Association analysis

1. Association analysis Genetics for Computer Scientists 15.3.-19.3.2004 Biomedicum & Department of Computer Science, Helsinki Päivi Onkamo

2. Lecture outline • Genetic association analysis • Allelic association • χ2 –test • Linkage disequilibrium (LD) process • Formulation of the computational problem for LD mapping • Limitations of the LD mapping • Approaches. For example: HPM

3. Genetic association analysis • Search for significant correlations between gene variants and phenotype • For example: Locus A for SLE: 100 cases and 100 controls genotyped

4. Allelic association = An allele is associated to a trait • Allele 1 seems to be associated, based on sheer numbers, but how sure can one be about it?

5. Affected Healthy  Allele 1 79 46 125 Allele 2 21 54 75  100 100 200

6. 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 Where • oi is the observed class frequency for class i, ei expected (under H0 of no association) • k is the number of classes in the table • Degrees of freedom for the test: df=(r-1)(s-1)

7. Affected Healthy  Allele 1 62.5 (79) 62.5 (46) 125 Allele 2 37.5 (21) 37.5 (54) 75  100 100 200 Expected df=1 p<<0,001

9. Interpretation of the test results • The p-value is low enough that H0 can be rejected = the probability that the observed frequencies would differ this much (or even more) from expected by just coincidence < 0.001 • χ2 –tables (Appendix), internet resources, etc.

10. Genetic association is population levelcorrelation 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 • Often, a gene is not a direct cause for the disease, but is in LD with a causative gene →

11. 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 • At equilibrium, the frequency of the AB haplotype should equal to the product of the allele frequencies of A and B, AB = AB. If this holds, then Ab = A b, aB = aB and ab = ab , as well. Any deviation from these valuesimplies LD.

12. Linkage disequilibrium (LD) • 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

13. An example

14. 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

15. LD mapping: Utilizing founder effect

16. Data: Searching for a needle in a haystack Disease gene Disease status SNP1 S2 ... ... a ? 2 1 1 a ? 1 2 1 1 2 2 1 1 2 1 2 1 2 1 1 2 2 1 2 2 1 2 1 1 2 2 1 1 1 1 1 1 1 c 2 1 ? ?c 1 1 ? ? 1 2 2 1 1 2 1 1 2 2 2 1 1 1 a 1 1 2 1a 1 1 1 2 1 1 2 1 1 2 2 2 2 2 1 1 2 1 2 2 ? 1 1 1 ? 1 … … … …

17. 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-to-marker 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

18. Limitations of the LD mapping • The relationship between the distance of the markers vs. the strength of LD: theoretical curve

19. Linkage disequilibrium (D’) for the African American (red) and European (blue) populations binned in 5 kb classes after removing all SNPs with minor allele frequencies less than 20%. 3429 SNPs were included (Source http://www.fhcrc.org/labs/kruglyak/PGA/pga.html)

20. 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 → limits the accuracy of association mapping

21. 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) • Taking disease models into consideration

22. A methodological project:Haplotype Pattern Mining (HPM)AJHG 67:133-145, 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

23. Algorithm • Find a set of associated haplotype patterns • number of gaps allowed (2) • maximum gap length (1 marker) • maximum pattern length (7 markers) • association threshold (2 = 9) • Score loci based on the patterns • Evaluate significance by permutation tests • Extendable to quantitative traits • Extendable to multiple genes

24. Example: a set of associated patterns Marker 01 02 03 04 05 06 07 08 2 P1 2 1 2 2 2 * * * 9.6 P2 2 1 2 2 2 1 * * 9.2 P3 2 1 2 2 * 1 1 * 8.9 P4 2 1 * 2 1 * * * 8.1 P5 1 * 1 2 2 * * * 7.4 P6 * * 1 2 2 1 2 * 7.1 P7 * 2 1 2 * * * * 7.1 P8 2 1 1 2 * * * * 6.9 P9 2 1 1 * * * * * 6.8 Score 5 6 7 7 6 3 2 0

25. 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

26. Score and localization: an example

27. 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.

28. Permutation surface (A=7.5 %). The solid line is the observed frequency.

29. Localization power with simulated SNP data (density 3 SNPs per 1 cM). Isolated population with a 500-year history was simulated. Disease model was monogenic with disease allele frequency varying from 2.5-10 % in the affecteds. 12.5 % of data was missing. Sample size 100 cases and 100 controls.

30. 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 + • Allows for gaps in haplotypes +

31. Flexible: easily extended to different types of markers, environmental covariates, and quantitative measurements + • optimal pattern search parameters may need to be specified case-wise - • no rigid statistical theory background - • requires dense enough map to find the area where DS gene is in LD with nearby markers.

32. Search of the susceptibility gene: • With good luck - and information from gene banks, pick up the correct candidate gene • Genetic region with positive linkage signal is saturated with markers, and this data is now searched for a secondary correlation – correlation of marker allele(s) with the actual disease mutation (LD)

33. Improved statistical methods to detect LD • Terwilliger (1995) • Devlin, Risch, Roeder (1996) • McPeek and Strahs (1999) • Service, Lang et al. (1999) • Statistical power of association test statistics • Long, Langley (1999). • Review on statistical approaches to gene mapping • Ott, Hoh (2000)