Learning ancestral genetic processes using nonparametric Bayesian models

Transcription

1 Learning ancestral genetic processes using nonparametric Bayesian models Kyung-Ah Sohn October 31, 2011 Committee Members: Eric P. Xing, Chair Zoubin Ghahramani Russell Schwartz Kathryn Roeder Matthew Stephens, University of Chicago In partial fulfillment of the requirements for the degree of Doctor of Philosophy. 1

2 Recent explosion of genomic data

3 Inference on human migration history Li, Hui, Kelly Cho, Judith R Kidd, and Kenneth K Kidd Genetic landscape of Eurasia and ʻadmixtureʼ in Uyghurs.. American journal of human genetics 85 (6) (December): 934 7; author reply Xu, Shuhua, and Li Jin A genome-wide analysis of admixture in Uyghurs and a high-density admixture map for disease-gene discovery.. American journal of human genetics 83 (3) (September):

4 Finding Disease Genes mutation G A Search for causal genes and mutations 4

5 Key challenges How to model complex inheritance processes underlying the data Realistic and flexible inheritance model 5 Images courtesy of thurj.org and stormfront.org

6 Key challenges Lack of large scale samples, data in high-dimensional space Need to exploit structural information in the data from genetically distinct but related groups Image courtesy of Nature Reviews: Genealogical trees, coalescent theory and the analysis of genetic polymorphisms. 3 (5) (May): doi: /nrg795. 6

7 Thesis goal Develop flexible non-parametric Bayesian models for learning ancestral genetic processes that efficiently utilize structural information in genetic data Biologically, provide practical tools that can reveal interesting characteristics of study populations Statistically, validate how non-parametric Bayesian models can help improving the performance of real applications 7

8 Theoretical component Nonparametric Bayesian models based on Dirichlet process and its extensions such as a hierarchical Dirichlet process or infinite hidden Markov model Combined with a haplotype inheritance model describing various genetic processes 8

9 SNP haplotypes Genetic polymorphism: a difference in DNA sequence among individuals, or populations Single Nucleotide Polymorphism (SNP): DNA sequence variation occurring when a single nucleotide - A, T, C, or G - differs between members of the groups Haplotypes Genotypes: sequences of an unordered pair of haplotype alleles in diploids, e.g. two haplotypes of (AATC) and (ACGG) form a genotype sequence of ({A,A}, {A,C}, {G,T}, {C,G}) 9

10 Thesis outline 1. Haplotype inference from multi-population data 2. Joint inference of population structure and recombination events 3. Local ancestry estimation in admixed populations 10

11 Application 1 A hierarchical Dirichlet process mixture model for haplotype reconstruction from multipopulation data (International Conference on Machine Learning 2006, Annals of Applied Statistics 2009) 11

12 Motivation Few existing programs have explicitly used the population labels in haplotype inference while a lot of datasets come from genetically distinct populations Each population has its own characteristics They are related and may share some components Develop a principled approach that explicitly exploit the population labels 12

13 Bayesian haplotype inference model mutation model A! founder haplotypes genotyping model H n1 H n2 individual haplotypes G n individual genotypes (observed) Each individual haplotype is a mixture of founder haplotypes Eric P. Xing, Michael I Jordan, and Roded Sharan Bayesian haplotype inference via the Dirichlet process.. Journal of computational biology : a journal of computational molecular cell biology 14 (3) (April): doi: /cmb

14 Bayesian haplotype inference model Dirichlet process prior! G 0 F mutation model " A! founder haplotypes genotyping model H n1 H n2 individual haplotypes G n individual genotypes (observed) Each individual haplotype is a mixture of founder haplotypes Eric P. Xing, Michael I Jordan, and Roded Sharan Bayesian haplotype inference via the Dirichlet process.. Journal of computational biology : a journal of computational molecular cell biology 14 (3) (April): doi: /cmb

15 Dirichlet Process A CDF, F on " follows a Dirichlet Process if for any measurable finite partition (B 1,B 2,.., B m ) of ", the joint distribution of the random variables ( F(B 1 ), F(B 2 ),, F(B m ) ) ~ Dirichlet( # G 0 (B 1 ),., # G 0 (B m ) ) where G 0 is the base measure and # is the scale parameter 15

16 Dirichlet Process Pólya urn model We associate mixture components (founders) with colors and samples (individual chromosomes) with balls in the Pólya urn model 16

17 DP mixture model A flexible haplotype inheritance model The number of founders can grow as large as needed by the given data Reasonable approximation to the coalescent theory Coalescent with mutation 17

18 Multi-population data 18

19 A hierarchical Dirichlet Process mixture Two level Pólya urn scheme - Assume population-specific DP - Use a common base measure distributed as another Dirichlet process - Atoms (or founder haplotypes) are shared across populations mutation model genotyping model 19

20 Performance Comparison of DP and HDP mixtures -Mode-1: ignore labels -Mode-2: handle each group separately Haplotype inference as a measurable application of DP and HDP mixture models 20

