Genotype Error Detection using Hidden Markov Models of Haplotype Diversity

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Genotype Error Detection using Hidden Markov
Models of Haplotype Diversity
Ion Mandoiu CSE Department, University of
Connecticut Joint work with Justin Kennedy and
Bogdan Pasaniuc
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Outline

• Introduction
• Likelihood Sensitivity Approach to Error
  Detection
• HMM-Based Algorithms
• Experimental Results
• Conclusion

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Single Nucleotide Polymorphisms

• Main form of variation between individual
  genomes single nucleotide polymorphisms (SNPs)
• High density in the human genome ? 1 ? 107 SNPs
  out of total 3 ? 109 base pairs

ataggtccCtatttcgcgcCgtatacacgggActata
ataggtccGtatttcgcgcCgtatacacgggTctata
ataggtccCtatttcgcgcCgtatacacgggTctata
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Haplotypes and Genotypes

• Diploids two homologous copies of each
  chromosome
• One inherited from mother and one from father
• Haplotype description of SNP alleles on a
  chromosome
• 0/1 vector 0 for major allele, 1 for minor
• Genotype description of alleles on both
  chromosomes
• 0/1/2 vector 0 (1) - both chromosomes contain
  the major (minor) allele 2 - the chromosomes
  contain different alleles

two haplotypes per individual
genotype
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Why SNP Genotypes?

• Identification and fine mapping of
  disease-related genes
• Methods Linkage analysis, allele-sharing,
  association studies
• Genotype data large pedigrees, sibling pairs,
  trios, unrelated

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Genotyping Errors

• A real problem despite advances in genotyping
  technology
• Zaitlen et al. 2005 found 1.1 inconsistencies
  among the 20 million dbSNP genotypes typed
  multiple times
• Error types
• Systematic errors (e.g., assay failure) detected
  by departure from HWE Hosking et al. 2004
• For pedigree data some errors detected as
  Mendelian Inconsistencies (MIs)
• Undetected errors
• E.g., if mother/father/child are all
  heterozygous, any error is Mendelian consistent
• Only 30 detectable as MIs for trios Gordon et
  al. 1999

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Effects of Undetected Genotyping Errors

• Even low error levels can have large effects for
  some study designs (e.g. rare alleles,
  haplotype-based)
• Errors as low as .1 can increase Type I error
  rates in haplotype sharing transmission
  disequilibrium test (HS-TDT) KnappBecker04
• 1 errors decrease power by 10-50 for linkage,
  and by 5-20 for association Douglas et al. 00,
  Abecasis et al. 01

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Related Work

• Improved genotype calling algorithms
• Di et al. 05, RabbeeSpeed 06, Nicolae et al.
  06
• Explicit modeling in analysis methods
• Sieberts et al. 01, Sobel et al. 02, Abecasis et
  al. 02,Cheng 06
• Computationally complex
• Separate error detection step
• Douglas et al. 00, Abecasis et al. 02, Becker et
  al. 06
• Detected errors can be retyped, imputed, or
  ignored in downstream analyses

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Outline

• Introduction
• Likelihood Sensitivity Approach to Error
  Detection
• HMM-Based Algorithms
• Experimental Results
• Conclusion

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Likelihood Sensitivity Approach to Error
Detection Becker et al. 06
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Likelihood Sensitivity Approach to Error
Detection Becker et al. 06
?
Likelihood of best phasing for original trio T
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Likelihood Sensitivity Approach to Error
Detection Becker et al. 06
Mother
Father
0 1 2 1 0 2
0 2 2 1 0 2
Child
0 2 2 1 0 2
?

• Large change in likelihood suggests likely error
• Flag genotype as an error if L(T)/L(T) gt R,
  where R is the detection threshold (e.g., R104)

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Implementation in FAMHAPBecker et al. 06

• Window-based algorithm
• For each window including the SNP under test,
  generate list of H most frequent haplotypes
  (default H50)
• Find most likely trio phasings by pruned search
  over the H4 quadruples of frequent haplotypes
• Flag genotype as an error if L(T)/L(T) gt R for
  at least one window

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Limitations of FAMHAP Implementation

• Truncating the list of haplotypes to size H may
  lead to sub-optimal phasings and inaccurate L(T)
  values
• False positives caused by nearby errors (due to
  the use of multiple short windows)
• Our approach
• HMM model of haplotype diversity ? all haplotypes
  are represented no need for short windows
• Alternate likelihood functions ? scalable runtime

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Outline

• Introduction
• Likelihood Sensitivity Approach to Error
  Detection
• HMM-Based Algorithms
• Experimental Results
• Conclusion

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HMM Model
(Figure from Rastas et al. 07)

• Similar to models proposed by Schwartz 04,
  Rastas et al. 05, KimmelShamir 05
• Unlike ScheetStephens 06, recombination ratios
  not modeled explicitly
• Block-free model, paths with high transition
  probability correspond to founder haplotypes

