Supplementary information
1. Methods for enrichment test
Functional variants have direct impact on gene expression and function. Putative set
of functional variants containing polymorphisms with direct impact on the gene
expression and function that is related to the phenotype are expected to be enriched in
association signals. We test the enrichment in low p-values of functional variants using
two complementary statistics: i) Simes1 test and ii) a VEGAS-like2 sum of squares test
(SST). Simes test is a generalization of the Bonferroni multiple testing adjustment and,
intuitively, is useful to detect enrichment in group of variants having a few, but strong,
signals. It is well known that Simes tests can be rather conservative for SNPs in high
linkage disequilibrium1. However, for testing enrichment in a set of variants (e.g.
promoter and methylation SNPs) with a relatively small number of SNPs spread over
many regions in the genome, the conservativeness of this test should be rather minimal.
SST is likely to be useful in detecting enrichment in a set of variants having many
signals of small effect2.
GWAS of large studies, e.g. PGC3, are known to yield a fair number of statistical
significant signals. Besides these significant signals, GWAS also harbor many small and
moderately large signals spread over the entire genome4. Thus, the statistics from a
large GWAS, are already enriched in small p-values. Consequently, to be considered as
candidate to containing causal variants, a putative set of variants should be enriched for
association signals "above" the background enrichment of the GWAS. For the Simes
test this objective is simply achieved by substituting the relative ranks of the absolute
statistics for the GWAS p-values. Assume
are the univariate
statistics from the GWAS. Let
be the rank of
taken in
decreasing order. Then, the relative rank "p-values" are
and their relevant
subset is used in deriving the background adjusted Simes test for the putative set of
variants.
The adjustment for background enrichment of SST is much more complex than the
one for the Simes test. Let SST statistic for the entire genome be
that
. It follows
, i.e. SST statistics behave like the sum of non-central
variables having non-centrality parameter
non-centrality parameter is estimated as
. Based on the scan statistics, the
. Consequently, under the null
hypothesis of no enrichment above the GWAS background, the distribution of the
square of a univariate scan statistic should be assumed to be
, not a central .
Assume that the statistics associated with SNPs in the putative set of variants are the
first
statistics in the scan, i.e.
. Then the SS statistic associated
with this set of variants is
. If the number of SNPs is large enough for the
Central Limit Theorem to provide a reasonable distributional assumption, under the null
hypothesis of no enrichment above GWAS background,
is approximately a normal
variable with mean
and variance
, i.e.
. To test for enrichment above background in the putative set of variants,
we compute the normally distributed statistic
and test
vs.
. The only unknown is
which can be estimated with reasonable accuracy
from LD of reference genotype data, e.g. European subjects from 1000 Genomes 5
available in Mach6 and Impute7 databases. However, most tested set of variants do not
have the very large number of SNPs needed to ensure that the Central Limit Theorem
provides a good approximation for the distribution of the enrichment statistic, .
Consequently, we assess the statistical significance of
via 50,000 simulations
assuming that the LD structure between selected SNPs is the one estimated from the
European subjects of 1000 Genomes project. In more detail, similar to VEGAS2, the
statistics associated with SNPs on a chromosome are assumed to have a multivariate
normal distribution with the variance matrix equal to the correlation between SNPs'
genotypes.
2. Network analyses
For network analysis of the shared SNPs between promoter and methylation and
between promoter and eQTL groups, we first mapped these SNPs to corresponding
genes. The genes were subsequently overlaid onto a global molecular network
developed based on the Ingenuity Pathways Knowledge Base and subnetworks of
these genes were extracted from the global network based on their connectivity using
the algorithm developed by Ingenuity Pathways Analysis (IPA)
(http://www.ingenuity.com/). For each subnetwork, IPA computes a score, which is
derived from the P-value of Fisher's exact test and indicates the likelihood of the interest
genes being found together in a network compared to that found by chance. The
enriched subnetworks were identified if their scores were greater than 3 (i.e. P < 0.001).
For each subnetwork, we included the top 3 biological functions provided by IPA to
represent the subnetwork’s functions.
3. Acknowledgement
The summary statistics of PGC schizophrenia,8 bipolar disorder,9 and major
depression10 were obtained from https://pgc.unc.edu/Sharing.php#SharingOpp. We are
grateful to the PGC investigators who produced and analyzed these datasets.
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