Human Genome Most human cells contain 46 chromosomes: Statistical Human Genetics Linkage and Association Haplotyping algorithms.

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1 Statistical Human Genetics Linkage and Association Haplotyping algorithms EECS 458 CWRU Fall 2004 Readings: Chapter 2&3 of An introduction to Genetics, Griffiths et al. 2000, Seventh Edition Some slides from the Lecture notes of Dr. Dan Geiger at Dr. Terry Speed's Class Homepages at Berkeley: Roadmap Mendel s law Linkage and the likelihood Loglikelihood ratio Marker map* Interval mapping, multipoint linkage analysis* Association Haplotyping algorithms *: will not cover in this class Human Genome Most human cells contain 46 chromosomes: 2 sex chromosomes (X,Y): XY in males. XX in females. 22 pairs of chromosomes, named autosomes. 1

2 Genetic Information Gene basic unit of genetic information. They determine the inherited characters. Genome the collection of genetic information. Chromosomes storage units of genes. Chromosome Logical Structure Marker Genes, SNP, Tandem repeats. Locus location of markers. Allele one variant form of a marker. Locus1 Possible Alleles: A1,A2 Locus2 Possible Alleles: B1,B2,B3 Genotypes Phenotypes At each locus (except for sex chromosomes) there are 2 genes. These constitute the individual s genotype at the locus. The expression of a genotype is termed a phenotype. For example, hair color, weight, or the presence or absence of a disease. Genetics: find the genes underlying phenotypes/disease 2

3 Mendel s Work Modern genetics began with Mendel s experiments on garden peas (Although, the ramification of his work were not realized during his life time). He studied seven contrasting pairs of characters, including: The form of ripe seeds: round, wrinkled The color of the seed albumen: yellow, green The length of the stem: long, short Mendel Gregor Experiments on Plant Hybridization. Transactions of the Brünn Natural History Society. Mendel s first law Characters are controlled by pairs of genes which separate during the formation of the reproductive cells (meiosis) A a A a Sexual Reproduction egg Meiosis sperm zygote gametes 3

4 P: AA X aa F1: Aa F1 X F1 Aa X Aa test cross Aa X aa Gametes: A a A AA Aa a Aa aa F2: 1 AA : 2 Aa : 1 aa Phenotype ~ ~ A a Gametes: A a a Aa aa Phenotype: ~ ~ 1A : 1 a Dominant vs. Recessive A dominant allele is expressed even if it is paired with a recessive allele. A recessive allele is only visible when paired with another recessive allele. Mendel s second law When two or more pairs of genes segregate simultaneously, they do so independently. A a; B b A B A b a B a b P AB = P A P B P Ab =P A P b P ab =P a P B P ab =P a P b 4

5 Exceptions to Mendel s Second Law Morgan s fruit fly data (1909): 2,839 flies Eye color A: red a: purple Wing length B: normal b: vestigial AABB x aabb AaBb x aabb AaBb Aabb aabb aabb Expected Observed 1, ,195 The pair AB stick together more than expected from Mendel s law. Morgan s explanation A A B B a b a b F1: A a B b a a b b F2: A a B b a b a b A a b b a B a b Crossover has taken place 5

6 Recombination Phenomenon (Happens during Meiosis) Male or female Recombination Haplotype Parental types: Recombinants: AaBb, aabb Aabb, aabb The proportion of recombinants between the two genes (or characters) is called the recombination fraction between these two genes. It is usually denoted by r or θ. For Morgan s traits: r = ( )/2839 = If r < 1/2: two genes are said to be linked. If r = 1/2: independent segregation (Mendel s second law). Purpose of human linkage analysis To obtain a crude chromosomal location of the gene or genes associated with a phenotype of interest, e.g. a genetic disease or an important quantitative trait. Examples: Cystic fibrosis (found), Diabetes, Alzheimer, and Blood pressure. 6

