This document summarizes a presentation on multi-trait modeling in polygenic scores. It discusses sparse regression models like LASSO to build polygenic risk scores (PRS) from large genetic datasets. It introduces multi-PRS models that combine disease PRS with biomarker PRS to improve disease prediction. It also presents genetic component-based PRS models called DeGAs-PRS that group genetic variants into components for enhanced interpretation. The presentation evaluates these multi-trait modeling approaches using large-scale UK Biobank data.

1. 複数の表現型を考慮したポリジェニック・スコア解析
Multi-trait modeling in polygenic scores
谷川 洋介
Yosuke Tanigawa
Postdoc @ Computational Biology Lab
(PI: Prof. Manolis Kellis), MIT CSAIL
2022/3/2 (Wed.) 10:05 am (JST) @ Zoom
大阪大学医学系研究科
バイオインフォマティクスセミナー
1
@yk_tani
https://yosuketanigawa.com/
Slides: https://bit.ly/20220302-tanigawa

2. Polygenic risk scores (PRSs) combine
genetic associations across many variants
1) Genome-wide association study (GWAS)
on large-scale cohorts
2) Polygenic risk scores (PRSs)
2
i-th individual G: genotype
j-th variant β: effect size
Bycroft et al., Nature (2018)

3. Polygenic risk scores (PRSs) combine
genetic associations across many variants
1) Genome-wide association study (GWAS)
on large-scale cohorts
2) Polygenic risk scores (PRSs)
3
i-th individual G: genotype
j-th variant β: effect size
Uffelmann et al., Nat Rev Methods Primers (2021)

4. PRS predictions are sometimes useful
4
Population stratification with genetics Instruments for causal inference
PRS may inform individuals with high genetic liability
PRS(biomarker)
associations with lifespan
Uffelmann et al., Nat Rev Methods Primers (2021); Wray et al., JAMA Psychiatry (2020); Sakaue*, Kanai*, et al., Nat Med (2020).

5. Outline: multi-trait modeling in polygenic scores
1. Sparse PRS models with snpnet
2. multi-PRS
3. DeGAs-PRS & multi-snpnet
5

6. Challenges and opportunities in PRS models
- To train PRS models:
- Identify set of genetic variants in the model
- Estimate effect size (β) for each
- Challenges
- Linkage-disequilibrium among genetic variants
- Large dataset (n = 300k, p = 1M+)
6
Khera, et al., Nat Gen (2018).
i-th individual G: genotype
j-th variant β: effect size

7. Challenges and opportunities in PRS models
- To train PRS models:
- Identify set of genetic variants in the model
- Estimate effect size (β) for each
- Challenges
- Linkage-disequilibrium among genetic variants
- Large dataset (n = 300k, p = 1M+)
- Bayesian models show improved predictive performance
- Genome-wide polygenic risk score (Khera et al) with 6M+ variants
7
Khera, et al., Nat Gen (2018).
i-th individual G: genotype
j-th variant β: effect size
We typically don’t assume
6M causal variants for
common complex traits

8. Sparse regression model with Lasso
- One alternative: regularized regression on individual-level data
- e.g. Lasso
- We developed Batch screening iterative Lasso (BASIL)
- Efficient screening based on “strong rule” (Tibshirani et al 2012)
- Solves Lasso via iterative procedure
8
Junyang Qian
Qian, Tanigawa, et al. PLOS Gen. (2020).

9. Batch screening iterative Lasso (BASIL)
BASIL (= BAtch Screening Iterative Lasso) in R snpnet package
9
3 steps per iteration
1. Screening
2. Lasso Fit (glmnet)
3. KKT Check
Qian, Tanigawa, et al. PLOS Gen. (2020).

10. BASIL/snpnet model are sparse, yet have
comparable predictive performance
- The snpnet PRS models (Lasso & Elastic-Net) have comparable
predictive performance with SBayesR
- Standing height was one of the most polygenic traits.
- Hight PRS model has 47k variants (5% of non-zero BETAs)
10
Qian, Tanigawa, et al. PLOS Gen. (2020).; Tanigawa, Qian, et al. PLOS Gen in press
Hold-out
test
set
R
2
Hold-out
test
set
AUC
snpnet snpnet

11. Outline: multi-trait modeling in polygenic scores
1. Sparse PRS models with snpnet
2. multi-PRS
3. DeGAs-PRS & multi-snpnet
11
Sparse snpnet PRS models show
competitive performance

12. Genetics of 35 biomarkers study in UK Biobank
12
Sinnott-Armstrong*, Tanigawa*, et al. Nat Gen. 2021
Joint work w/ Nasa
Sinnott-Armstrong

13. Genetics of 35 biomarkers study in UK Biobank
13
Cardiovascular
Bone and Joint
Diabetes
Liver
Hormone
Renal
Polygenic risk scores (PRSs) for 35 biomarkers
Sinnott-Armstrong*, Tanigawa*, et al. Nat Gen. 2021

14. Take extreme in PRS for biomarkers
Compare odds ratio for disease
outcome relative to 40-60%ile bin
Applied PheWAS for ~160 diseases
Disease cases are enriched in PRS tails
14
Lewis, C. M. & Vassos, E.
Genome Medicine (2020).
Sinnott-Armstrong*, Tanigawa*, et al. Nat Gen. 2021
top/bottom 1%, 10%, etc.

