Informative SNP Selection Based on Multiple Linear Regression

1. Informative SNP Selection Based on Multiple Linear Regression Jingwu He Alex Zelikovsky

2. Outline • SNPs, haplotypes, and genotypes • Tagging problem formulation • Tagging based on multiple linear regression • Experimental results

3. Human Genome • Length of Human Genome (DNA) 3 billionbase pairs: A,C,G, or T. • Our DNA is similar. 99.9% of DNA is common.

4. SNPs • Genome difference between any two people  0.1% of genome • These differences are Single Nucleotide Polymorphisms (SNPs). • Total number of SNPs in human genome 107 SNP SNP SNP A A C A G C C A . . . . T T C G G G T C . . . . A G T C A C C G . . . . C G G A A C A G C C A . . . . T T C G G G T C . . . . A G T C A C C G . . . . C A A A A C A T G C C A . . . . T T C G G G T C . . . . A G T C A C C G . . . . G A A A C A G C C A . . . . T T C G G G T C . . . . A G T C A C C G . . . . C G G

5. . . . C A G C C A . . . . T T C G G G T C . . . . A G T C A C C G . . . . C A A Haplotype 1 from A Genotype 1 from A Haplotype 2 from A Haplotype 3 from B Genotype 2 from B Haplotype 4 from B Haplotyes and Genotypes • Human = diploid organism: two different “copies” of each chromosome, one from mother, one from father. One copy from A C C G G G G . . . C A G C C A . . . . T T C G G G T C . . . . A G T C A C C G . . . . Another copy from A C A A . . . C A T T G C C A . . . . T T C G G G G T C . . . . A G T C A G A A C C G . . . . One copy from B Another copy from B G . . . C A C G C C A . . . . T T C G G G T C . . . . A G T C G A C C G . . . . C G G • Since individuals differ in SNPs, we keep only SNPs. • Haplotype: SNPs in a single “copy” of a chromosome • Genotype: A pair of haplotypes

6. Cause of Variation: Mutations and Recombinations Mutation Recombinations One nucleotide is replaced with other G -> A One chromatid recombine with another.

7. Encoding • SNPs are generally bi-allelic • only two alleles in single SNP: wild type and mutation • 0 stands for wide type, 1 stands for mutation Heterozygous homozygous

8. Outline • SNPs, haplotypes, and genotypes • Tagging problem formulation • Tagging based on multiple linear regression • Experimental results

9. Tagging Motivation • Decrease SNP genotyping cost and data analysis • Many SNPs are linked (strongly correlated) • Genotype only informative SNPs tag SNPs, other SNPs are inferred from tag SNPs • Perform data analysis only on tag SNPs. • Cost-saving ratio = m/k Use only tag SNPs to infer non-tag SNPs

10. Tagging Problem Step 1: Find tags (SNP position) in sample: Find tags (0, 1, 2) Step 2: Reconstruct complete haplotype Computation Methods • Problem formulation • Given the full pattern of all SNPs in a sample • Findthe minimum number of tag SNPs that will allow the reconstruction of the complete haplotype for each individual. • Tag Selection Algorithm • SNP Prediction Algorithm

11. Tagging Methods • Tagging Methods • HapBlock (K. Zhang, M.S. Waterman, et al.) • Greedy algorithm for tag selection • Majority voting for prediction • V. Bafna, B.V. Halldorson et al. • Graph algorithm for tag selection • Majority voting for prediction • STAMPA (E. Halperin and R. Shamir) • Dynamic programming for tag selection • Majority voting for prediction • ….. • Tagging based on Multiple Linear Regression • Greedy Selection • Multiple Linear Regression for Prediction

12. SNP Prediction Algorithm Predicting

13. Tag Selection based on Prediction • Choose the optimal k tags • It is NP-hard, m choose k • (m= No. of total SNPs, k= No. of tags) • Use Stepwise (greedy) Tag Selection Algorithm (STA) to reduce the cost and time • Starts with the best tag t0, i.e., tag that minimizes error when predicting with Ak all other tags. • Then STA finds such tag t1, which would be the best extension of {t0}, and continues adding best tags until reaching the set of tags of the given size k.

14. Projection Method forSNP Prediction Choose resolution minimizing its distance d to spanning of tag space span (T) possible resolutions s0 = 0 . . . 2 . . . s2 = 1 . . . s1= d0 d2 d1 tagt2 projections span(T) 0 tagt1

15. Data Sets • Daly et al • 616 kilobase region of human Chromosome 5q31 genotyping 103 SNPs for 129 trios. • Seven ENCODE regions from HapMap. • Regions ENr123 and ENm010 from 2 population: 45 singles Han Chinese (HCB) and 44 singles Japanese(JPT). • Three regions (ENm013, ENr112, ENr113) from 30 CEPH family trios obtained from HapMapSTAMPA (E. Halperin and R. Shamir) • Two gene regions: STEAP and TRPM8 • genotyping 23 and 102 SNPs for 30 trios

16. Experimental Results Directly to genotype data

17. Multivariate Linear Regression Tagging • Genotype tagging • uses fewer tags (e.g., up to two times less tags to reach 90% prediction accuracy) than STAMPA (E. Halperin and R. Shamir, ISMB 2005 and Bioinformatics) • Statistical tagging • Linear recombination of tags statistically cover non-tag SNPs • Traditional methods use single tag to cover non-tag SNPs • uses on average 30% fewer tags than IdSelect (C.S. Carlson et al. 2004) for statistical covering all SNPs.

18. Thank youAny Questions?