Ronnie A. Sebro

1. Ronnie A. Sebro Haplotype reconstruction BMI 374 10/21/2004

2. Mendelian Laws of Inheritance • Law of Segregation • Alleles separate when gametes are formed • Law of Independent assortment • Allele pairs separate independently during formation of gametes • Mendelian Inheritance • Each offspring receives one allele from male parent, and the other from female parent

3. Complex Diseases • Polygenic or multifactorial diseases • Run in families, but do not show Mendelian (monogenic) inheritance • Complex interaction between disease susceptibility genes, and environmental factors • Examples: asthma, schizophrenia

4. Finding disease genes • Two common methods employed • Pedigree analysis • Linkage analysis • Affected individuals inherit/share the same portion of the genome • Case-control analysis • Association analysis • Affected individuals have different allele frequencies (higher or lower) than controls

5. Definitions • Marker – small segments of DNA with specific features • Types of markers • SNPs • AATAA vs. AACAA • Microsatellites (STRs) • -CAGCAGCAG- vs. –CAGCAGCAGCAGCAG- • Locus - physical position of a marker on a chromosome • Homozygous – when both alleles at a locus are the same • Heterozygous – when the alleles at a locus are different

6. Definitions • Haplotype • All alleles, one from each locus that are on the same chromosome • Recombinant • An individual who inherited a haplotype not identical to that inherited by his/her parent • Phase • Information about which alleles are inherited from each parent

7. Genotypes Haplotypes Example

8. Enumerating Haplotypes • Consider an individual heterozygous at 3 loci e.g 1 2 1 2 1 2 • Several possible haplotypes • Haplotype space can be potentially huge • For n SNPs – 2n haplotypes

9. Finding disease genes • Both tests (association based tests, and pedigree linkage analysis tests) tentatively converge • Convergence is at the point of requiring to find a haplotype/allele in tight association (LD) or inherited by all affected individuals • Putative disease locus thereby identified

10. Why Haplotype? • Single allele vs. Haplotype • Advantages of using haplotype • Improved Power ! • Disadvantages of using haplotype • Haplotypes aren’t readily known

11. Data generated from sequencer in the following format (SNPs) 1 1 0 0 1 1 1 1 1 1 2 1 2 0 0 0 2 2 2 2 1 2 1 3 1 2 1 1 2 1 2 1 2 1 4 1 2 0 1 2 1 2 2 2 Genotypes are known Haplotypes are unknown Pedigree Problem

12. Haplotyping • Haplotyping can be done at molecular level – whole genome derived haplotypes (ref. Douglas et al., 2001) • Algorithms preferred because • Lower cost of genotyping • Fast and accurate algorithms

13. Current Haplotyping Algorithms • Algorithms used for unphased data • Clark Algorithm (Andy Clark @ Penn State) • E-M Algorithm (Stephens et al. ) • Bayesian Haplotype Inference (Jun Liu et al.)

14. Clark Algorithm • Enumerate haplotypes which exist with certainty in the sample (individuals heterozygous at 0 or 1 loci) • Assigns ambiguous haplotypes to those in the known list • Solutions are dependent on the order in which the individuals with unresolved haplotype phase are entered • The algorithm does not assume HW equilibrium

15. Estimate population haplotype probabilities is via maximum likelihood estimation; finding the values of the haplotype probabilities which optimize the probability of the observed data The maximum likelihood estimates of the haplotype probabilities are obtained by maximization of the likelihood This is a missing data problemAssumption of HW equilibrium Software EH (Xie and Ott, 1993) and EH+ (Zhao, Curtis and Sham) E-M Algorithm

16. Bayesian Algorithm • A dirichlet prior distribution is used for the haplotype frequencies • Uses a Gibbs sampler: enables handling of many SNP loci • Implemented in program HAPLOTYPER

17. Errata in data • Genotyping Errors • (quite common esp. with SNPs) • Missing data • MCAR • MAR • Non-ignorable missingness • Marker order errors

18. Overview • Discuss paper dealing with estimation of haplotypes in pedigrees (i.e. some information about phase) • Minimum-Recombinant Haplotyping in Pedigrees (Qian & Beckmann) • Useful for the HAPMAP project! • Useful also for association analyses with the Transmission Disequilibrium Test (TDT)

19. Paper 1 • Minimum-Recombinant Haplotyping in Pedigrees • Notation • Methods (Algorithm) • Results • Shortcomings of algorithm

20. Recombination Principles • Minimum-Recombination Principle • In nature, recombination is a rare event • The most probable haplotypes are those that minimize the total number of recombinations needed in the pedigree • Double-Recombinants • Naturally these are even rarer events, especially over such short intervals (10cM)

21. Notation • Consider a pedigree of J family members and a set of L linked marker loci • Individual – any family member • Parent – a family member with at least 1 child • Founder – a parent without his/her parents • Offspring – a family member with at least one parent

22. Notation • Define individual “genotyped” at locus l iff: • The genotype at locus l is known (from DNA) • The genotype data can be determined from 1º relatives • Ungenotyped parent (other genotyped) • Informative if both haplotypes transmitted • Partially informative only one haplotype transmitted • Genotyped offspring • Informative if at least one genotyped parent

23. Notation • Parental source (PS) – allele that is maternally or paternally derived • Grandparental source (GS) – the parental source of each parental allele

