Haplotyping. Biostatistics 666
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1 Haplotyping Biostatistics 666
2 Previously Introduction to te E-M algoritm Approac for likeliood optimization Examples related to gene counting Allele frequency estimation recessive disorder Allele frequency estimation ABO blood group Introduction to aplotype frequency estimation
3 Today: Haplotype Frequencies Evolution of aplotype estimation metods Clark s greedy algoritm Excoffier and Slatkin s E-M algoritm Stepens et al s coalescent based algoritm Using estimated aplotypes in association studies
4 Useful Roles for Haplotypes Linkage disequilibrium studies Summarize genetic variation Selecting markers to genotype Identify aplotype tag SNPs Candidate gene association studies Help interpret single marker associations Capture te effect of ungenotyped alleles Identify regions of recent ancestry among individuals Date interesting alleles Identify regions undergoing natural selection
5 Te problem Haplotypes are ard to measure directly X-cromosome in males Sperm typing Hybrid cell lines Oter molecular tecniques Instead, statistical reconstruction is often required
6 Typical Genotype Data Two alleles for eac individual Cromosome origin for eac allele unknown Many aplotype pairs can fit observed genotype Observation C G Marker1 T C Marker2 G A Marker3 Possible States C G C G T C C T G A G A C G C G C T T C A G A G
7 Use Information on Relatives Family information can elp determine aplotype pase Proportion of Pase Known Haplotypes Still, many ambiguities can remain Especially wit larger numbers of markers Can you tink of examples were parental information elps resolve pase? Can you tink of examples were parental information leaves pase ambiguous? Markers Unrelateds w/parents Parents + Sibling
8 Wat if tere are no relatives? Rely on linkage disequilibrium Assume tat Population consists of small number of distinct aplotypes Haplotypes tend to be similar to eac oter
9 Clark s Haplotyping Algoritm Clark (1990 Mol Biol Evol 7: One of te first aplotyping algoritms Computationally efficient Very fast and widely used in 1990 s More accurate metods are now available Predictions from te coalescent can be used to model performance
10 Clark s Haplotyping Algoritm Find unambiguous individuals Wat kinds of genotypes will tese ave? Initialize a list of known aplotypes Resolve ambiguous individuals If possible, use two aplotypes from list Oterwise, use one known aplotype and augment list If unpased individuals remain Assign pase randomly to one individual Augment aplotype list and continue from previous step
11 Cain of Inference (Clark, 1990
12 Can Te Algoritm Get Started? Wat kinds of genotypes do we need to get started? Wat kinds of aplotype pairs do we need to get started? Wat is te probability of tese occurring?
13 Probability of Failing To Start
14 Distribution of Orpaned Alleles
15 Distribution of Anomalous Matces
16 Notes Clark s Algoritm is extremely fast More likely to start wit large sample Orpaned alleles and anomalous matces may occur Solution wit te least orpaned alleles is usually te one wit te fewest anomalous matces
17 Te E-M Haplotyping Algoritm Excoffier and Slatkin (1995 Mol Biol Evol 12: Provide a clear outline of ow te algoritm can be applied to genetic data Combination of two strategies E-M statistical algoritm for missing data Counting algoritm for allele frequencies Refines Clark s algoritm by incorporating frequency information
18 E-M Algoritm For Haplotyping 1. Guesstimate aplotype frequencies 2. Use current frequency estimates to replace ambiguous genotypes wit fractional counts of pased genotypes 3. Estimate frequency of eac aplotype by counting 4. Repeat steps 2 and 3 until frequencies are stable
19 Expected Haplotype Counts i i i i i i i G H G G G i i p H P p p n n (n G H n G, ( ~, (, ( ˆ ( ˆ 2 ˆ 2 E wit G compatible pairs Haplotype ~ type G of genotypes Number of, to corresponding Unpased genotype, ( aplotype
20 Notation used in Excoffier and Slatkin paper P c i1 m 1... m P(aplotype pair c L m c s c 1 i1 P( ik il c i1 n P( ik il no.of observed penotypes index for individual penotypes no.of eterozygous markers for penotype aplotype pairs compatible for penotype probability of penotype Likeliood For clarity, try replacing ' penotype' wit 'observed genotype combination'
21 Notation used in Excoffier and Slatkin paper combinatio n' observed genotype wit ' penotype' ' try replacing For clarity, frequencie s for next iteration allele ( 2 1 for genotype proportion fitted ( ( penotype y of probabilit ( for eterozygotes and omozygotes genotype y of probabilit ( at round aplotype frequency of..., 1 1 ( 1 ( ( ( ( 1 ( ( 2 ( ( ( ( ( ( 2 ( 1 m c i l k g it g t l k g l k g l k g c i il ik g g l k g k g l g k l k g g g g P p P P n n P P P p p p P g p p p
22 Computational Cost (for SNPs Consider sets of m unpased genotypes Markers 1..m If markers are bi-allelic 2 m possible aplotypes 2 m-1 (2 m + 1 possible aplotype pairs 3 m distinct observed genotypes 2 n-1 reconstructions for n eterozygous loci For example, if m = 10 = 1024 = 524,800 = 59,049 = 512