7 Linkage Strategies I Traditional (from the 1980s or earlier) Linkage analysis on pedigrees Association studies: candidate genes Allele-sharing methods: Affected siblings Animal models: identifying candidate genes Newer (from the 1990s) Focus on special populations (Finland) Haplotype-sharing (many variants) Pedigree loop Founders Family trio Nuclear family Father Genotypes {1 2} {1 2} {2 2} {1 1} {1 1} {1 1} {2 2} {2 1} {1 2} {1 2} {2 2} {2 2} {1 2} {1 2} {2 2} {1 2} Mother ID Num Children H A 1 /A 1 Fictitious Example for Finding Disease Genes 1 2 D A 2 /A 2 D D A 2 A 2 Phase inferred H H H D 3 4 H D A 1 A 2 A 1 /A 2 A 2 /A 2 A 2 A 2 Recombinant D D A 1 A 2 D A 1 /A 2 5 We use a marker with codominant alleles A 1 /A 2. We speculate a locus with alleles H (Healthy) / D (affected) If the expected number of recombinants is low (close to zero), then the speculated locus and the marker are tentatively physically closed. 7

8 Linkage Strategies II On the horizon (here) Single-nucleotide polymorphism (SNPs) Functional analyses: finding candidate genes Needed (starting to happen) New multilocus analysis techniques, especially Ways of dealing with large pedigrees Better phenotypes: ones closer to gene products Large collaborations Horses for courses Each of these strategies has its domain of applicability Each of them has a different theoretical basis and method of analysis Which is appropriate for mapping genes for a disease of interest depends on a number of matters, most importantly the disease, and the population from which the sample comes. The disease matters Definition (phenotype), prevalence, features such as age at onset Genetics: nature of genes (Penetrance), number of genes, nature of their contributions (additive, interacting), size of effect Other relevant variables: Sex, obesity, etc. Genotype-by-environment interactions: Exposure to sun. 8

9 The population matters History: pattern of growth, immigration Composition: homogeneous or melting pot, or in between Mating patterns: family sizes, mate choice Frequencies of disease-related alleles, and of marker alleles Ages of disease-related alleles Complex traits Definition vague, but usually thought of as having multiple, possibly interacting loci, with unknown penetrances; and phenocopies. Affected only methods are widely used. The jury is still out on which, if any will succeed. Few success stories so far. Important: heart disease, cancer susceptibility, diabetes, are all complex traits. We focus more on simple traits where success has been demonstrated very often. About 6-8 percent of human diseases are thought o be simple Mendelian diseases. Design of gene mapping studies How good are your data implying a genetic component to your trait? Can you estimate the size of the genetic component? Have you got, or will you eventually have enough of the right sort of data to have a good chance of getting a definitive result? Power studies. Simulations. 9

10 Analysis A very large range of methods/programs are available. Effort to understand their theory will pay off in leading to the right choice of analysis tools. Trying everything is not recommended, but not uncommon. Many opportunities for innovation. Interpretation of results of analysis An important issue here is whether you have established linkage. The standards seem to be getting increasingly stringent. What p-value or LOD should you use? Dealing with multiple testing, especially in the context of genome scans and the use of multiple models and multiple phenotypes, is one of the big issues. Replication of results This has recently become a big issue with complex diseases, especially in psychiatry. Nature Genetics suggested in May 1998 that they will require replication before publishing results mapping complex traits. Simulations by Suarez et al (1994) show that sample sizes necessary for replication may be substantially greater than that needed for first detection. 10

