SNP chips
Advanced Microarray Analysis
Mark Reimers,
Dept Biostatistics, VCU, Fall 2008
Affy SNP chips
SNP Chip Probe Design
• 10 25-mers
overlapping the SNP
• Alleles A & B
• Sense and Anti-sense
– or PM and MM (old)
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
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
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
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!
CRLMM Overview
1. Normalize intensity on each chip separately by
2. Summarize qA+, qB+, qA-, qB- by median polish:
M+ = qA+ - qB+ ; M- = qA-- qB3. Model log ratio bias on each chip by
4. Estimate log ratio bias using E-M
– Where Zi indexes which SNP state is likely
– k = 1,2,3 for AA, AB, BB
Normalization – Step 1
• Regress (PM) intensity on sequence
predictors and fragment length
g(L) and 95% CI on one chip
hb(t) for all four bases on two chips
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
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
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
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!
Final Step: Calling
• Aim: separation in two-dimensional logratio space:
• Accuracy > 99.85% on all Hapmap calls