Abstract
Statistical factor analysis methods have previously been used to remove
noise components from high-dimensional data prior to genetic
association mapping and, in a guided fashion, to summarize biologically
relevant sources of variation. Here, we show how the derived factors
summarizing pathway expression can be used to analyze the relationships
between expression, heritability, and aging. We used skin gene
expression data from 647 twins from the MuTHER Consortium and applied
factor analysis to concisely summarize patterns of gene expression to
remove broad confounding influences and to produce concise
pathway-level phenotypes. We derived 930 “pathway phenotypes” that
summarized patterns of variation across 186 KEGG pathways (five
phenotypes per pathway). We identified 69 significant associations of
age with phenotype from 57 distinct KEGG pathways at a stringent
Bonferroni threshold (
[MATH:
P<5.38×10−5 :MATH]
). These phenotypes are more heritable (
[MATH:
h2=0.32
:MATH]
) than gene expression levels. On average, expression levels of 16% of
genes within these pathways are associated with age. Several
significant pathways relate to metabolizing sugars and fatty acids;
others relate to insulin signaling. We have demonstrated that factor
analysis methods combined with biological knowledge can produce more
reliable phenotypes with less stochastic noise than the individual gene
expression levels, which increases our power to discover biologically
relevant associations. These phenotypes could also be applied to
discover associations with other environmental factors.
Keywords: aging, factor analysis, gene expression, heritability, linear
mixed models
__________________________________________________________________
Aging is a multifactorial process reflecting how the physical state of
an organism accumulates changes. Among these, we observe changes in
gene expression. Microarrays and more recent RNA-seq technologies allow
the simultaneous quantification of cell population average mRNA
abundance for thousands of genes. In the case of aging, consistent
patterns of age-related changes in gene expression have been observed
across several tissues and species ([38]Lu et al. 2004), such as
overexpression of inflammation and immune-response genes and
underexpression of genes involved in energy metabolism in older samples
([39]de Magalhaes et al. 2009). Given this commonality of function
among genes that show age-related changes in expression, we decided to
investigate aging-dependent gene expression in the context of
biological knowledge of the function of genes, as provided by pathway
annotations.
Array expression experiments generate high-dimensional structured data
sets in which there are correlated patterns across large numbers of
genes. Some of these are due to known technical or biological effects
such as batch effects and cell growth stage, which, when not the focus
of the analysis, can be removed by fitting them as covariates. However,
even after this, there is typically substantial structural correlation.
In previous studies, these can be represented by linear components of
expression measurements, or factors, that can be inferred using methods
such as principal components analysis (PCA) or factor analysis
([40]Leek and Storey 2007; [41]Parts et al. 2011). When the aim is to
discover local effects, such as cis genetic regulation, the resulting
factors can be treated as nuisance variables and removed from further
analysis. This has been seen to increase power in analysis
([42]Pickrell et al. 2010). Conversely, if the aim is to differentiate
between a case and control condition using expression, then factors
viewed as global phenotypes could be more effective classifiers than
local phenotypes ([43]Hastie et al. 2000).
Recently, we applied factor analysis methods in a two-stage procedure
to generate phenotypes representing expressions of groups of genes
([44]Stegle et al. 2012). After regressing out global factors, as in
[45]Parts et al. (2011), expression levels for groups of functionally
related genes, as defined by annotations from pathway databases, were
treated as new expression datasets and the same factor analysis methods
were used to construct pathway factors. The factors constructed on
pathway sets of genes were taken as concise summaries of common
expression variation across each pathway. We tested these factor values
as phenotypes and refer to them as phenotype factors or, in some cases,
just phenotypes.
Here, we apply this method to gene expression data from abdominal skin
tissues from 647 samples. Unlike previous studies that have
concentrated on genetic variants that regulate multiple genes within a
pathway ([46]Stegle et al. 2012), we focus here on discovering
associations between gene expression and age. We obtain our pathway
gene sets from the Kyoto Encyclopedia of Genes and Genomes (KEGG)
pathways ([47]Kanehisa et al. 2004). Subsequently, by looking for
associations between these new pathway phenotypes and age, we discover
groups of functionally related genes with a common response to aging
that can be used as biomarkers describing molecular changes with age.
