Summary of paper "Pathways-Driven Sparse Regression Identifies Pathways and Genes Associated with High-Density Lipoprotein Cholesterol in Two Asian Cohorts", Silver M, Chen P, Li R, Cheng C-Y, Wong T-Y, et al. In PLOS Genetics, 2013

1. Pathways-Driven Sparse Regression Identifies
Pathways and Genes Associated with High-Density
Lipoprotein Cholesterol in Two Asian Cohorts
Silver M, Chen P, Li R, Cheng C-Y, Wong T-Y, et al.
In PLOS Genetics, 2013

2. Introduction
• Genes do not act in isolation, but interact in complex
networks or pathways
• Rather than univariate approaches, a joint modelling
approach, a dual-level, sparse regression model is proposed
• can simultaneously identify pathways and genes for pathway
selection
• Pathways-driven gene selection in a search for pathways and genes
associated with variation

3. Sparse group lasso model
• N individuals, P SNPs, (N x P) genotype matrix X, L pathways
• Assumptions
• All P SNPs may be mapped to L groups or pathways
• Pathways are disjoint or non-overlapping
causal SNPs
causal pathways
Pathway level constraint SNP level constraint
𝛼 controls how the sparsity constraint is
distributed between the two penalties
𝜆 controls the degree of sparsity in 𝛽

4. SGL model estimation
• To estimate 𝛽 𝑆𝐺𝐿
,
• block, or group-wise coordinate gradient
descent (BCGD) algorithm
• Select a pathway 𝑙
• Select SNP 𝑗 in selected pathway 𝑙
• Pathway, SNP partial residuals
• Regress out the current estimated effects of all
other pathways and SNPs

5. SGL simulation study 1
• Hypothesis
• causal SNPs are enriched in a given pathway
• pathway-driven SNP selection using SGL will outperform
simple lasso selection
• Randomly select 5 causal SNPs from a single pathway / all
2500 SNPs (without pathway information)

6. The problem of overlapping pathways
• Genes and SNPs may map to multiple pathways
• The optimization is no longer separable into groups
(pathways)
• Not be able to select pathways independently
• By duplicating SNP predictors, SNPs belonging to
more than one pathway can enter the model
separately
• SNPs are selected in each pathway whose joint
effects pass a pathway selection threshold,
irrespective of overlaps between pathways
• Pathways are independent
• they do not compete in the model estimation process
Partially overlapping causal SNPs

7. The problem of overlapping pathways
•
• each pathway is regressed against the phenotype vector y
• Only coordinate gradient descent within selected
pathway (SGL-CGD)
• Under the independence assumption, the estimation of
each 𝛽𝑙
∗
doesn’t depend on the other estimates 𝛽 𝑘
∗
• Need only record the set of selected SNPs in each
selected pathway

8. SGL simulation study 2
Figure 5. SGL Simulation Study with overlapping pathways
Table 1. Mean number of pathways and SNPs selected by each model
at each effect size, γ, across 2000 MC simulations
• SNPs are mapped to 50 overlapping pathways,
each containing 30 SNPs
• Each pathway overlaps any adjacent pathway
by 10 SNPs
• The number of selected pathways or SNPs
increases with decreasing effect size, as the
number of pathways close to the selection
threshold set

9. SGL simulation study 2
• Pathway and SNP selection power and
False positive rates (FPR) at MC
simulation z
• SGL-CGD consistently outperforms SGL,
both in terms of pathway selection
sensitivity and control of false positives
• SGL-BCGD typically has a higher FPR
than SGL-CGD, since more SNPs are
selected from non-causal pathways
• SGL-CGD is more often able to select
both causal pathways, and to select
additional causal SNPs that are missed
by SGL
Figure 6. SGL-CGD vs SGL-BCGD performance

10. Pathway and SNP selection bias
• Biasing factors
• pathway size, varying patterns of SNP-SNP correlations, and gene
sizes
• An adaptive weight-tuning strategy to reduce selection bias
• tuning the pathway weight vector 𝑤 to ensure that each pathway
must have an equal chance of being selected

11. Ranking variables
• A resampling strategy
• calculate pathway, gene and SNP selection frequencies by repeatedly
fitting the model over B subsamples of the data, at fixed values for 𝛼 and
𝜆
• exploit knowledge of finite sample variability obtained by subsampling, to
achieve better estimates of a variable's importance
• can rank pathways, genes and SNPs in order of their strength of
association with the phenotype
• Pathways or SNPs and genes are ranked in order of their selection
probabilities

12. Simulation study 3
• Evaluate ranking strategies
• Use real genotype and pathways data
• genome-wide SNP dataset ‘SP2’
• KEGG pathways database
• SNP ranking
• TP: selected SNPs that tag at least one causal
SNP
• FP: selected SNPs which do not tag any causal
SNP
• gene ranking
• TP: selected causal genes(map to true causal SNP)
• FP: selected non-causal genes
• Compared with SNP and gene rankings
using a univariate, regression-based
quantitative trait test (QTT)
K: the number of causal SNPs
GV, TV: proportion of trait variance

