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 ,

, ,

by median polish: M+ =

- ; M- =

-

3. 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

hb(t) for all four bases on two chipsg(L) and 95% CI on one chip

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:

• reflects allele bases

• But what is k?

• Estimate by E-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 log-ratio space:

• Accuracy > 99.85% on all Hapmap calls