24. For a nuclear family: denote the alleles of parent 1 denote the alleles of parent 2 denote the alleles of offspring j denote the paternal and maternal alleles of parent 1 denote the paternal and maternal alleles of parent 2 denote the paternal and maternal alleles of offspring j denote the GS of paternal and maternal alleles of individual j denote the minimum and maximum allele values, respectively Notation

25. denotes PS-unknown genotype with alleles a and b denotes PS-known haplotype with paternal allele A and maternal allele B (ab) = (cd) denotes that genotypes (ab) and (cd) are equal (ab) ≠ (cd) denotes that genotypes (ab) and (cd) are not equal denotes that allele c is a constituent allele of genotype (ab) denotes that allele c is not a constituent allele of genotype (ab) Notation

26. Flexible Locus • Type 1 • If trio are all heterozygotes, and at least 1 parent and offspring not haplotyped

27. Flexible Locus • Type 2 • Two alternative haplotype assignments at locus l in a founder result in equal number of recombinant offspring

28. Flexible Locus • Type 3 • If two alternative haplotype assignments at locus l in offspring result in equal number of recombinants

29. Rules • Divide pedigree into nuclear trios • Apply rules to each trio until all individuals haplotyped, or no further inference possible • Rule 1: Input missing genotype at unambiguous loci in each parent conditional on spouse and child genotypes • Rule 2: Assign haplotype at each unambiguous ocus in each offspring, conditional on parental genotypes • Rule 3: Assign haplotypes at each unambiguous locus in each founder, conditional on haplotypes in offspring and the criterion of minimum recombinants in each nuclear family

30. Rules • Rule 4: Assign haplotypes at each unambiguous locus in each offspring, conditional on haplotypes in parents and the criterion of minimum recombinants in each trio • Rule 5: Impute a missing genotype at each unambiguous locus in each parent, conditional on haplotypes in offspring and the criterion of minimum recombinants in each nuclear family • Rule 6: Locate a locus with at least one individual in a nuclear family that is flexible at this locus, enumerate the haplotype configuration into multiple configurations, retaining all configuration with the minimum recombinants

31. Implementation • Raw genotype data

32. Implementation • Rule 1: • Impute missing genotype at each unambiguous locus in each parent, conditional on genotypes in spouse and offspring

33. Implementation • Rule 2: • Assign a haplotype at each unambiguous locus in each offspring, conditional on genotypes in parents in each parent-offspring trio

34. Implementation • Rule 3: Assign haplotypes at each unambiguous locus in each founder, conditional on haplotypes in offspring and the criterion of minimum recombinants in each nuclear family

35. Implementation • Rule 4: Assign haplotypes at each unambiguous locus in each offspring, conditional on haplotypes in parents and the criterion of minimum recombinants in each trio

36. Implementation • Rule 5: Impute a missing genotype at each unambiguous locus in each parent, conditional on the haplotypes in offspring and the criterion of minimum recombinants in each nuclear family

37. Implementation • Second application of rules 2 and 3

38. Implementation • Rule 6: Locate a locus with at least one individual in a nuclear family that is flexible at this locus, enumerate the haplotype configuration into multiple configurations with alternative haplotype assignments at each flexible locus in these individuals. • Retain all configurations with the minimum recombinants • Reapplication of rule 3

39. Results • A pedigree with Episodic ataxia • 29 total individuals • Genotyped at 9 polymorphic markers • 2 individuals not genotyped • Simulation study • Looped marriage structure in a pedigree with ataxia telangiecstasia

40. Results • High degree of concordance with the maximum-likelihood method • Identical haplotype configuration obtained with GENEHUNTER (ML based) in >99% of pedigrees analyzed.

41. Simulation Results

42. Genotype Errors • Impact of genotype errors investigated • Generated genotype data on 1000 pedigrees, each pedigree containing one incorrect allele in a random individual at a random marker • Mean number of recombinants increased from 5 to 6.2 (1.2) • 44% of these additional recombinants were double recombinants • All four correct MRHCs were reconstructed in 84% of pedigrees

43. Marker errors • The consequence of incorrect marker order on imputing haplotypes was investigated • Marker loci 2-7 (of the 9 loci involved for the EA study) were permuted (6! -1 ways) • Of the 719 orderings • None produced MRHCs with fewer than 5 recombinants • Only 5% had the same number of recombinants as the correct ordering • Chances of recovering all four MRHCs was 20% and 0% when 2 and 6 marker loci were incorrectly ordered

44. Conclusions • Both genotype errors and incorrect marker order can produce additional recombinants in reconstructing haplotypes • Sensitivity analyses suggest that incorrect marker orderings may have a larger impact than genotyping errors

45. Conclusions • This haplotyping method is applicable to both STRs and SNP data • Total computational requirement due to enumeration in a pedigree with J family members and L loci is on the order O(J2L3) • Computational requirements for SNP data are 3-10 times larger than for STRs (more flexible loci)

46. Shortcomings • A genotyped individual with neither genotyped parents nor genotyped offspring cannot be analyzed in this algorithm • Same problem above, even if multiple siblings and other relatives are genotyped • Likelihood-based methods are able to assign haplotypes to individuals who are uninformative using this rule-based method