13. Simulation study 3
TPR: The proportion of subsamples in
which the correct causal pathway is
selected
Figure 7. A–F: SNP and gene ranking performance for the six different scenarios

14. Pathway mapping
• Genes are mapped to pathways using information on
gene-gene interactions.
• Many SNPs and genes do not map to any known
pathway.
• Genes and SNPs may map to more than one pathway.
• Many SNPs cannot be mapped to a pathway since
they do not map to a mapped gene.
Available SNPs
492,639 SNPs (SP2)
515,503 SNPs (SiMES)
Genes: GRCH36/hg18
21,004 genes
239,757 SNPs (SP2)
251,089 SNPs (SiMES)
mapped to
18,845 genes (SP2)
18,919 genes (SiMES)
within 10kbp
Pathways: KEGG
185 Pathways containing
5,267 distinct genes
SNP to gene
mapping
75,389 SNPs (SP2)
78,933 SNPs (SiMES)
mapped to
4,734 genes (SP2)
4,751 genes (SiMES)
and 185 pathways
SNP to pathway
mapping

15. Results
• Pathways-driven SNP selection on the SP2 and SiMES
datasets separately using SGL
• Combine this with the subsampling procedure to highlight
pathways and genes associated with variation
• Compare results from both datasets

16. • Compare with the resulting pathway and
SNP selection frequency distributions with
null distributions
• A greater number of SNPs contribute to
increase the number of pathways
• The number of SNPs may affect the
resulting pathway and SNP rankings
• Optimal 𝛼=?
Table 5. Separate combinations of regularisation
parameters, 𝜆 and 𝛼 used for analysis of the SP2 dataset.
Pathway level constraint SNP level constraint
Pathway and SNP selection results

17. Pathway and SNP selection results
Figure 11. Empirical and null pathway selection
frequency distributions for all 185 KEGG pathways
with the SP2 dataset
Figure 12. Empirical and null SNP selection
frequency distributions with the SP2 dataset
Figure 14. Empirical and null pathway (top) and
SNP (bottom) selection frequency distributions for
the SiMES dataset
𝛼 = 0.85
𝛼 = 0.95
clearer separation of
empirical and null
distributions
Biased empirical pathway and
SNP selection frequency
distributions
𝛼 = 0.95

18. Pathway and SNP selection results
Figure 13. SP2 dataset: scatter plots comparing empirical and null
selection frequencies presented in Figures 11 and 12
Figure 15. SiMES dataset: Scatter plots comparing empirical and null pathway (left)
and SNP (right) selection frequencies presented in Figure 14

19. • Increased correlation between empirical and null selection
frequency distributions at the lower 𝛼 increase bias in the
empirical results
• The selection of too many SNPs will add noise, bias
Table 6. SP2 dataset: Pearson correlation coefficients (r) and p-
values for the data plotted in Figure 13
Table 9. SiMES dataset: Pearson correlation coefficients (r) and
p-values for the data plotted in Figure 15.
Pathway and SNP selection results

20. Top 30 pathways and genes
... … … … …
Table 7. SP2 dataset: Top 30 pathways, ranked by pathway selection frequency, 𝜋 𝑝𝑎𝑡ℎ
.
Table 8. SP2 and SiMES datasets: Top 30 genes ranked by
gene selection frequency, 𝜋 𝑔𝑒𝑛𝑒
.
... … … …

21. Top 30 pathways
... … … … …
Table 10. SiMES dataset: Top 30 pathways, ranked by pathway selection frequency, 𝜋 𝑝𝑎𝑡ℎ
.

22. Comparison of ranked pathway and gene lists
• Pathway rankings
Figure 16. Comparison of top-k SP2 and SiMES pathway rankings
Normalized Canberra distance(left), FDR q-values (right)
Table 11. Consensus set of important pathways, Ψ25
𝑝𝑎𝑡ℎ
, for SP2 and
SiMES datasets with k = 25.
closest agreement when k = 25

23. Comparison of ranked pathway and gene lists
• Gene rankings
Figure 17. Comparison of top-k SP2 and SiMES gene rankings, for k = 1,…,500.
Normalized Canberra distance(left), FDR q-values (right)
Table 13. Top 30 consensus genes ordered by their average rank, 𝜓244
𝑔𝑒𝑛𝑒
closest agreement when k=244

24. Discussion
• A method for the detection of pathways and genes associated with a
quantitative trait
• uses a sparse regression model, the sparse group lasso, that enforces sparsity at
the pathway and SNP level.
• identify important pathways and also maximize the power to detect causal SNPs
• Simulation studies
• SGL has greater SNP selection power than lasso
• a modified SGL-CGD estimation algorithm that treats pathways as independent,
may offer greater sensitivity for the detection of causal SNPs and pathways
• combines with a weight-tuning algorithm to reduce selection bias
• a resampling technique is designed to provide a robust measure of variable
importance

25. Thank you
Q & A