With data from a twin cohort containing both monozygotic and dizygotic
twins, we can estimate proportions of variance explained by age,
genetic variation, common environmental variation, and unique
environmental variation (noise). Stochasticity in gene expression,
which will form part of the unique environment component, is believed
to play a role in the aging process ([48]Bahar et al. 2006). By
investigating sources of variation within the pathway phenotypes, we
find that they are more robust than the expression of individual genes,
with less unique environment variation. This explains some of our
success at discovering associations with age.
Materials and Methods
Expression profiling
The data analyzed here are part of the MuTHER project (Multiple Tissue
Human Expression Resource, [49]http://www.muther.ac.uk/; [50]Nica et
al. 2011) and were downloaded from the ArrayExpress archive, accession
no. E-TABM-1140. In summary, the study included 856 Caucasian female
individuals [336 monozygotic (MZ) and 520 dizygotic (DZ) twins]
recruited from the TwinsUK Adult twin registry ([51]Moayyeri et al.
2012). The age at sampling ranged from 39 to 85 years, with a mean age
of 59 years. Punch biopsy samples (8 mm) were taken from relatively
photo-protected infra-umbilical skin. Subcutaneous adipose tissue was
dissected from each biopsy sample and the remaining skin tissue was
weighed and stored in liquid nitrogen. Expression profiling of this
skin tissue was performed using Illumina Human HT-12 V3 BeadChips, with
200 ng of total RNA processed according to the protocol supplied by
Illumina. All samples were randomized prior to array hybridization and
the technical replicates were always hybridized on different BeadChips.
Raw data were imported to the Illumina Beadstudio software and probes
with fewer than three beads present were excluded. Log2-transformed
expression signals were then normalized separately per tissue with
quantile normalization of the replicates of each individual followed by
quantile normalization across all individuals as previously described
([52]Grundberg et al. 2012). Post-QC expression profiles were
subsequently obtained for 647 individuals. The Illumina probe
annotations were cross-checked by mapping the probe sequence to the
NCBI Build 36 genome with MAQ ([53]Li et al. 2008). Only uniquely
mapping probes with no mismatches and either an Ensembl or a RefSeq ID
were kept for analysis. Probes mapping to genes of uncertain function
(LOC symbols) and those encompassing a common SNP (1000G, release June
2010) were further excluded, leaving 23,555 probes used in the
analysis.
Gene expression pathway factors
In a two-step approach, factor analysis methods were first used to
discover patterns of common variation across the entire dataset. The
software package PEER ([54]Parts et al. 2011) was applied using the
default settings and using technical measurements (experimental batch,
RNA quality and concentration) as covariates to create five global
factors, which in total explained 35.7% of the variation in the
dataset. For each individual, a factor is a weighted sum of all the
gene expression measurements of that individual. The weights are chosen
so that the factors iteratively explain the maximum amount of variation
in the dataset subject to certain prior assumptions; these factors
produce concise summaries of consistent patterns of expression for
large numbers of genes.
We then used KEGG pathway annotation (186 pathways) as prior
information to group genes into pathways. This allows inference of PEER
factors for each pathway that we refer to as phenotype factors, in
contrast to the global factors previously described. As before, these
factors are weighted sums of gene expression measurements, but in this
case only of genes within the pathway. Because global factors have been
removed from the dataset prior to calculation of phenotype factors,
these factors are unlikely to capture global effects on gene
expression, but instead capture pathway specific patterns of
expression. If a large enough module of genes within the pathway is
co-expressed, then one factor will capture the same pattern of
co-expression across individuals. Equally, groups of genes could show
opposite patterns of expression; this antagonistic gene expression can
also be reflected as a factor value that correlates across individuals
with one set of genes and is anti-correlated with the other set of
genes. Individual genes can contribute positively or negatively to the
weighted sum (indicated by the sign of the corresponding weight),
meaning that a positive correlation between age and phenotype factor
can be induced by negative correlations with individual genes.
We grouped the expression data set into 186 pathway subsets. For each
pathway we created five pathway phenotypes using PEER with the default
settings. We consider the learned pathway factor values across
individuals as five new phenotypes that can be investigated for
associations with age. An alternative strategy would be to choose
different numbers of factors based on the cumulative amount of variance
explained. For the sake of simplicity and as a proof of principle, in
this analysis we chose to use five factors because they explained a
substantial amount of the variance in expression (17.5%) without too
large of a multiple testing burden. The sixth factor, on average, would
have explained 2.2% more of the variance.
