Pei, Lei Zhang, Christopher J. Papasian, Yu-Ping Wang, Hong-Wen Deng
Supplementary Table 1. Comparisions between parameters used in our study and
reported in Gogrle et al.(Gogele et al. 2012).
Parameter
Majority in Gogele et al.
Values in the present study
Number of studies
2-21
5-50
Sample size
761-74,053
10,000-100,000
Weighting scheme
Inverse variance
Inverse variance
Phenotype distribution
Continuous
Continuous
Mode of inheritance
Additive
Additive
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Supplementary Figure 1. The distribution of the locus effects of the 1,000
simulated independent causal SNPs. The 1,000 causal SNPs together account for
50% of phenotypic variance. The locus effects were generated with an inverse gamma
distribution (for details, see Methods).
3
B
Supplementary Figure 2. The effects of variations of LD levels and allele
frequencies on between-study heterogeneity. Between-study heterogeneity was
measured by I2 index (Higgins et al. 2003) (for details, see Methods). 10 studies were
simulated from 3 populations with proportions 60%:30%:10%. For comparison, we
add the “Ideal” line, which represents the scenario that the causal SNP was tested
directly under a homogeneous setting in terms of effect size and allele frequency
across all individual studies. Panel A shows the effects of variation of LD levels (r2)
between causal SNP and the proxy marker. Distinct lines relate to the r2 in three
populations of 0.8-0.8-0.8, 0.3-0.5-0.8, and 0.7-0.8-0.9, respectively (see Methods for
4
details); h2 on the x-axis represents heritability (phenotypic variation explained by the
SNP). Panel B shows the effects of variation of allele frequencies (see Methods for
details). The causal SNP was tested directly. Allele frequencies were generated using
the Balding-Nichols model(Balding and Nichols 1995). Different lines relate to the h2
values of 0, 0.1%, 0.3%, 0.5% and 1%, respectively.
5
Supplementary Figure 3. Average I2 estimates under different parameter settings. I2 is a measure of between-study heterogeneity (for details,
6
2
2
see Methods).  wp
and  bp
represent within- and between-population variances, respectively. 10 individual studies were simulated from three
populations with proportions 60%:30%:10%. Panels A, B and C, the mean effect for the causal SNP (  o in Equation 1 in Methods section) was the
same in all populations in terms of both magnitude and direction; k is the number of studies included in meta-analysis. Panels D and E, “+00”
denotes that the SNP only had effects in studies from the 1st population and “+-0” denotes that the SNP presented effects with the same magnitude
but at opposite directions in samples from the 1st and 2nd populations, while that from the 3rd population had no effect.
7
Supplementary Figure 4. Type-I error rate and power estimates for rare variants
(MAF=0.005). 10 individual studies were simulated from three populations with
proportions 60%:30%:10%. “FE” and “RE” denote fixed-effects and random-effects
meta-analysis, respectively. The suffixes “pop1” and “total” denote meta-analyses
including studies from the first population, and all three populations, respectively (see
Methods for details). Panel A shows type-I error rate estimations. Within-population
variance was set to be 0.6 and the significant level was set at 0.05. Panel B shows
power estimations. Within-population variance was set at 0.6 and between-population
2
variance (  bp
) was set at 0.1. h2 on the x-axis represents heritability (phenotypic
variation explained by the SNP). Significant level was set at 5x10-8.
8
Supplementary Figure 5. Power estimates of individual GWA studies and their meta-analyses when testing a single SNP. Panels A and B
present the power estimates of the fixed-effects (FE) model and Panels C and D present the power estimates of the random-effects (RE) model. k is
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2
2
the number of studies included in meta-analysis and “k=1” denotes an individual GWA study.  wp
and  bp
represent within- and between-
population variance, respectively. Panels A and C: studies included in a meta-analysis were ideally homogeneous; Panels B and D: only withinpopulation variation was present. h2 represents phenotypic variation explained by the SNP.
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Supplementary Figure 6. Power of meta-analysis for identifying at least a specified number of loci on a genome-wide scan. The
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distribution of the causal locus effects is shown in Supplementary Figure 1. “FE” and “RE” denote fixed- and random-effects meta-analyses,
respectively. k is the number of studies included in meta-analysis. Panels A, B, C, and D present the results for k=5, 10, 20, and 50, respectively.
