1. SNP chips Advanced Microarray Analysis Mark Reimers, Dept Biostatistics, VCU, Fall 2008

2. Affy SNP chips

3. SNP Chip Probe Design 10 25-mers overlapping the SNP Alleles A & B Sense and Anti-sense –or PM and MM (old)

4. RMA for SNP chips Initial Affy software wasn’t very accurate Rabbee & Speed (2006) proposed RLMM, an RMA-like method using: –Quantile normalization –Two variables ( A & B signals) –Discriminant analysis Much better than Affy software Variant (BRLMM) adopted by Affy

5. Discriminating SNPs Estimate common covariance to clusters on ‘training’ set (Hapmap) data Separate clusters by Mahalanobis metric Use pre-defined clusters & metric to tell apart alleles on new data

6. Success Rate 90% (MPAM) to 98% (CRLMM) called at comparable accuracy on HapMap data –Cross-validation estimate BUT New chips don’t have same distributions as ‘training’ set

7. CRLMM - a heroic solution RLMM couldn’t be extended across labs Still problems with several hundred SNPs CRLMM addresses both these issues by careful normalization Achieves accuracy of 99.85% on hets; 99.95% on homozygotes Most complicated statistical calculation in BioC!

8. CRLMM Overview 1.Normalize intensity on each chip separately by 2.Summarize   ,   ,   ,    by median polish: M+ =    -    ; M- =    -    3.Model log ratio bias on each chip by 4.Estimate log ratio bias using E-M –Where Z i indexes which SNP state is likely –k = 1,2,3 for AA, AB, BB

9. Normalization – Step 1 Regress (PM) intensity on sequence predictors and fragment length h b (t) for all four bases on two chips g(L) and 95% CI on one chip

10. Normalization – Step 1 Too many h b (t)’s –Impose constraint: h b (t) is a cubic spline with 5 df on [1,25] Forces neighboring values of h to be close Allows variation in smoothness (unlike loess) Subtract fitted values from signal BUT: bias still present

11. Step 2 – Summarization Median Polish –Tukey’s exploratory method for arrays of numbers –Iterative method Subtract medians of each row and each column (and accumulate) until medians converge Robust Fast

12. Step 3 – Ratio Normalization Fit bias function: –of form:  reflects allele bases But what is k? Estimate by E-M f L (L) for one chip 

13. E-M Algorithm Systematic way to ‘guess and improve’ Start with putative assignments to classes –i.e. guess k based on overall separations Estimate bias for each k: f i,k Use residuals from fit to classify again Repeat until converge!

14. Final Step: Calling Aim: separation in two-dimensional log- ratio space: Accuracy > 99.85% on all Hapmap calls