Pathway factor and phenotype association
Association tests were performed using the linear mixed models defined
in Box 1: between each pathway factor and chronological age and between
single genes and chronological age. These models have been implemented
by the lme4 package ([55]Bates et al. 2014) in R (R Core Team 2013).
For each phenotype a likelihood ratio test of the full model, which
includes the age term, and the null model (without modeling age) were
used to assess evidence for an age effect. P values produced by this
analysis were assessed for significance, allowing for multiple testing
using a Bonferroni-adjusted threshold. Permuted datasets were created
that maintained the twin structure by permuting singletons, DZ twins,
and MZ twins separately and ensuring that twin pairs were kept
together.
Significant associations between phenotype factors and age were further
investigated to trace the particular genes within the pathway driving
the signal. We report genes with a Bonferroni significant P value that
accounts for the number of genes within the pathway that was tested.
Heritability analysis
To compute heritability, the proportion of environmental variance
explained by age, and the proportion of variance explained by unique
environment, we fitted the full model from Box 1. Then, the genetic
component to variation was estimated as twice the additional
correlation of MZ twins relative to DZ twins. The environmental
component to the phenotype was the sum of the contribution from the
fixed age effect, the random noise term, and the shared environmental
component, again estimated from the difference between MZ and DZ.
Estimates of these proportions are constrained to lie between 0 and 1
inclusive.
[56]graphic file with name 839fx1.jpg
[57]Open in a new tab
Single-gene based pathway enrichment analysis
We compared the significant pathways found by our factor analysis
methods to those found by looking for enrichment of single gene
associations with age. First, we tested each gene for association with
age using the methods described in Box 1 and produced a list of
Bonferroni significant genes P
[MATH: <0.05 :MATH]
(this list contained 682 differentially expressed genes). For each
pathway, we applied a Fisher’s exact test to infer whether the
proportion of significantly associated genes within the pathway was
greater than would be expected by chance. We also investigated whether
using an FDR cut-off for significant age associations would produce
more significant pathways or whether power would be diluted by
including too many false positives. When re-running the analysis using
a less stringent threshold (3487 genes were associated with age with
FDR
[MATH: <0.05 :MATH]
), we found fewer significant pathways and results correlated less well
with the results of the factor based analysis [Spearman correlation of
0.36 (P =
[MATH:
5.1×10−7 :MATH]
) compared to 0.49 for Bonferroni, P =
[MATH:
2.1×10−12 :MATH]
]. A complete list of all significant single-gene age associations (FDR
[MATH: <0.05 :MATH]
; 3487 genes), with estimates of effect size and direction, can be
found in [58]Supporting Information, [59]File S1.
Results
The first stage of the analysis was to remove the effect of both known
and unknown nuisance variables from the gene expression data. Using
PEER software, we estimated five global factors that explained 35.7% of
the variation in the complete gene expression data. Because the aim of
this analysis was to find pathway specific responses to aging, we
treated these global factors as nuisance covariates and regressed these
out of the data, together with batch and RNA quality that are known
experimental confounders. Data were then divided into subsets of genes
within 186 KEGG pathways that contained more than 10 genes with probes
in our dataset. For each pathway, five factors were estimated using
PEER as described above, which explained, on average, 17.5% of the
residual variation of all genes within this pathway after removing the
global factors. For the 186 KEGG pathways, this produced 930 phenotypes
that were tested for association with age (see Materials and Methods
for details). In total, 69 significant associations (
[MATH:
P<5.38×10−5 :MATH]
, the Bonferroni-adjusted threshold) from 57 distinct pathways were
identified. The most significant 20 pathways are listed in [60]Table 1,
and a list of all 57 significant pathways can be found in [61]Table S1.
Table 1. List of 20 pathways most significantly associated with age.