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Supplementary Figure 7. Power of meta-analysis to identify a SNP for various significance levels on a genome-wide scan. The distribution
of the causal locus effects is shown in Supplementary Figure 1. “FE” and “RE” denote fixed- and random-effects meta-analyses, respectively. k
13
is the number of studies included in meta-analysis. Panels A, B, C, and D present the results for k=5, 10, 20, and 50, respectively.
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Supplementary Figure 8. Power of meta-analysis to replicate findings from individual
GWA studies. The distribution of the causal locus effects is shown in Supplementary Figure
15
1. “FE” and “RE” denote fixed- and random-effects meta-analyses, respectively. k is the
number of studies included in meta-analysis. Panels A, B and C present the results for k=5, 20,
and 50, respectively. Tables on the top right of the figures give the average number of
significant SNPs identified at a genome wide significant level by each method. “Overlapped”
denotes that samples from GWA studies were included in the meta-analysis and
“independent” denotes that samples from GWA studies and meta-analysis were independent.
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Supplementary Figure 9. Replicability between independent meta-analyses. The distribution
of the causal locus effects is shown in Supplementary Figure 1. “FE” and “RE” denote fixed- and
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random-effects meta-analyses, respectively. k is the number of studies included in meta-analysis.
Panels A, B and C present the results for k=5, 20, and 50, respectively. Tables on the top right of
the figures give the average number of significant SNPs identified by each method.
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A
Supplementary Figure 10. Type-I error rate and power estimate for meta-analysis with
2
2
sample structure from real data.  bp
and  wp
denote between- and within-population variance,
respectively. “FE” and “RE” denote fixed-effects and random-effects meta-analysis, respectively.
The suffixes “total” denotes meta-analysis including all studies and “CEU” denotes meta19
analysis including studies with subjects of European ancestry. Panel A and B display the type-I
2
error rate estimates and panel C displays the power estimates. Panel A:  bp
= 0; panel B:
2
2
2
=0.6; panel C:  bp
= 0.1 and  wp
=0.6.
 wp
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Supplementary notes
Simulations with sample structure from real data
We simulated individual studies with sample sizes exactly equal to a recently published metaanalysis (Estrada et al. 2012). Specifically, 17 studies with a total sample size of 34,910
individuals were simulated, of which, 16 studies included subjects of European ancestry and 1
study included Chinese subjects. Allele frequencies in each population were sampled using the
Balding-Nichols model (Balding and Nichols 1995). The ancestral allele frequency for the causal
variant was set at 0.1 and the genetic distance measure Fst between Caucasian and Chinese was
set at 0.11 (Nelis et al. 2009). We estimated the type-I error and power under different
heterogeneity settings and found that false negative and positive results were introduced under
the heterogeneity setting (Supplementary Fig. 10).
Relationship between heterogeneity and ancestral allele frequency
The magnitude of heterogeneity effects decreased with increasing ancestral MAF p0. To interpret
this, we wrote the definition of heritability
h 2  var( G ) / var( Y ) ,
where G and Y denoted genotypic effect and phenotypes, respectively. When h2 and var(Y) were
fixed, var(G) was fixed as well. Under the additive mode of inheritance,
var( G )    2 p  (1  p ) ,
so that each effect size θi was calculated by i 
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h 2  var( y )
Therefore, the difference in θi,
2 pi (1  pi )
.
which determined the magnitude of heterogeneity effects, was in turn determined by the
reciprocal of the square root of pi (1  pi ) Each individual pi was drawn from the beta
distribution Beta(p0(1-Fst)/Fst, (1-p0)(1-Fst)/Fst). The mean and variance of this distribution were
p0 and Fstp0(1-p0), respectively. Because Fst was set at a small value (0.05), pi was concentrated
on a small range towards p0. Together, the change in θi was negatively correlated with pi(1-pi).
Effects of heterogeneity on rare variants
Heterogeneity effects were less severe for rare variants than for common variants. To interpret
this, we wrote the model for simulating phenotype as following:
yij  ij xij   ,  ~ N (0, 2 ), var(  ij )   ij .
Where yij and xij denote the phenotype and genotype, respectively. The heterogeneity statistic
1
Q  i  j wij (  ij  ˆ )2 and wij  .
 ij
The variation of observed effect sizes i  j (  ij  ˆ )2 was determined by between- and withinpopulation variances, which were set to be the same for SNPs with different MAFs. In a linear
regression model,  ij 
 2
var( x )

 2
2 p(1  p )
, which will decrease with increasing MAF, p, of the
test SNP. So  ij for rare variants is higher than that for common variants and higher
 ij corresponds to lower heterogeneity.
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