15. Disease cases are enriched in PRS tails
Take extreme in PRS for biomarkers
Identify diseases with biomarker PRS
associations
Compare odds ratio for disease
outcome relative to 40-60%ile bin
Applied PheWAS for ~160 diseases
15
Sinnott-Armstrong*, Tanigawa*, et al. Nat Gen. 2021

16. Multi-PRS - a linear combination of
a disease PRS and biomarker PRSs
- Multiple observations suggest “biomarkers → disease” links
- PRS-PheWAS analysis
- Biomarkers are more heritable than disease
- Mendelian Randomization
- We define Multi-PRS as weighted sum of PRSs
i.e. w1
(PRS1
) + w2
(PRS2
) + w3
(PRS3
) + …
16
Sinnott-Armstrong*, Tanigawa*, et al. Nat Gen. 2021

17. Weights of multi-PRS comes from another
penalized regression model (e.g. Lasso)
Multi-PRS: w1
(PRS1
) + w2
(PRS2
) + w3
(PRS3
) + …
17
Sinnott-Armstrong*, Tanigawa*, et al. Nat Gen. 2021
Example:
Multi-PRS(Chronic kidney disease) =
- 0.75 x PRS(eGFR)
- 0.41 x PRS(Creatinine)
+ 0.30 x PRS(Cystatin C)
+ 0.25 x PRS(Bilirubin)
…

18. multi-PRS improves disease prevalence prediction
Chronic kidney
disease (CKD)
Other diseases in
UK Biobank
18
Sinnott-Armstrong*, Tanigawa*, et al. Nat Gen. 2021

19. multi-PRS models improves incident disease
prediction in FinnGen
The multi-PRS model is replicated in Finnish cohort (FinnGen)
19
Nina Mars
Sinnott-Armstrong*, Tanigawa*, et al. Nat Gen. 2021

20. - Why does multi-PRS work?
- Quantitative traits have more power (J. Yang et al 2010)
- Genetic correlation between biomarkers and disease
- Phenotyping challenges in some disease phenotypes
- Two complementary approaches to improve
predictive performance
- 1) Sample size → increase in power
- 2) Multi-trait analysis
What we learned from multi-PRS?
20

21. Outline: multi-trait modeling in polygenic scores
1. Sparse PRS models with snpnet
2. multi-PRS
3. DeGAs-PRS & multi-snpnet
21
Sparse snpnet PRS models show
competitive performance
Multi-trait PRS can improve
performance of disease PRS

22. Multi-PRS
Genetics Biomarkers (Molecular traits) Disease
Genetic component-based model as an alternative
Genetic components
Genetic component-based multi-trait PRSs
22

23. Extreme polygenicity & pleiotropy in
the genetics of common complex traits
23
Genetic
variants
Complex
traits
- Polygenicity: many variants - one trait
- Pleiotropy: one variant - many traits
- Large number of associations in
population-based cohorts
- Can we group them together for enhanced interpretation?

24. Decomposition of genetic associations (DeGAs)
provides “genetic components”
24
Tanigawa*, Li*, et al. Nat Comm (2019).
Decomposition
with tSVD
Jiehan Li

25. Genetic component-based PRS models with
DeGAs-PRS (dPRS)
- PRS of individuals as the
weighted sum of
component-PRS
- Offers interpretation
- patient subtyping based
on genetic risk profiles
25
Aguirre, Tanigawa, et al. Eur J Hum Gen (2021).
Genetics Genetic components Disease
Matthew Aguirre

26. Sparse reduced-rank regression (SRRR) in
multiSnpnet fits sparse component-based PRS
26
Qian, Tanigawa, et al. Ann Appl Stat (in press).
(1)
(2)
Junyang Qian
- Example: Asthma & clinically related traits
- Predictive performance improvements
for asthma & basophil count
- Component-analysis with SVD offers
interpretation

27. Summary: multi-trait modeling in polygenic scores
1. Sparse PRS models with snpnet
2. multi-PRS
3. DeGAs-PRS & multi-snpnet
27
Sparse snpnet PRS models show
competitive performance
Multi-trait PRS can improve
performance of disease PRS
Genetic component-based PRS
models offer interpretation
Slides: https://bit.ly/20220302-tanigawa

28. Future directions
Polygenic risk score research:
- PRS with integrative genomics
- Single-cell biology & Epigenomics
- Cell-type-specific biological knowledge
- Clinical relevance and application
- Enhance transferability of PRS across populations
My current scientific training:
28
Postdoc training with
Prof. Manolis Kellis
at

29. Acknowledgements
Dept. Biomedical Data Science
- Matthew Aguirre
- Manuel A. Rivas
- the Rivas lab
Dept. Statistics
- Junyang Qian
- Trevor Hastie
- Rob Tibshirani
Dept. Genetics, Stanford
- Nasa Sinnott-Armstrong
- Jonathan Pritchard
University of Helsinki
- Nina Mars
- Samuli Ripatti
29
Funding supports:
Nasa Sinnott-Armstrong
Junyang Qian
Manuel A. Rivas Rivas lab members
M. Aguirre N. Mars R. Tibshirani & T. Hastie

30. References
1. Qian, Tanigawa, et al. PLoS Gen. (2020). (PMID: 33095761)
- Batch screening iterative Lasso (BASIL) & R snpnet package
2. Tanigawa, Qian, et al. PLoS Gen. (in press) (doi: 10.1101/2021.09.02.21262942)
- Phenome-wide application of BASIL/snpnet
3. Sinnott-Armstrong*, Tanigawa*, et al. Nat Gen. (2021). (PMID: 33462484)
- Genetics of 35 biomarkers, multi-PRS
4. Tanigawa*, Li*, et al. Nat Comm (2019). (PMID: 31492854)
- DeGAs - decomposition of genetic associations
5. Aguirre, Tanigawa, et al. Eur J Hum Genet. (2021). (PMID: 33558700)
- DeGAs-PRS (dPRS)
6. Qian, Tanigawa, et al. Ann Appl Stat. (in press). (doi: 10.1101/2020.05.30.125252)
- Sparse reduced rank regression (SRRR) & R multiSnpnet package
30
Slides: https://bit.ly/20220302-tanigawa