KEGG_ID Pathway P of Pathway Factor No. of Genes in Pathway Number of
Age-Associated Genes Heritability
00900 Terpenoid Backbone Biosynthesis 6.23
[MATH:
×10−13 :MATH]
13 6 0.00
00980 Metabolism of Xenobiotics by Cytochrome P450 6.47
[MATH:
×10−13 :MATH]
54 6 0.09
01040 Biosynthesis of Unsaturated Fatty Acids 1.11
[MATH:
×10−12 :MATH]
17 6 0.25
00100 Steroid Biosynthesis 1.33
[MATH:
×10−12 :MATH]
14 12 0.41
00650 Butanoate Metabolism 1.51
[MATH:
×10−12 :MATH]
27 8 0.39
04146 Peroxisome 1.56
[MATH:
×10−12 :MATH]
64 17 0.45
00830 Retinol Metabolism 1.93
[MATH:
×10−12 :MATH]
48 6 0.45
00010 Glycolysis Gluconeogenesis 3.59
[MATH:
×10−12 :MATH]
49 12 0.42
00051 Fructose and Mannose Metabolism 3.99
[MATH:
×10−12 :MATH]
32 8 0.32
00290 Valine Leucine and Isoleucine Biosynthesis 1.15
[MATH:
×10−11 :MATH]
11 3 0.00
00561 Glycerolipid Metabolism 2.63
[MATH:
×10−11 :MATH]
38 6 0.34
00620 Pyruvate Metabolism 4.20
[MATH:
×10−11 :MATH]
35 11 0.37
00770 Pantothenate and COA Biosynthesis 4.76
[MATH:
×10−11 :MATH]
16 4 0.48
00280 Valine Leucine and Isoleucine Degradation 5.79
[MATH:
×10−11 :MATH]
35 10 0.51
00020 Citrate Cycle TCA Cycle 1.12
[MATH:
×10−10 :MATH]
23 8 0.43
04916 Melanogenesis 3.34
[MATH:
×10−10 :MATH]
93 10 0.00
04910 Insulin Signaling Pathway 3.70
[MATH:
×10−10 :MATH]
122 13 0.45
00565 Ether Lipid Metabolism 5.89
[MATH:
×10−10 :MATH]
27 3 0.00
00350 Tyrosine Metabolism 9.44
[MATH:
×10−10 :MATH]
32 4 0.34
00640 Propanoate Metabolism 1.03
[MATH:
×10−9 :MATH]
26 6 0.59
[62]Open in a new tab
List of 20 pathways most significantly associated with age, together
with the total number of genes in the pathway, the number of genes
within pathways significantly associated with age (
[MATH: P<0.05 :MATH]
, corrected using Bonferroni for the total number of genes in the
pathway), and the heritability of the pathway factor.
We also explored an alternative method for finding pathway related to
aging, looking for enrichment in the number of significantly associated
genes falling into a particular pathway, analogous to the method used
by the DAVID methodology ([63]Huang et al. 2009). This discovered a
total of seven significant pathways ([64]Table S2). Thus, applying
factor analysis methods to discover significantly associated pathways
uncovered eight-times as many hits. All pathways discovered by single
gene enrichment methods were also discovered using factor analysis.
There is strong concordance between P values discovered by the two
methods (Spearman correlation = 0.49, P
[MATH:
=2.1×10−12 :MATH]
). [65]Figure 1 shows a Q-Q plot of P values for both methods against
the theoretical P values under the complete null hypothesis. We see
enrichment of significant P values for both methods, but this is not
present when analyzing the permuted data with factor analysis methods
(green dots). This suggests that age plays a widespread role in the
expression of these pathways.
Figure 1.
[66]Figure 1
[67]Open in a new tab
Q-Q plot of observed P values against theoretical P values for factor
analysis (red dots) and single gene–based methods (in blue).
Permutations (in green) show the results of a combined analysis of 10
permuted datasets. Horizontal lines show Bonferroni significance
thresholds accounting for different numbers of tests (186 tests for
single gene measures in blue, 930 for factor analysis in red, and 9300
for the combined 10 permutation analyses in green).
To investigate which genes drove the significant pathway associations,
we examined how many genes within a significant pathway showed
significant age associations ([68]Table 1 and [69]Table S1). On
average, 16% of genes within the pathways have
[MATH: P<0.05 :MATH]
after adjusting for the number of genes in the pathway, with a minimum
of 1 gene and maximum of 24. The proportion is similar between pathways
of different sizes, in contrary to the traditional pathway enrichment
analysis, where there is bias toward large pathways.
Different KEGG pathways can contain overlapping sets of genes, because
they can describe related biological function. Because of this, our
significant associations with age for different pathways could be
related as a common underlying effect on a given set of genes. To
explore whether the observed age associations are unique to their
pathway or common to multiple pathways, we calculated the Spearman
correlation between those phenotypes. There are 24 pathway phenotypes
with a correlation greater than 0.8 with at least one other phenotype
([70]Table S3). These phenotypes frequently relate to metabolism and
form a highly connected set ([71]Figure S1). We infer from this that
there could be a common effect of age acting on these phenotype
factors. However, these form only a minority of the phenotype factors
with significant signal.