21 Comparison with benchmark algorithms 21

22 Sensitivity analysis on hyper parameters 22

23 Discussions Explicitly leverage population labels in haplotype inference using a hierarchical Dirichlet process mixture model Recombination not taken into account and a divide-and-conquer scheme called Partition-Ligation is used to deal with long sequences 23

24 Application 2 Spectrum: Joint Inference of Population Structure and Recombination events ( NIPS 2007, ISMB 2007, BA 2007) 24

25 Inheritance process x after one generation x... x after many generations x x x x 25

26 A new model for population representation Basic assumption Modern chromosomes are derived from hypothetical founder chromosomes via recombination and mutation Hypothetical founder chromosomes Individual chromosome Each individual chromosome is a mosaic of founders 26

27 Population analysis Given population data, recover the pool of hypothetical founders and their association with individual haplotypes haplotypes Hypothetical Founder Association 27

28 How to recover the association Use hidden Markov models (HMM) c 1 c c3 2 cn Hidden State sequence Observation sequence How many founders? Use an infinite HMM (Beal et al. ( 2002), Teh et al. (2006)) 28

29 Infinite hidden Markov model (Hidden Markov Dirichlet Process) Transition between infinite number of founders Infinite dimensional transition matrix modeled by a hierarchical Dirichlet process : each row modeled with a DP - rows coupled by a common base measure under another DP 29

30 Infinite HMM model for population analysis H... " A? c 1 c 2 c3 " cn H 30

31 Infinite HMM model for population analysis Founder allele reconstruction Inferring population structure Inferring recombination hotspot H... " A? c 1 c 2 c3 " cn H 31

32 Discussion A new haplotype model using an infinite hidden Markov model allows joint inference of population structure and recombination events Provide an alternative way of characterizing a population 32

33 Application 3 Robust Estimation of Local Ancestry in Admixed Populations (In submission) 33

34 Recently admixed population African Americans: multiple sources of ancestry (African / European) African European 34 Local Genetic Ancestry

35 Admixture mapping in recently admixed populations Percent ancestry from population A 80% 60% Patients Controls 40% 20% Candidate Disease locus 0% Chromosome position 35

36 Local genetic ancestry estimation Input Ancestral populations (train data) African European Admixed individual (test data) aaaaaaaeeee Output 36

37 Challenges Real ancestral populations are not available for study Use un-admixed modern descendants How to reflect the discrepancy in the statistical model How to encode ancestral population data 37

38 Previous Work 1. Allele-frequency-based approach probability of allele A European African Model individual-based approach EUROPEAN AFRICAN

39 Our approach Founder-based population model Hypothetical Founder African European

40 Local ancestry estimation Hypothetical Founder African European African American

41 How to construct the pool of founders Associate each population with a unique infinite HMM and link them hierarchically by using a common base measure under DP ihmm for population 1 ihmm for population 2 41

42 Hidden Markov Model Hidden state: S=(founder indicator k, population indicator j) Transition model: recombination between founders & between populations 42

43 Local ancestry model using infinite HMMS A new haplotype-based ancestry model Unique population encoding based on founder haplotypes Leverage the structural relatedness between multiple ancestral populations Insensitive to the choice of ancestral population data Robust under deviation from typical modeling assumption 43

44 Error rates as a function of train data size Even when only limited amount of reference data are available, our method still performs very well Error rates Data 1 Data 2 Data 3 x-axis: number of individuals per train population 44

45 Robustness under deviation from modeling assumption Our method HAPMIX LAMP More accurate (lower error rates), and most robust (errors do not increase much) x-axis: deviation from modeling assumption 45

46 Analysis of HGDP dataset Geographic location Training: YRI CEU JPT+CHB MAYA African Middle East Europe Asia Oceania American 46

47 Analysis of HGDP dataset 47

48 Discussion A new population representation model using non-parametric Bayesian approach of infinite HMMs Efficiently exploit the shared structural information across multiple populations Insensitive to the amount of train data, robust under deviation from modeling assumption Reveal interesting characteristics of the study populations 48

49 Conclusion We have presented nonparametric Bayesian models for learning ancestral genetic processes Systematically handle grouped data by using hierarchical models Explicitly exploit the structural information Provide a flexible haplotype inheritance model that can incorporate various genetic properties 49

50 Conclusion Future work - Improve computational complexity - Computation in dynamic programming: O( (KJ)^2 * T ) per chromosome per iteration - Reduce redundant computation - Parallelization - Fine-scaled analysis of real datasets - Combination of admixture mapping and association study 50

51 Dedicated to my family: Celine, KiHyun, and my parents 51

52 Thank you 52

53 HDP mixture model for multipopulation haplotype inference 53

54 Result on three-way admixture 54

55 Biological Terms Genetic admixture Mixing of genetically distant populations local ancestry: locus-by-locus ancestry in an admixed individual chromosome