11 Topics not mentioned Exclusion mapping, interference, variance component methods, twin studies, non parametric linkage (sib-pair, ibd-based) and much more. Some of these topics plus others are covered in three books: Handbook of Human Genetic Linkage by J.D. Terwilliger & J. Ott (1994) Johns Hopkins University Press. Ordered, not available at the library. Analysis of Human Genetic Linkage by J. Ott, 3rd Edition (1999), Johns Hopkins University Press. Handbook of Statistical Genetic by Balding, 2nd Edition (2003), Wiley. Gene Mapping image credit: U.S. Department of Energy Human Genome Program Probability of a pedigree Input data: marker genotypes M, phenotypes T, relationship, with missing (always) Objective: calculate the joint probability of P(M,T) Components: founder probabilities, transmission probabilities, and penetrance probabilities Method: candidate genes, 2 point analysis, interval mapping, multipoint mapping. 11

12 One locus: founder probabilities Founders are individuals whose parents are not in the pedigree. They may of may not be typed. Either way, we need to assign probabilities to their actual or possible genotypes. This is usually done by assuming Hardy-Weinberg equilibrium. (There is a good story here.) If the frequency of D is.01, H-W says 1 pr(dd ) = 2x.01x.99 Genotypes of founder couples are (usually) treated as independent. 1 2 dd pr(pop Dd, mom dd ) = (2x.01x.99)x(.99) 2 One locus: transmission probabilities Children get their genes from their parents genes, independently, according to Mendel s laws; also independently for different children d d pr(kid 3 dd pop 1 Dd & mom 2 Dd ) = 1/2 x 1/2 One locus: transmission probabilities - II d d D D pr(3 dd & 4 Dd & 5 DD 1 Dd & 2 Dd ) = (1/2 x 1/2)x(2 x 1/2 x 1/2) x (1/2 x 1/2). The factor 2 comes from summing over the two mutually exclusive and equiprobable ways 4 can get a D and a d. 12

13 One locus: penetrance probabilities Pedigree analyses usually suppose that, given the genotype at all loci, and in some cases age and sex, the chance of having a particular phenotype depends only on genotype at one locus, and is independent of all other factors: genotypes at other loci, environment, genotypes and phenotypes of relatives, etc. Complete penetrance: DD pr(affected DD ) = 1 Incomplete penetrance: DD pr(affected DD ) =.8 One locus: penetrance - II Age and sex-dependent penetrance (see liability classes) D D (45) pr( affected DD, male, 45 y.o. ) =.6 One locus: putting it all together In general shaded means affected, blank means unaffected d d D D Assume penetrances pr(affected dd ) =.1, pr(affected Dd ) =.3 pr(affected DD ) =.8, and that allele D has frequency.01. The probability of this pedigree is the product: (2 x.01 x.99 x.7) x (2 x.01 x.99 x.3) x (1/2 x 1/2 x.9) x (2 x 1/2 x 1/2 x.7) x (1/2 x 1/2 x.8) 13

14 One locus: putting it all together - II Note that we begin by multiplying founder gene frequencies, followed by founder penetrances. Next we multiply transmission probabilities, followed by penetrance probabilities of offspring, using their independence given parental genotypes. If there are missing or incomplete data, we must sum over all mutually exclusive possibilities compatible with the observed data. The general strategy of beginning with founders, then non-founders, and multiplying and summing as appropriate, has been codified in what is known as the Elston-Stewart algorithm for calculating probabilities over pedigrees. It is one of the two widely used approaches. The other is termed the Lander-Green algorithm and takes a quite different approach. Both are hidden Markov models, both have compute time/space limitations with multiple individuals/loci (see next), and extending them beyond their current limits is the ongoing outstanding problem. Two loci: linkage and recombination D D T T 1 2 d d t t T t 3 3 Son 3 produces sperm with D-T, D-t, d-t or d-t in proportions: T t D (1-θ)/2 θ/2 1/2 d θ/2 (1-θ)/2 1/2 1/2 1/2 Two loci: linkage and recombination - II Son produces sperm with DT, Dt, dt or dt in proportions: T t D (1-θ)/2 θ/2 1/2 d θ/2 (1-θ)/2 1/2 1/2 1/2 θ = 1/2 : independent assortment (cf Mendel) unlinked loci θ < 1/2 : linked loci θ 0 : tightly linked loci Note: θ > 1/2 is never observed If the loci are linked, then D-T and d-t are parental, and D-t and d-t are recombinant haplotypes 14

