SNP chips

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 wasnt 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 dont
• have same distributions
• as training set

7
CRLMM - a heroic solution

• RLMM couldnt 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

• Normalize intensity on each chip separately by
• Summarize qA, qB, qA-, qB- by median polish
  M qA - qB M- qA-- qB-
• Model log ratio bias on each chip by
• Estimate log ratio bias using E-M
• Where Zi 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

hb(t) for all four bases on two chips
g(L) and 95 CI on one chip
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Normalization Step 1

• Too many hb(t)s
• Impose constraint
• hb(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
• Tukeys exploratory method for arrays of numbers
• Iterative method
• Subtract medians of each row and each column (and
  accumulate) until medians converge
• Robust
• Fast

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Step 3 Ratio Normalization

• Fit bias function
• of form
• m reflects allele bases
• But what is k?
• Estimate by E-M

m
fL(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 fi,k
• Use residuals from fit to classify again
• Repeat until converge!

14
Final Step Calling

• Aim separation in two-dimensional log-ratio
  space
• Accuracy gt 99.85 on all Hapmap calls