3.8 Selecting
Significant SNPs with
the Multiple
Hypothesis
Adjustment
In general, GWAS tests the phenotype association of more than a
million SNPs. Thus, the p-value threshold for selecting phenotypeassociated SNPs needs to be adjusted for the multiple hypothesis
test. There are several methods for multiple hypothesis correction
of the p-value threshold (see Note 5).
3.8.1 Bonferroni
Correction
The Bonferroni correction is the strictest correction of the p-value
threshold. The corrected threshold is calculated as follows:
α bonf ¼
α
N
where α is the original p-value threshold, N is the total number of
hypotheses (i.e., the total number of SNPs), and α bonf is the new
threshold after Bonferroni correction. If we initially set the p-value
threshold at 0.05 and the total number of SNPs as N, then the
corrected threshold will be 0.05/N. If the given GWAS has sufficient statistical power, we should be able to identify a number of
SNPs that pass this threshold. However, the Bonferroni correction
is very conservative, which might leave only a few SNPs that pass
the corrected threshold.
3.8.2 S ˇ ida´k Correction
S ˇ ida ´k correction is a slightly relaxed correction compared to Bonferroni [24]. The S ˇ ida ´k corrects the original p-value threshold using
the following equation:
α sidak ¼ 1 À 1 À α
ð
Þ
1=N
where α is our original p-value threshold, N is the total number of
SNPs, and α sidak is the S ˇ ida ´k-corrected α. While S ˇ ida ´k correction
can provide less conservative correction as compared to Bonferroni,
the effect is marginal. S ˇ ida ´k correction does a poor job if the SNPs
are negatively dependent on each other. For this reason, S ˇ ida ´k
correction is not a very popular option.
3.8.3 BenjaminiHochberg Correction
Benjamini-Hochberg (BH) correction provides a more relaxed
threshold as compared to the above two methods. It is calculated
as follows:
α BH ¼
α
N
 r
where α is the original p-value threshold, N is the total number of
SNPs, r is the rank of the SNPs when sorted by their significance
scores, and α BH is the new p-value threshold after correction. The
BH correction has different thresholds for each SNP (or linked
gene), since the rank parameter is adopted. This makes BH correction more relaxed and one of the most widely used correction
methods.
200
Tak Lee and Insuk Lee
Significant SNPs with
the Multiple
Hypothesis
Adjustment
In general, GWAS tests the phenotype association of more than a
million SNPs. Thus, the p-value threshold for selecting phenotypeassociated SNPs needs to be adjusted for the multiple hypothesis
test. There are several methods for multiple hypothesis correction
of the p-value threshold (see Note 5).
3.8.1 Bonferroni
Correction
The Bonferroni correction is the strictest correction of the p-value
threshold. The corrected threshold is calculated as follows:
α bonf ¼
α
N
where α is the original p-value threshold, N is the total number of
hypotheses (i.e., the total number of SNPs), and α bonf is the new
threshold after Bonferroni correction. If we initially set the p-value
threshold at 0.05 and the total number of SNPs as N, then the
corrected threshold will be 0.05/N. If the given GWAS has sufficient statistical power, we should be able to identify a number of
SNPs that pass this threshold. However, the Bonferroni correction
is very conservative, which might leave only a few SNPs that pass
the corrected threshold.
3.8.2 S ˇ ida´k Correction
S ˇ ida ´k correction is a slightly relaxed correction compared to Bonferroni [24]. The S ˇ ida ´k corrects the original p-value threshold using
the following equation:
α sidak ¼ 1 À 1 À α
ð
Þ
1=N
where α is our original p-value threshold, N is the total number of
SNPs, and α sidak is the S ˇ ida ´k-corrected α. While S ˇ ida ´k correction
can provide less conservative correction as compared to Bonferroni,
the effect is marginal. S ˇ ida ´k correction does a poor job if the SNPs
are negatively dependent on each other. For this reason, S ˇ ida ´k
correction is not a very popular option.
3.8.3 BenjaminiHochberg Correction
Benjamini-Hochberg (BH) correction provides a more relaxed
threshold as compared to the above two methods. It is calculated
as follows:
α BH ¼
α
N
 r
where α is the original p-value threshold, N is the total number of
SNPs, r is the rank of the SNPs when sorted by their significance
scores, and α BH is the new p-value threshold after correction. The
BH correction has different thresholds for each SNP (or linked
gene), since the rank parameter is adopted. This makes BH correction more relaxed and one of the most widely used correction
methods.
200
Tak Lee and Insuk Lee