23 E-M Algoritm for Haplotyping Cost grows rapidly wit number of markers Typically appropriate for < 25 SNPs Fewer microsatellites More accurate tan Clark s metod Fully or partially pased individuals contribute most of te information
24 Enancements to E-M List only aplotypes present in sample Gradually expand subset of markers under consideration, eliminating aplotypes wit zero or low estimated frequency from consideration at eac stage SNPHAP [Clayton (2001] HAPLOTYPER [Qin et al. (2002]
25 Divide-And-Conquer Approximation Number of potential aplotypes increases exponentially Number of observed aplotypes does not Approximation Successively divide marker set Run E-M on eac segment Prune aplotype list as segments are ligated Computation order: ~ m log m Exact E-M is order ~ 2 m 0 time (ms markers Exact E-M Approximation
26 Furter Refinements More modern metods try to furter improve aplotype estimation by favoring sets of similar aplotypes Stepens et al. (2001 Am J Hum Genet 68: Genealogical approac
27 Wat te Genealogy Implies Haplotypes are similar to eac oter Known Haplotypes Individual 1 Genotype: Individual 2: Genotype:
28 Cromosome Genealogies Past * * * * * * * * * * Present
29 Metod based on Gibbs sampler MCMC metod Stocastic, random procedure Improves solution gradually Given initial set of aplotypes Sample aplotypes for one individual at a time, assuming oter aplotypes are true Repeat a few million times
30 Update Procedure I Pick individual U to update at random Calculate aplotype frequencies F in all oter individuals Since everyone is pased, tis is done by counting Sample new aplotypes for U from conditional distribution of U s aplotypes given F
31 Update Procedure I Tis procedure would produce an estimate of aplotype frequencies equivalent to tose obtained by E-M Stepens et al (2001 suggested an alternative estimate of F
32 Update Procedure II Estimate F from te oter individuals Construct F* to include aplotypes in F and also oter similar aplotypes (possibly differing at a few sites Update U s aplotypes conditional on F*
33 Stepens' Formula Pr( H is te probability of observing aplotype given previous set H Pr( H S n n n S n n P S Coalescence Sum over aplotypes S mutations before coalescence Sum over number of mutations Mutation Matrix
34 Furter Refinements Tis naïve strategy becomes impractical for very long aplotypes List of aplotypes for eac individual could become too long Instead, we can proceed by selecting a sort segment of te aplotype to update at random
35 Hypotesis Testing Often, aplotype frequencies are not final outcome. For example, we may wis to compare two groups of individuals Are aplotypes similar in two populations? Are aplotypes similar in patients and ealty controls?
36 Simplistic approac Calculate aplotype frequencies in eac group Find most likely aplotype for eac individual Compare aplotype reconstructions in te two groups
37 Simplistic approac Calculate aplotype frequencies in eac group Find most likely aplotype for eac individual Compare aplotype reconstructions in te two groups NOT RECOMMENDED!!!
38 Observed Case Genotypes Te pase reconstruction in te five ambiguous individuals will be driven by te aplotypes observed in individual 1
39 Inferred Case Haplotypes Tis kind of penomenon will occur wit nearly all population based aplotyping metods!
40 Observed Control Genotypes Note tese are identical, except for te single omozygous individual
41 Inferred Control Haplotypes Ooops Te difference in a single genotype in te original data as been greatly amplified by estimating aplotypes
42 Hypotesis Testing II Never impute case and control aplotypes separately Instead, consider bot groups togeter Scaid et al (2002 Am J Hum Genet 70: Zaytkin et al (2002 Hum Hered. 53:79-91 Anoter alternative is to use maximum likeliood
43 Hypotesis Testing III Estimated aplotype frequencies, imply a likeliood for te observed genotypes L P(H i H~ Gi
44 Hypotesis Testing III Estimated aplotype frequencies, imply a likeliood for te observed genotypes L P(H i H~ Gi individuals aplotype pair frequency possible aplotype pairs, conditional on genotype
45 Hypotesis Testing III Calculate 3 likelioods: Maximum likeliood for combined sample, L A Maximum likeliood for control sample, L B Maximum likeliood for case sample, L C L 2ln B C ~ 2 df L L A df corresponds to number of non-zero aplotype frequencies in large samples
46 Significance in Small Samples In realistic sample sizes, it is ard to estimate te number of df accurately Instead, permute case and control labels randomly
47 Final tougts Compare alternative reconstructions Cange input order Cange random seeds Cange starting values Wen analyzing case-control studies Randomize case-control labels
48 Summary Describe principles underlying aplotype estimation in unrelated individuals Heuristic algoritms Te E-M algoritm Genealogical approac
49 Furter Reading Clark AG (1990 Inference of Haplotypes from PCR-amplified samples of diploid populations. Mol Biol Evol 7:
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