15 Two loci: estimation of recombination fractions D D T T T t d d t t d d t t T t T t d d t t t t Recombination only discernible in the father. Here ˆθ = 1/4 (why?) This is called the phase-known double backcross pedigree. Two loci: phase Suppose we have data on two linked loci as follows: T t d d t t T t Was the daughter s D-T from her father a parental or recombinant combination? This is the problem of phase: did father get D-T from one parent and d-t from the other? If so, then the daughter's paternally derived haplotype is parental. If father got D-t from one parent and d-t from the other, these would be parental, and daughter's paternally derived haplotype would be recombinant. Two loci: dealing with phase Dd Phase is incompleteness in genetic information, specifically, in parental origin of alleles at heterozygous loci. Often it can be inferred with certainty from genotype data on parents. Often it can be inferred with high probability from genotype data on several children. In general genotype data on relatives helps, but does not necessarily determine phase. In practice, probabilities must be calculated under all phases compatible with the observed data, and added together. The need to do so is the main reason linkage analysis is computationally intensive, especially with multilocus analyses. 15

16 Two loci: founder probabilities Two-locus founder probabilities are typically calculated assuming linkage equilibrium, i.e. independence of genotypes across loci. If D and d have frequencies.01 and.99 at one locus, and T and t have frequencies.25 and.75 at a second, linked locus, this assumption means that DT, Dt, dt and dt have frequencies.01 x.25,.01 x.75,.99 x.25 and.99 x.75 respectively. Together with Hardy-Weinberg, this implies that Dd D d D d d D d D Tt T t t T T t t T pr(ddtt ) = (2 x.01 x.99) x (2 x.25 x.75) = 2 x (.01 x.25) x (.99 x.75) + 2 x (.01 x.75) x (.99 x.25). This last expression adds haplotype pair probabilities. Two loci: transmission probabilities T t d d t t T t Initially, this must be done with haplotypes, so that account can be taken of recombination. Then terms like that below are summed over possible phases. Here only the father can exhibit recombination: mother is uninformative. pr(kid DT/dt pop DT/dt & mom dt/dt ) = pr(kid DT pop DT/dt ) x pr(kid dt mom dt/dt ) = (1-θ)/2 x 1. Two Loci: Penetrance In all standard linkage programs, different parts of phenotype are conditionally independent given all genotypes, and two-loci penetrances split into products of one-locus penetrances. Assuming the penetrances for DD, Dd and dd given earlier, and that T,t are two alleles at a co-dominant marker locus. Pr( affected & Tt DD, Tt ) = Pr(affected DD, Tt ) Pr(Tt DD, Tt ) =

17 Two loci: phase unknown double backcross We assume below pop is as likely to be DT / dt as Dt / dt. T t d d t t T t T t d d t t t t Pr (all data θ ) = pr(parents' data θ ) pr(kids' data parents' data, θ) = pr(parents' data) {[((1-θ)/2) 3 θ/2]/2+ [(θ/2) 3 (1-θ)/2]/2} This is then maximised in θ, in this case numerically. Here θ = 0.5 Log (base 10) odds or LOD scores Suppose pr(data θ) is the likelihood function of a recombination fraction θ generated by some 'data', and pr(data 1/2) is the same likelihood when θ= 1/2. Statistical theory tells us that the ratio L = pr(data θ*) / pr(data 1/2) provides a basis for deciding whether θ =θ* rather than θ = 1/2. This can equally well be done with Log 10 L, i.e. LOD(θ * ) = Log 10 {pr(data θ*) / pr(data 1/2)} measures the relative strength of the data for θ = θ* rather than θ = 1/2. Usually we write θ, not θ* and calculate the function LOD(θ). Facts about/interpretation of LOD scores Positive LOD scores suggests stronger support for θ* than for 1/2, negative LOD scores the reverse. Higher LOD scores means stronger support, lower means the reverse. LODs are additive across independent pedigrees, and under certain circumstances can be calculated sequentially. For a single two-point linkage analysis, the threshold LOD 3 has become the de facto standard for "establishing linkage", i.e. rejecting the null hypothesis of no linkage. When more than one locus or model is examined, the remark in 4 must be modified, sometimes dramatically. 17

