Fully powered polygenic prediction using summary statistics

Transcription

1 Fully powered polygenic prediction using summary statistics Alkes L. Price Harvard T.H. Chan School of Public Health October 7, 015 To download slides of this talk: google Alkes HSPH

2 Summary statistics are widely available Nat Genet editorial, July 01

3 Outline 1. A brief history of summary statistic genetics. Introduction to polygenic prediction using summary statistics 3. LDpred method for polygenic prediction using summary statistics 4. Application of LDpred to real data sets

4 Outline 1. A brief history of summary statistic genetics. Introduction to polygenic prediction using summary statistics 3. LDpred method for polygenic prediction using summary statistics 4. Application of LDpred to real data sets

5 Definition of summary statistics Definition: Summary statistics consist of: GWAS association z-scores for each typed or imputed SNP + Sample sizes on which z-scores were computed (may vary by SNP) Note: Many applications also require LD information computed from a reference panel (e.g Genomes or UK10K) using a population very similar to the target sample.

6 Meta-analysis can be performed using summary statistics Evangelou & Ioannidis 013 Nat Rev Genet

7 Joint and conditional analysis can be performed using summary statistics Yang et al. 01 Nat Genet

8 Lee et al. 013 Bioinformatics; Pasaniuc et al. 014 Bioinformatics also see Park et al. 015 Bioinformatics, Lee et al. 015 Bioinformatics Imputation can be performed using summary statistics

9 Rare variant meta-analysis can be performed using summary statistics Lee et al. 013 AJHG; Hu et al. 013 AJHG; Liu et al. 014 Nat Genet also see Clarke et al. 013 PLoS Genet, Tang & Lin 015 AJHG

10 Genetic variance and covariance can be inferred using summary statistics Palla & Dudbridge 015 AJHG; Bulik-Sullivan et al. 015 Nat Genet

11 Functional enrichment can be inferred using summary statistics Pickrell 014 AJHG; Kichaev & Pasaniuc 015 AJHG; Finucane et al. 015 Nat Genet

12 Many projects at ASHG 015 using summary statistics Invited talks Pickrell, Pasaniuc, Im (this session) Platform talks 11 Gusev, 77 Cichonska, 0 Golan, 7 Park Posters 791 Kichaev, 797 Shi, 807 Roytman, 860 Salem, 868 Pare, 1301 Wu, 1334 Zhu, 1357 Chatterjee, 1477 Brown, 1618 Li, 1668 Khawaja, 1686 Lee, 1687 Zhao, 178 Torres, 1867 O Connor

13 Outline 1. A brief history of summary statistic genetics. Introduction to polygenic prediction using summary statistics 3. LDpred method for polygenic prediction using summary statistics 4. Application of LDpred to real data sets

14 Genetic prediction: why care? Erbe et al. 01 J Dairy Sci; Goss et al. 011 New Engl J Med

15 Using only genome-wide significant SNPs is a Stone Age genetic prediction method How should we conduct genetic prediction, Fred? ˆ k ˆ i x i (published SNPs) ik φ k = phenotype for sample k β i = effect size for SNP i x ik = genotype for SNP i, sample k Prediction r is less than half the r attained by polygenic prediction PGC-SCZ 014 Nature; Vilhjalmsson et al. 015 AJHG

16 Polygenic prediction can be performed using genome-wide summary statistics ˆ k ˆ i x i (all GWAS SNPs) ik φ k = phenotype for sample k β i = effect size for SNP i x ik = genotype for SNP i, sample k

17 Daetwyler et al. 008 PLoS ONE; Wray et al. 013 Nat Rev Genet also see Speed & Balding 014 Genome Res (multiblup) Is polygenic prediction using raw genotypes more accurate than using summary statistics? Answer: slightly. h g = heritability explained by SNPs M = number of (unlinked) SNPs N = number of training samples r h g h g h g M / N < r h g h g (1 h r g ) M / N using summary statistics: fit each SNP individually using raw genotypes: fit all SNPs simultaneously (BLUP prediction; Henderson 1975 Biometrics)

18 Accounting for non-infinitesimal architectures can improve polygenic prediction Infinitesimal (Gaussian) architecture: i ~ N 0, hg / M ˆ hg i ~ i N 0,1 / N => E( i ˆ i ) ˆ i hg M / N Uniform shrink on estimated effect sizes is appropriate ˆi

19 Accounting for non-infinitesimal architectures can improve polygenic prediction Non-infinitesimal architecture: (e.g. point-normal mixture, mixture of normals, etc.) Non-uniform shrink on estimated effect sizes is appropriate ˆi