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HMM Training

• Previous works use EM training of HMM based on
  unrelated genotype data
• Our 2-step algorithm exploits pedigree info
• Step 1 Infer haplotypes using pedigree-aware
  algorithm based on entropy-minimization
• Step 2 train HMM based on inferred haplotypes,
  using Baum-Welch

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Complexity of Computing Maximum Phasing
Probability

• For unrelated genotypes, computing maximum
  phasing probability is hard to approximate within
  a factor of O(f½-?) unless ZPPNP, where f is the
  number of founders
• For trios, hard to approx. within O(f1/4 -?)
• Reductions from the clique problem

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Alternate Likelihood Functions

• Viterbi probability (ViterbiProb) the maximum
  probability of a set of 4 HMM paths that emit 4
  haplotypes compatible with the trio
• Probability of Viterbi Haplotypes (ViterbiHaps)
  product of total probabilities of the 4 Viterbi
  haplotypes
• Total Trio Probability (TotalProb) total
  probability P(T) that the HMM emits four
  haplotypes that explain trio T along all possible
  4-tuples of paths

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Efficient Computation of Viterbi Probability for
Trios

• For a fixed trio, Viterbi paths can be found
  using a 4-path version of Viterbis algorithm in
  time
• K3 speed-up by factoring common terms

Where
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Overall Runtimes

• Viterbi probability
• Likelihoods of all 3N modified trios can be
  computed within time using
  forward-backward algorithm
• Overall runtime for M trios
• Probability of Viterbi haplotypes
• Obtain haplotypes from standard traceback, then
  compute haplotype probabilities using forward
  algorithms
• Overall runtime
• Total trio probability
• Similar pre-computation speed-up
  forward-backward algorithm
• Overall runtime

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Outline

• Introduction
• Likelihood Sensitivity Approach to Error
  Detection
• HMM-Based Algorithms
• Experimental Results
• Conclusion

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Datasets

• Real dataset Becker et al. 2006
• 35 SNP loci on chromosome 16 covering a region of
  91kb
• 551 trios
• Synthetic datasets
• 35 SNPs, 30-551 trios
• Preserved missing data pattern of real dataset
• Haplotypes assigned to trios based on frequencies
  inferred from real dataset
• 1 error rate, four error insertion models
• Random allele
• Random genotype
• Heterozygous-to-homozygous
• Homozygous-to-heterozygous

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Experimental Setup

• Two strategies for handling MIs
• Set all three individuals to unknown prior to
  error detection, or
• Set child only to unknown (preserving parents
  original data)
• Two testing strategies
• Test one SNP genotype ViterbiProb-1,
  ViterbiHaps-1, TotalProb-1
• Simultaneously test three SNP genotypes at the
  same locus ViterbiProb-3, ViterbiHaps-3,
  TotalProb-3

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Comparison with FAMHAP (Random Allele Errors)
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Children vs. Parents (Random Allele Errors)
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Error Model Comparison(TrioProb-1 Parents)
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Error Model Comparison(TrioProb-1 Children)
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TrioProb-1 Results on Real Dataset

• Becker et al. 06 resequenced all trio members
  at 41 loci flagged by FAMHAP-3
• 23 SNP genotypes were identified as true errors
• 413-23100 resequenced SNP genotypes agree with
  original calls
• Predictive value for R104 is between 18/2669
  and 24/2692, compared to 23/4156 for FAMHAP-3

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Pedigree Info vs. Sample Size Effect
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Unrelated vs. Trio Likelihood Sensitivity
Unrelated ViterbiProb-1 Likelihood ratios
(children)
Trio ViterbiProb-1 Likelihood ratios (children)
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Combining Likelihood Functions (Children, Random
Allele Model)
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Combining Likelihood Functions (Parents, Random
Allele Model)
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Outline

• Introduction
• Likelihood Sensitivity Approach to Error
  Detection
• HMM-Based Algorithms
• Experimental Results
• Conclusion

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Conclusion

• Proposed efficient methods for error detection in
  trio genotype data based on a HMM model of
  haplotype diversity
• Significantly improved detection accuracy
  compared to FAMHAP
• High sensitivity even for very low FP rates
• Runtime linear in SNPs and trios
• Ongoing work
• Iterative error detection
• Fix MIs using likelihood before error detection
• Correct errors with high likelihood ratio, then
  recompute likelihood ratios (possibly after
  re-phasing and HMM re-training)
• Integration with genotype calling algorithms
• Combine low level intensity data with
  haplotype-based likelihoods
• Most useful when less pedigree info is available
  (unrelated, sibling pairs w/o parent genotypes,
  parents in trios)
• Locus specific thresholds, p-values
• Via simulations similar to Douglas et al. 00

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Questions?