18 Assumptions underpinning most 2-point human linkage analyses Founder Frequencies: Hardy-Weinberg at each locus. Random mating, Linkage equilibrium across loci, known allele frequencies; founders independent. Transmission: Mendelian segregation, no mutation. Penetrance: single locus, no room for dependence on relatives' phenotypes or environment. Known disease model (including phenocopy rate). Implicit: phenotype and genotype data correct, marker order and location correct Comment: Some analyses are robust, others can be very sensitive to violations of some of these assumptions. Non-standard linkage analyses can be developed. Beyond two-point human linkage analysis The real challenges and more interesting strategies are interval mapping and multipoint linkage analysis, but going there would take more time than we have today. References HLK Whitehouse: Towards an Understanding of the Mechanism of Heredity, 3rd ed. Arnold 1973 Kenneth Lange: Mathematical and statistical methods for genetic analysis, Springer 1997 Elizabeth A Thompson: Statistical inference from genetic data on pedigrees, CBMS, IMS, Jurg Ott : Analysis of human genetic linkage, 3rd edn Johns Hopkins University Press 1999 JD Terwilliger & J Ott : Handbook of human genetic linkage Johns Hopkins University Press Handbook of Statistical Genetic by Balding, 2nd Edition (2003), Wiley. 18

19 Project topic: efficient calculation of the linkage probability Elston-Stewart algorithm Lander-Green algorithm Genehunter ( AJHG 96 58: ) Allegero (Nat Genet 00 25(1):12-13) Merlin (Nat Genet 02 30(1):97-101) Superlink (Bayesian network) Bioinformatics v18 S1: S189-S198(ISMB02), RECOMB03 SAGE Association analysis Population based association Allelic association and χ 2 test Linkage disequilibrium Limitations of the LD mapping Haplotype based (datamining) approaches: HPM, HapMiner Haplotype based (statistical) approaches* Family based association (TDT) * * Not coverred in this class Some slides from Päivi Onkamo Biomedicum & Department of Computer Science, Helsinki Association Studies Are the really independent? Coalescent theory! 19

20 Genetic association analysis Search for significant correlations between gene variants and phenotype For example: Locus A for 100 cases and 100 controls genotyped Allele 1 Affected 79 Unaffected 46 Allele Allele 1 seems to be associated with the disease based on the table, but how sure can one be about it? Allelic association = An allele is associated to a trait Affected Healthy Σ Allele Allele Σ

21 The idea is to compare the observed frequencies to frequencies expected under hypothesis of no association between alleles and the occurrence of the disease (independency between variables) Test statistic 2 χ k ( oi ei ) = i = 1 ei Where o i is the observed class frequency for class i, e i expected (under H 0 of no association) k is the number of classes in the table Degrees of freedom for the test: df=(r-1)(s-1) 2 Expected Affected Healthy Σ Allele (79) 62.5 (46) 125 Allele (21) 37.5 (54) 75 Σ ( o χ = i, j ij ( ) eij ) ( ) = e ij ( ) = ( ) df=1 p<<0,001 Interpretation of the test results The p-value is low enough that H 0 can be rejected = the probability that the observed frequencies would differ this much (or even more) from expected by just coincidence < Multiple testing problem 21