20 Accounting for non-infinitesimal architectures can improve polygenic prediction Infinitesimal (Gaussian) architecture: i ~ N 0, hg / M ˆ hg i ~ i N 0,1 / N => E( i ˆ i ) ˆ i hg M / N Uniform shrink on estimated effect sizes is appropriate Non-infinitesimal architecture: (e.g. point-normal mixture, mixture of normals, etc.) Non-uniform shrink on estimated effect sizes ˆi is appropriate Standard heuristic approach: P-value thresholding ˆ ˆ k i x (Note: requires optimization of ik P T threshold in validation samples) i P-value < P T Purcell et al. 009 Nature; Chatterjee et al. 013 Nat Genet; Dudbridge 013 PLoS Genet ˆi

21 Purcell et al. 009 Nature; Stahl et al. 01 Nat Genet also see Rietveld et al. 013 Science (COJO) Accounting for linkage disequilibrium Problem: can improve polygenic prediction ˆ k ˆ i x i P-value < P T ik does not account for LD b/t SNPs Standard heuristic approaches: Random LD-pruning: prune SNPs (e.g. r < 0.), removing one of each pair of linked SNPs (decide randomly which SNP to remove) Informed LD-pruning (LD-clumping): prune SNPs, removing one of each pair of linked SNPs (remove SNP with less significant P-value in training data)

22 Pruning + Thresholding is widely used Purcell et al. 009 Nature; Lango Allen et al. 010 Nature; Ripke et al. 011 Nat Genet; Stahl et al. 01 Nat Genet; Deloukas et al. 013 Nat Genet; Ripke et al. 013 Nat Genet; Chatterjee et al. 013 Nat Genet; Dudbridge 013 PLoS Genet; PGC-SCZ 014 Nature

23 Pruning + Thresholding is widely used, but does not attain maximum prediction accuracy Simulations at different proportions p of causal SNPs: Non-infinitesimal Non-infinitesimal Infinitesimal Infinitesimal h g Vilhjalmsson et al. 015 AJHG

24 Outline 1. A brief history of summary statistic genetics. Introduction to polygenic prediction using summary statistics 3. LDpred method for polygenic prediction using summary statistics 4. Application of LDpred to real data sets

25 LDpred computes posterior means under a ˆ point-normal prior, accounting for LD k where E ( i ˆ i ) x i (all GWAS SNPs) E ˆ ) ( i i ik φ k = phenotype for sample k β i = effect size for SNP i x ik = genotype for SNP i, sample k are posterior mean effect sizes Vilhjalmsson et al. 015 AJHG

26 LDpred computes posterior means under a ˆ point-normal prior, accounting for LD k E ( i ˆ i ) x i (all GWAS SNPs) ik φ k = phenotype for sample k β i = effect size for SNP i x ik = genotype for SNP i, sample k where E( ˆ i i ) are posterior mean effect sizes based on point-normal prior with parameters: h g = heritability explained by SNPs (estimated from training data) p = proportion of causal SNPs (optimized in validation samples) LD from a reference panel Use validation samples as LD reference (restrict to SNPs with validation data) Vilhjalmsson et al. 015 AJHG

27 In the special case of no LD between SNPs, posterior means can be computed analytically E ˆ ( i i ) hg h g Mp / N p i ˆ i h g = heritability explained by SNPs p = proportion of causal SNPs M = number of (unlinked) SNPs N = number of training samples where p i h g / p Mp h g p / Mp 1/ N 1/ N e ( h g ˆ i e ( h / Mp 1/ N ) g ˆ i / Mp 1/ N ) 1 p 1/ N e ˆ i (1/ N ) is the posterior probability that i 0, i.e. SNP i is causal (generalizes uniform shrink when p = 1: infinitesimal prior, no LD)

28 In the special case of infinitesimal prior (with LD), posterior means can be computed analytically E( i ˆ ) i D M Nh g I 1 ˆ i h g = heritability explained by SNPs M = number of (unlinked) SNPs N = number of training samples where D is an LD matrix from a reference panel (generalizes uniform shrink when D = I: infinitesimal prior, no LD)

29 General case of non-infinitesimal prior with LD: posterior means cannot be computed analytically

30 General case of non-infinitesimal prior with LD: posterior means cannot be computed analytically Possible solutions: Assume 1 causal variant per locus

31 General case of non-infinitesimal prior with LD: posterior means cannot be computed analytically Possible solutions: Assume 1 causal variant per locus Iterative approach

32 General case of non-infinitesimal prior with LD: posterior means cannot be computed analytically Possible solutions: Assume 1 causal variant per locus Iterative approach MCMC