We next explored how different sources of variation in the different
phenotypes analyzed here affect our ability to discover age
associations. We calculated the heritabilities, the proportion of
environmental variance explained by age, and the proportion of variance
explained by the unique environment (Box 1) for KEGG pathways, global
factors (which we have treated as nuisance covariates), and for
individual genes ([72]Figure 2, global factor histograms are not shown
because there are too few phenotypes). The relative differences in
sources of variation between global and pathway factors and the
individual genes are shown in [73]Figure 3. We see that as we move away
from local phenotypes (individual genes) to pathway phenotypes and then
to global phenotypes, the proportion of variation explained by unique
environment decreases. This is because there is a stochastic component
to each single gene’s expression: by taking a weighted average of a
number of genes, we average away this component. If all else were to
remain constant, then this reduction in stochastic noise would
simultaneously increase heritability (as the total variance decreases)
and boost the ability to discover associations with biological meaning,
such as age. We see in the first panel of [74]Figure 3 that the
relative contribution of unique environment to pathway phenotypes is
smaller than the contribution to genes. This also partly explains the
results shown in the second and third panels: a greater proportion of
variance is explained by age and genetic factors (heritability) for
pathway factors than individual gene measurements.
Figure 2.
[75]Figure 2
[76]Open in a new tab
Histograms showing the proportion of environmental variation explained
by age, heritability, and the proportion of variance explained by the
unique environment for pathway factors and the individual gene
measurements.
Figure 3.
[77]Figure 3
[78]Open in a new tab
The relative importance of sources of variation to global, pathway, and
gene phenotypes. Measures of variation shown are the proportion of
variance explained by unique environment, proportion of variance
explained by genetics (heritability), and the proportion of
environmental variation explained by age. To show more clearly the
differences in relative importance of these measures to different
classes of phenotypes, all proportions are scaled such that
contribution to gene phenotypes equals one. Numbers above the bars give
the absolute, unscaled proportions.
When considering global factors, as expected the unique environment is
greatly reduced. However, there is not a strong influence of aging and
heritability in this case is still moderate. This is likely because age
and genetics do not act in a consistent way across large sets of genes.
[79]Leek and Storey (2007) argued that global factors can capture
experimental noise and batch effects. This is consistent with our
findings. Heritabilities and proportion of variance explained by age
for each pathway are reported in [80]Table S4.
We also looked for novel genetic associations with these pathway
phenotypes not seen as single gene expression associations. However,
this was unsuccessful despite the increased heritability in pathway
factors. This is likely due to the genetic architecture of gene
regulation. Genes are regulated both in cis, where a nearby variant
effects the expression of a single gene, and in trans, where a long
range regulatory effect can hit multiple genes ([81]Grundberg et al.
2012). The genetics of pathway phenotypes is a combination of cis
effects on individual genes and trans effects, potentially affecting
multiple genes in the pathway. However, trans variants typically have
much smaller effect size: the increase in the reliability of pathway
phenotypes is insufficient to compensate for the lower power to
discover trans effects. Thus, the only associations discovered were
when single genes loaded heavily enough on a pathway to indirectly
reflect a cis association that could also be detected by a single gene
test.
Discussion
We have seen that both the heritability and the proportion of
environmental variance explained by age are greater for pathway
phenotypes than for individual genes. Consistent with this, we found a
greater proportion of associations for the pathway phenotypes than
using single gene tests using this same dataset ([82]Glass et al. 2013;
23% compared with 7% of phenotypes are significantly associated with
age when using the same 0.05 FDR threshold adopted in that article).
This can be explained by our findings regarding the influence of unique
environment on pathway phenotypes relative to single genes.
Stochasticity in gene expression, which contributes to the unique
environment component that we measure, has been seen to increase with
age. For example, animal model studies ([83]Bahar et al. 2006;
[84]Herndon et al. 2002) have reported increased cell-to-cell variation
in gene expression with age- and tissue-specific decline of functions
associated with stochastic events. Others have found genes associated
with longevity to be strongly regulated in older animals with low
levels of stochasticity and higher levels of heritability
([85]McCarroll et al. 2004; [86]Viñuela et al. 2012). The aim of our
analysis was to find mean effects rather than variance effects
(although both effects are often seen together). By reducing the unique
environment variance component using pathway factor analysis methods,
we arguably focus much more on systematic longevity changes with age
rather than the environmental stochasticity. However, it is difficult
to make inference about causality with gene expression: we cannot know
whether we are observing changes in expression that are driving the
aging process or markers for it. Previous studies have suggested that
the latter may be the case, because often changes in gene expression
occur in response to aging ([87]de Magalhaes et al. 2009).
