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Hae Kyung Im, PhD

Predicting Disease Risk

Polygenic Risk Scores

April 18, 2022

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Polygenic Additive Model

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Polygenic Additive Model

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Estimating Parameters of Polygenic Additive Model

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Can we fit all SNPs at the same time?

Why can’t we estimate betas by least squares?

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Estimating Parameters of Polygenic Additive Model

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Can we fit all SNPs at the same time?

Why can’t we estimate betas by least squares?

Too many parameters and too few observations

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Rule of Thumb

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10 data points per parameter

In a pinch, at least 5 data points per parameter

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Solution: Random Effects Reduces # Parameters

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Can we fit all SNPs at the same time?

Why can’t we estimate betas by least squares?

Too many parameters and too few observations

Assume

and estimate just the

Solution

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Mixed Effects Modeling

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are random

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Connection to EMMAX Used To Account for Population Structure?

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Y

Recall EMMAX, mixed effects approach to adjust for population structure and relatedness

Y = x_test · β_test + u + ε
u ~ N(0,σ²·K)

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Review: norm of vectors

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L2 Norm of Vector

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In a GWAS we minimize the L2 norm of the error term

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In a GWAS we minimize the L2 norm of the error term

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Which one do you think is the L1 norm?

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Prediction of Complex Traits

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Simple Polygenic Risk Score

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Nature 2009

Just use GWAS effect sizes

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Tricks to Deal with Too Many Parameters

Model βs as random effects
Use GWAS effects (fit one SNP at a time, ignoring the rest)
Penalized likelihood is another way to deal with too many parameters

also referred to as regularization

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Best Linear Unbiased Prediction (BLUP)/Ridge

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Penalized regression

Ridge

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LASSO/Elastic Net Prediction

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Penalized regression

LASSO

Elastic Net

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Whole Genome Prediction Approaches

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Advantages of Simple Polygenic Scores

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Main advantage easy to get or calculate, scalable

GWAS results publicly available

vs. multivariate approaches (ridge, elastic net, BSLMM) need individual data

although some fine-mapping methods allow inferring

multivariate regression results from summary statistics

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Polygenic Scores Can Be Improved Using LD Information

Pruning and thresholding (PRSice)
Lasso-sum (Mak et al)
LD-Pred (Vilhjálmsson)
RSS (Zhu)
S-BayesR (Lloyd-Jones)
PRS-CS

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Zhu, X., & Stephens, M. (2017). Bayesian large-scale multiple regression with summary statistics from genome-wide association studies. AOAS

Vilhjálmsson et al. (2015). Modeling Linkage Disequilibrium Increases Accuracy of Polygenic Risk Scores. AJHG

Mak,et al (2017). Polygenic scores via penalized regression on summary statistics. Genetic Epidemiology, 41(6), 469–480.

Luke R. Lloyd-Jones (2019). Improved polygenic prediction by Bayesian multiple regression on summary statistics. BioRxiv.

Ge, T., Chen, CY., Ni, Y. et al. Polygenic prediction via Bayesian regression and continuous shrinkage priors. Nat Commun 10, 1776 (2019). https://doi.org/10.1038/s41467-019-09718-5

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Importance of Having Good LD Reference Data

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All the methods listed in the previous page rely on having good LD reference data.

With increasing sample sizes, methods that use summary statistics and infer results similar to having individual level data are critical.

- Summary statistics from GWAS are being widely shared.

- LD reference from the same study is not, this is something that needs to change

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What about Deep Learning?

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"In all, over the range of traits evaluated in this study, CNN performance was competitive to linear models, but we did not find any case where DL outperformed the linear model by a sizable margin."

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DNA Sequencing to Gene Expression

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https://www.nature.com/articles/s41592-021-01252-x

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Clinical Utility of Genetic Predictions

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Genomic Prediction of Height in UK Biobank

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Lello et al (2018). Accurate Genomic Prediction of Human Height. Genetics

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Prevalence of Coronary Artery Disease Increases with PRS

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Khera et al (2018) Nature Genetics

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Prevalence of Type 2 Diabetes Increases with PRS

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Mahajan et al (2019) Nature Genetics

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Breast Cancer: PRS is Predictive of Risk

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Mavaddat N et al Polygenic Risk Scores for Prediction of Breast Cancer and Breast Cancer Subtypes. Am J Hum Genet. 2019 Jan 3;104(1):21-34. doi: 10.1016/j.ajhg.2018.11.002. Epub 2018 Dec 13. PMID: 30554720; PMCID: PMC6323553.