22 Genetic association is population level correlation with some known genetic variant and a trait: an allele is over-represented in affected individuals From a genetic point of view, an association does not imply causal relationship. Tow-step strategy: do linkage analysis first to find a candidate region, then do association fine mapping. Often, a gene is not a direct cause for the disease, but is in LD with a causative gene Haplotype Frequencies Locus B Total B b Locus A A a π AB π ab π Ab π ab π A π a Total π B π b 1.0 Linkage disequilibrium (LD) Linkage equilibrium: π AB = π A π B. If this holds, then π Ab = π A - π AB = π A - π A π B = π A π b, similarly: π ab = π a π B and π ab = π a π b. Any deviation from these values implies LD. There are many reasons that cause LD. Under random mating assumption, LD will decay generation by generation maily due to recombination 22

23 Before mutations A Mutations G C G After mutations A G C G C C Recombination After Recombinations A G C G C C A C Measures of Linkage Disequilibrium D := π AB - π A π B ; Thus: π AB = π A π B + D, which implies: π Ab = π A - π AB = π A - π A π B D = π A π b D, similarly: π ab = π a π B D, π ab = π a π b + D. So D -π A π B, D -π a π b, D π A π b, D π a π B (based on haplotype frequencies can not be negative). D is hard to interpret: Sign is arbitrary (one could set A, B to be the common alleles and a, b to be the minor alleles) The range of epends on allele frequencies, hard to compare between markers Alternative measures: D, r 2. Devlin B., Risch N. (1995) A Comparison of Linkage Disequilibrium Measures for Fine-Scale Mapping. Genomics 29:

24 Alternative measures D' = D max( π π, π π ) A D max( π π, π π ) A B b a a b B if if D < 0 D 0 Ranges between 1 and +1 More likely to take extreme values when allele frequencies are small ±1 implies at least one of the haplotypes was not observed Alternative measures Ranges between 0 and 1 1 when D achieves maximum/minimum and the two markers provide identical information 0 when they are in perfect equilibrium r 2 = 2 D π π π π A a B b Linkage disequilibrium (LD) Closely located genes often express linkage disequilibrium to each other: Locus 1 with alleles A and a, and locus 2 with alleles B and b, at a distance of a few centimorgans from each other, but may also due to many other reasons LD follows from the fact that closely located genes are transmitted as a block which only rarely breaks up in meioses An example: Locus 1 marker gene Locus 2 disease locus, with allele b as dominant susceptibility allele with 100% penetrance 24

25 An example Association evaluated Locus 1 also seems associated, even though it has nothing to do with the disease association observed just due to LD LD mapping utilizing founder effect A new disease mutation born n generations ago in a relatively small, isolated population The original ancestral haplotype slowly decays as a function of generations In the last generation, only small stretches of founder haplotype can be observed in the disease-associated chromosomes Linkage Disequilibrium Mapping Affected Ancestral haplotypes Normal Present-day haplotypes 25

26 Data: Searching for a needle in a haystack Disease gene Disease status SNP1 S a? a? c 2 1?? c 1 1?? a a ? 1 1 1? 1 Task is to find either an allele or an allele string (haplotype) which is overrepresented in disease-associated chromosomes markers may vary: SNPs, microsatellites populations vary: the strength of marker-tomarker LD Many approaches: old-fashioned allele association with some simple test (problem: multiple testing) TDT; modelling of LD process: Bayesian, EM algorithm, integrated linkage & LD Haplotype Based Methods for Case-Control Data 100 normal and 100 affected, 2 loci L1 L2 # Cases # Controls Allele frequencies L1 #cases #control L2 #cases #control

27 Limitations: LD is random process LD is a continuous process, which is created and decreased by several factors: genetic drift population structure natural selection new mutations founder effect recombination limits the accuracy of association mapping Research challenges Haplotyping methods needed as prerequisite for association/ld methods or, searching association directly from genotype data (without the haplotyping stage) Better methods for measurement of the association (and/or the effects of the genes) Takingdisease models into consideration Haplotype Pattern Mining (HPM) AJHG 67: , 2000 Search the haplotype data for recurrent patterns with no pre-specified sequence Patterns may contain gaps, taking into consideration missing and erroneous data The patterns are evaluated for their strength of association Markerwise score of association is calculated 27