Of the 57 significant pathways, we frequently see four types of
pathway, all of which have been previously linked with aging: insulin
signaling; sugar and fatty acid metabolism; xenobiotic metabolism; and
cancer-related pathways.
We find the insulin signaling pathway (hsa04910) to be highly
associated with age in our data (
[MATH:
P=3.7×10
−10 :MATH]
). Much evidence has accumulated for the influence of the insulin
signaling pathway on longevity, originating in C. elegans, where
lowered insulin/IGF-1 signaling (IIS) can lead to a significant
increase in life span ([88]Friedman and Johnson, 1988). This effect has
also been seen in the fruit fly D. melanogaster ([89]Clancy et al.
2001) and in mice ([90]Holzenberger et al. 2003). Outside of model
organisms, it has been observed that variants in FOXO transcription
factors related to this pathway can affect longevity in humans
([91]Willcox et al. 2008).
In addition to those related to insulin, our list of age-associated
pathways includes many that are involved in metabolism or glycolosis.
Examples of these include biosynthesis of unsaturated fatty acids
(hsa00980), butanoate metabolism (hsa00650), glycolysis gluconeogenesis
(hsa00010), fructose and mannose metabolism (hsa00051), and valine
leucine and isoleucine biosynthesis (hsa00290). It has previously been
suggested that metabolism-related pathways play roles in aging and
aging-related diseases ([92]Barzilai et al. 2012). In particular,
[93]Houtkooper et al. (2011) showed that glucose and compounds involved
in the metabolism of glucose were biomarkers of aging in liver and
muscle tissue in mice.
Other aging-related pathways include those involved in the metabolism
of xenobiotics that allow cells to deactivate and excrete unexpected
compounds. One example is glutathione metabolism (hsa00480,
[MATH:
P=1.45×10−7 :MATH]
); glutathione is a well-known antioxidant that protects against cell
damage by reactive oxygen species ([94]Pompella et al. 2003).
Finally, previous studies have shown that cancer risk is positively
associated with age after childhood ([95]Finkel et al. 2007; [96]de
Magalhães 2013). For example, cellular senescence, when a cell loses
the ability to divide, can form a break on cancer development, and
clearing such senescent cells can delay the development of
age-associated disorders ([97]Baker et al. 2011). There are a number of
pathways on our list that have been linked to cancer, particularly skin
cancer. These include melanogenesis (hsa04916,
[MATH:
P=3.34×10−10 :MATH]
), the PPAR signaling pathway (hsa03320,
[MATH:
P=1.83×10−9 :MATH]
), the hedgehog signaling pathway (hsa04340,
[MATH:
P=1.12×10−7 :MATH]
), and glioma (hsa05214,
[MATH:
P=4.26×10−7 :MATH]
)
In addition to age, other phenotypes have been linked to expression
patterns of multiple genes. For example, BMI has been linked to
expression patterns in adipose tissue of multiple genes within a group
that share a common trans master regulator, and such phenotypes could
mediate between expression and diseases such as type 2 diabetes
([98]Small et al. 2011). Principal components and factor analysis have
also been suggested as a way to build classifiers for binary traits
([99]Hastie et al. 2000), perhaps to predict prognosis of disease from
gene expression data. The ability of pathway phenotypes to provide
reliable measures of expression with direct biological interpretation
means they could also be applied in these situations to understand the
relationship between expression and such phenotypes.
Our analysis shows that factor analysis applied to gene expression data
effectively reduces stochastic noise in summaries of gene expression
patterns, giving more power to discover associations. These phenotypes
are substantially more heritable than individual genes. Using them we
can improve our ability to identify biological processes underpinning
aging. This is consistent with the idea that removing latent factors
that exert broad effects on gene expressions increases power in
associations. We show that the same idea can be used to create pathway
factors that are robust and interpretable. Finally, our analysis
reveals pathways that have been seen to be important in longevity from
a number of previous studies as well as novel pathways that can be
further investigated.
Acknowledgments