Hidden Markov Models for the Assessment of Chromosomal Alterations using High-throughput SNP Arrays

Transcription

1 Hidden Markov Models for the Assessment of Chromosomal Alterations using High-throughput SNP Arrays Department of Biostatistics Johns Hopkins Bloomberg School of Public Health November 18, 2008

2 Acknowledgments Rob Scharpf Giovanni Parmigiani Rafael Irizarry + Benilton Carvalho Jonathan Pevsner + Nate Miller, Eli Roberson, Jason Ting

3 Trisomy

4 Karyotypes General Cytogenetics Information

5 FISH Courtesy of the Pevsner Laboratory

6 SNP chip data

7 Deletion copy number AA AB BB Mb Chr Chr 12

8 Amplification 10 8 AA AB BB copy number 2 1 Mb Chr 7

9 Uniparental Isodisomy 5 4 AA AB BB 3 copy number Mb Chr 1 Chr 2

10 Cancer samples

11 Mosaicism copy number 1 AA AB BB Mb Chr 2

12 Estimation 1 By SNP: Estimate genotype and copy number for each SNP. 2 Within a sample: Borrow strength between SNPs to infer regions of LOH and copy number changes. 3 Between samples: Comparison between normal and disease populations to find chromosomal alterations associated with disease.

13 SNPchip S4 classes and methods

14 The structure of the data we observe At each SNP, we observe a noisy measure of the true copy number and genotype (and possibly also measures of confidence in those estimates).

15 Another HMM...? Novel (and we believe, important) HMM features: 1 Model the observation sequence of genotype calls and copy number jointly (Vanilla) 2 Integrate confidence estimates of the genotype calls and copy number estimates (ICE) QuantiSNP and PennCNV also model genotype and copy number jointly! Colella et. al. (2007), QuantiSNP: an objective Bayes hidden-markov model..., Nucleic Acids Res 35(6): Wang et. al. (2008), PennCNV: An integrated hidden-markov model designed for..., Genome Research 17:

16 The Vanilla HMM components Observations ĈN and ĜT Hidden states Initial state probability distribution Transition probabilities Emission probabilities

17 Hidden states

18 Transition probabilities Following suggestions in the literature, we model the transition probabilities as a function of the distance d between SNPs. Specifically, let θ(d) 1 e 2d denote the probability that SNP i is not informative (I c ) for SNP at i + 1. For example: τ =P { (d) = P { = P { P i+1 i, d } i+1, I i, d } + P i+1, I c i, d i+1 I, i, d } P { I i, d } + i+1 I c, i, d P I c i, d = P { } θ(d).

19 Emission probabilities We assume conditional independence between copy number estimates and the genotype calls. For example: f( c CN, c GT ) = f( c CN ) f( c GT ) n o n o = f ccn ց f cgt = β ց n ccn o β n cgt o.

20 More information The confidence in genotype calls can differ substantially between SNPs! 4 Concordant 2 AA AB BB Discordant called BB (AB) Sense Antisense

21 Integrating confidence estimates for genotype calls Let S cgt be the confidence score for the genotype estimate. We can estimate from Hapmap the following densities: n o n o n f SĤOM ĤOM, HOM, f SĤOM ĤOM, HET, f S HET d HET, d o n HOM, f S HET d HET, d o HET. Note: n o f SĤOM ĤOM, n f S HET d HET, d o n o f SĤOM ĤOM, HOM n f S HET d HET, d o HOM.

22 Emission Probabilities - Loss Recall that f( c CN, c GT ) = f( c CN ) f( c GT ) n o n o = f ccn ց f cgt = β ց n ccn o β n cgt o. If the state for a particular SNP is Loss, we have β n cgt, S cgt o = f n o n cgt f S cgt GT, c o.

23 Emission Probabilities - Retention For retention, the true genotype can be HET or HOM: β n cgt, Sd GT o n o n = f cgt f S GT d GT, c o n o n = f cgt f S GT d, HOM GT, c o n + f S d GT, HET GT, c o n o n = f cgt f S GT d HOM, GT, c o n f HOM GT, c o n + f S GT d HET, GT, c o n f HET GT, c o n o n = f cgt f S GT d HOM, GT c o n f HOM GT, c o n + f S GT d HET, GT c o n f HET GT, c o

24 Copy number and genotype calls for chromosome A D B C E

25 Vanilla and ICE HMMs for genotype and copy number Deletion Normal LOH Amplification A D B C E 2 1 Van ICE A D B E Van ICE Mb

26 A HapMap sample Deletion Normal LOH Amplification 1 Van ICE Van ICE Mb

27 Many HapMap samples

28 SNP Trio

29 HMM for SNP Trio chromosome 10 chromosome 22 BPI BPI UPI F UPI F UPI M UPI M MI D MI D MI S non BPI MI S non BPI BPI BPI position (Mb) position (Mb)

30 De novo deletion

31 Homozygous and hemizygous deletions GF GM M A B S

32 Homozygous and hemizygous deletions GF GM M A B S Grandfather Grandmother Mother Aunt Brother Sister AB 0.01 BB 0.05 AB AB AB 0.06 BB AA 0.27 NC AA AA AB 0.12 BB AB 0.15 NC AA AA AB BB AB NC AA AA AA 0.30 AA BB 0.20 NC NC BB BB 0.22 BB AB 0.03 NC BB BB AB 0.09 AA AB NC BB BB AB AA BB 0.01 NC BB 0.04 BB BB 0.14 NC AB 0.17 NC AA AA AA AA AB 0.01 NC AA AA AA 0.16 AA AB NC BB BB AB 0.13 AA AB 0.01 NC BB BB AB AA BB 0.16 NC BB BB BB 0.10 BB AB 0.06 NC AA AA AB 0.07 BB AA 0.17 NC AA AA AB BB BB 0.02 NC BB BB AB 0.13 AA AA 0.21 NC AA AA AB 0.20 BB BB 0.05 BB 0.11 BB 0.15 BB 0.29 AB 0.13 AB -0.01

33 References Carvalho B, Bengtsson H, Speed TP, Irizarry RA (2007) Exploration, normalization, and genotype calls of high-density oligonucleotide SNP array data. Biostatistics, 8(2): Scharpf RB, Ting JC, Pevsner J, Ruczinski I (2007). SNPchip: R classes and methods for SNP array data. Bioinformatics, 23(5): Scharpf RB, Parmigiani G, Pevsner J, Ruczinski I (2008). Hidden Markov models for the assessment of chromosomal alterations using high-throughput SNP arrays. Annals of Applied Statistics, 2(2): Ting J, Ye Y, Thomas G, Ruczinski I, Pevsner J (2006). Analysis and visualization of chromosomal abnormalities in SNP data with SNPscan. BMC Bioinformatics, 7(1):25. Ting J, Roberson E, Miller N, Lysholm A, Stephan D, Capone G, Ruczinski I, Thomas G, Pevsner J (2007). Visualization of uniparental inheritance, Mendelian inconsistencies, deletions and parent of origin effects in single nucleotide polymorphism trio data with SNPtrio. Human Mutation, 28(12):

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