28 Algorithm 1. Find a set of associated haplotype patterns number of gaps allowed (2) maximum gap length (1 marker) maximum pattern length (7 markers) association threshold (χ 2 = 9) 2. Score loci based on the patterns Evaluate significance by permutation tests Extendable to quantitative traits Extendable to multiple genes Example: a set of associated patterns Marker χ 2 P * * * 9.6 P * * 9.2 P * 1 1 * 8.9 P4 2 1 * 2 1 * * * 8.1 P5 1 * * * * 7.4 P6 * * * 7.1 P7 * * * * * 7.1 P8 Score * 6 * 3 * 2 * P * * * * * 6.8 Pattern selection The set of potential patterns is large. Depth-first search for all potential patterns Search parameters limit search space: number of gaps maximum gap length maximum pattern length association threshold 28

29 Score and localization: an example Permutation tests random permutation of the status fields of the chromosomes 10,000 permutations HPM and marker scores recalculated for each permuted data set proportion of permuted data sets in which score > true score empirical p- value. HapMiner Li and Jiang

30 A New Haplotype Similarity Measure Combination of the length of the longest common sub-string and the number of matched base pairs; Both measures have been used and corresponding to the recombination events and point mutations; Weighed according to the distance from the central point. A New Haplotype Similarity Measure h1: h2: Score: h1: h2: Weight1: Score: 2.6 h3: h4: h3: h4: Weight1: Weight2: Whole Genome Scan 30

31 The World Is Not Perfect! Penetrance (Not everyone with diseasemutant alleles got affected.) Phenocopies (Affected individuals may not have disease-mutant alleles; more than 90%.) Data with noise A Density-Based Clustering Algorithm Haplotype Association Mapping A contingency table for each cluster: Cluster C Remaining #case m m-m #control n n-n 31

32 Algorithm 1. for each marker i 2. consider the haplotype segment surrounding it 3. apply the density-based clustering algorithm 4. calculate z-score for each cluster 5. output the max z-score and the associated cluster Properties Data mining approach (clustering) Nonparametric/Model-free Ideal for fine mapping/scalable for whole genome-wide scan Population based haplotype association (individual haplotypes) No assumptions on haplotype structure Report DS positions as well as haplotype patterns Experimental Data Public data sets (Toivonen et al. 00) Isolated population, size from 300 to 100,000 in 500 years 100 cm, microsatellite/snp marker Dominant disease Proportion of mutation-carrying chromosomes: 2.5%, 5%, 7.5%, 10% Sample sizes: 200/400 32

33 Results Simulated data from Toivonen et al. 00 Results (cont d) Results (cont d) 33

34 HLA Data Set Public data set (Herr et al. 00) 25 markers, 14Mb on chromosome 6 Known type 1 diabetes-susceptibility locus 89 from 385 families (normal parents with 2 affected children) Haplotyping by our PedPhase program Haplotypes in children are cases (213), untransmitted are controls (143) Results on a Real Data Set Our results: highest score of 3.72 at D6S2444. Herr et al Recently developments Permutation tests Multiple genes and gene-gene interactions Genotype vectors 34

35 Benefits & drawbacks Non-parametric, yet efficient approach; no disease model specification is needed + Powerful even with weak genetic effects and small data sets + Robust to genotyping errors, mutations, missing data + optimal pattern search parameters may need to be specified case-wise - no rigid statistical theory background - For HPM, the significance of the patterns can not be assessed, the frequencies of patterns depend on the sample size HapMiner shows more consistent results with the increasing density of markers. Can be extended to multiple genes, genotype vectors. New haplotype-based statistical methods McPeek and Strahs (1999) Liu et al. (2001) Molitor & Thomas (2003) Tzeng et al. (2003) 35