33 General case of non-infinitesimal prior with LD: posterior means cannot be computed analytically Solution: use MCMC. Initialize i = 0 At each big iteration For each SNP i Re-sample i based on Point-normal prior on i Observed ˆ ~ N( D, D / N) N T ˆ 1 D D ( ˆ D ) f ( i ˆ) ~ f ( i ) e, where f ) reflects point-normal prior (based on and p) ( i h g

34 General case of non-infinitesimal prior with LD: posterior means cannot be computed analytically Solution: use MCMC. Initialize i = 0 At each big iteration For each SNP i Re-sample i based on Point-normal prior on i Observed ˆ ~ N( D, D / N) 100 big iterations generally suffice for convergence Rao-Blackwellization: average the posterior means sampled Related MCMC methods for prediction from raw genotypes are described in Erbe et al. 01 J Dairy Sci, Zhou et al. 013 PLoS Genet, Moser et al. 015 PLoS Genet

35 LDpred performs well in simulations Simulations with real genotypes, 1% of SNPs causal

36 Understanding polygenic prediction Let s hide away and dance. -- Freddie K. Let s hide away with data. -- Alkes

37 Outline 1. A brief history of summary statistic genetics. Introduction to polygenic prediction using summary statistics 3. LDpred method for polygenic prediction using summary statistics 4. Application of LDpred to real data sets

38 Data from WTCCC 007 Nature. Results are similar to MCMC-based methods that require raw genotypes: Zhou et al. 013 PLoS Genet, Moser et al. 015 PLoS Genet LDpred performs well on within-cohort prediction of WTCCC traits

39 Data from WTCCC 007 Nature. Results are similar to MCMC-based methods that require raw genotypes: Zhou et al. 013 PLoS Genet, Moser et al. 015 PLoS Genet LDpred performs well on within-cohort prediction of WTCCC traits R nag R obs R liab (see Lee et al. 01 Genet Epidemiol)

40 Data from WTCCC 007 Nature. Results are similar to MCMC-based methods that require raw genotypes: Zhou et al. 013 PLoS Genet, Moser et al. 015 PLoS Genet LDpred performs well on within-cohort prediction of WTCCC traits Dominated by HLA

41 Data from WTCCC 007 Nature. Results are similar to MCMC-based methods that require raw genotypes: Zhou et al. 013 PLoS Genet, Moser et al. 015 PLoS Genet LDpred performs well on within-cohort prediction of WTCCC traits Do not validate in new cohort

42 but within-cohort prediction accuracy may be too good to be true R nag Training: WTCCC Validation: WTCCC Training: WTCCC Validation: WGHS CAD TD Results presented for LDpred; similar relative results for other methods Cryptic relatedness? Population structure? (Wray et al. 013 Nat Rev Genet)

43 LDpred performs well on summary statistics with independent validation cohorts Training N=70K PGC-SCZ 014 Nature; MGS replication sample

44 LDpred performs well on summary statistics with independent validation cohorts Training N=70K Training N=30K Training N=60K

45 LDpred performs well on summary statistics with independent validation cohorts Training N=70K Training N=30K Training N=60K Training N=70K Training N=90K

46 LDpred performs well on summary statistics with independent validation cohorts Height: complexities due to population stratification. Including PCs can improve prediction accuracy. (Chen et al. 015 Genet Epidemiol) Training N=130K (Lango Allen et al. 010 Nature)

47 Conclusions Explicitly modeling both LD and non-infinitesimal architectures improves polygenic prediction from summary statistics. Polygenic prediction should be evaluated using independent validation cohorts. Although polygenic predictions are not yet clinically useful, prediction accuracies will increase as sample sizes increase (bounded by heritability explained by SNPs; ). h g

48 and Future directions Polygenic prediction in non-european samples is challenging. How to combine training data from Europeans (large sample size) with training data from target population (small sample size)? (cross-population genetic correlation; Poster 1477 Brown) Enrichment of heritability in functional annotation classes could potentially be used to improve polygenic prediction (Poster 1357 Chatterjee) Methods for large raw genotype data sets (e.g. UK Biobank) should be developed in parallel with summary statistic methods (Platform talk 38 Loh; Platform talk 170 Young)

49 Acknowledgements Bjarni Vilhjalmsson + Vilhjalmsson et al. 015 AJHG co-authors Everyone in alkesgrp. Please check out our other ASHG 015 talks: Platform talk 11 Gusev Large-scale transcriptome-wide association study Platform talk 38 Loh Platform talk 196 Bhatia Platform talk 35 Galinsky Population differentiation analysis of 54,734 Platform talk 346 Hayeck Platform talk 354 Palamara Leveraging distant relatedness to quantify Contrasting regional architectures of schizophrenia Haplotypes of common SNPs explain a large Mixed model association with family-biased