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PRS + Family History Improves Risk Prediction

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Kachuri, L., Graff, R.E., Smith-Byrne, K. et al. Pan-cancer analysis demonstrates that integrating polygenic risk scores with modifiable risk factors improves risk prediction. Nat Commun 11, 6084 (2020). https://doi.org/10.1038/s41467-020-19600-4

Fig. 3: Predicted 5-year absolute risk trajectories across strata defined by family history and percentiles of the polygenic risk score (PRS) distribution.

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Do PRS work for everyone?

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Portability of Prediction Across Ancestries

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Martin et al 2019 NG https://www.nature.com/articles/s41588-019-0379-x

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Ancestry Composition of Current GWAS

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Martin et al 2019 NG https://www.nature.com/articles/s41588-019-0379-x

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Allele Frequency and LD Differ Across Ancestries

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Martin et al 2019 NG https://www.nature.com/articles/s41588-019-0379-x

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PRS Does Not Transfer Well Across Populations

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Martin et al 2019 NG https://www.nature.com/articles/s41588-019-0379-x

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Investments in more diverse samples are being made

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Bioethical Issues with Embryo Screening

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Embryo Selection Active Area of Research

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Utility of polygenic embryo screening for disease depends on the selection strategy

Polygenic risk scores (PRSs) have been offered since 2019 to screen in vitro fertilization embryos for genetic liability to adult diseases, despite a lack of comprehensive modeling of expected outcomes. Here we predict, based on the liability threshold model, the expected reduction in complex disease risk following polygenic embryo screening for a single disease. A strong determinant of the potential utility of such screening is the selection strategy, a factor that has not been previously studied. When only embryos with a very high PRS are excluded, the achieved risk reduction is minimal. In contrast, selecting the embryo with the lowest PRS can lead to substantial relative risk reductions, given a sufficient number of viable embryos. We systematically examine the impact of several factors on the utility of screening, including: variance explained by the PRS, number of embryos, disease prevalence, parental PRSs, and parental disease status. We consider both relative and absolute risk reductions, as well as population-averaged and per-couple risk reductions, and also examine the risk of pleiotropic effects. Finally, we confirm our theoretical predictions by simulating ‘virtual’ couples and offspring based on real genomes from schizophrenia and Crohn’s disease case-control studies. We discuss the assumptions and limitations of our model, as well as the potential emerging ethical concerns.

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Embryo Selection Active Area of Research

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Whole-genome risk prediction of common diseases in human preimplantation embryos

Preimplantation genetic testing (PGT) of in-vitro-fertilized embryos has been proposed as a method to reduce transmission of common disease; however, more comprehensive embryo genetic assessment, combining the effects of common variants and rare variants, remains unavailable. Here, we used a combination of molecular and statistical techniques to reliably infer inherited genome sequence in 110 embryos and model susceptibility across 12 common conditions. We observed a genotype accuracy of 99.0–99.4% at sites relevant to polygenic risk scoring in cases from day-5 embryo biopsies and 97.2–99.1% in cases from day-3 embryo biopsies. Combining rare variants with polygenic risk score (PRS) magnifies predicted differences across sibling embryos. For example, in a couple with a pathogenic BRCA1 variant, we predicted a 15-fold difference in odds ratio (OR) across siblings when combining versus a 4.5-fold or 3-fold difference with BRCA1 or PRS alone. Our findings may inform the discussion of utility and implementation of genome-based PGT in clinical practice.

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Orchid Offers Preconception Testing

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https://twitter.com/alexia/status/1380236427485667335

Are they helping eliminate disease or implementing eugenics?

You can check out Lior Pachter's opinionated take on this subject

https://liorpachter.wordpress.com/2021/04/12/the-amoral-nonsense-of-orchids-embryo-selection/

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Effect on Schizophrenia Risk Selection

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Title Text

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Fig. 1: Hazard ratios (HR) per one standard deviation (SD) increase in the standardized polygenic risk score (PRS).