Probe-Level Analysis of Affymetrix GeneChip Microarray Data

Transcription

1 Probe-Level Analysis of Affymetrix GeneChip Microarray Data Ben Bolstad Michigan State University February 15, 2005

2 Outline for Today's Talk A brief introduction to microarrays and the Affymetrix GeneChip Technology Pre-processing Background Correction Normalization Probe Level Modeling and its applications

3 The Human Genome The cell is the fundamental working unit of every living organism. Humans: trillions of cells (metazoa); other organisms like yeast: one cell (protozoa). Cells are of many different types (e.g. blood, skin, nerve cells), but all can be traced back to a single cell, the fertilized egg.

4 Genes The human genome is distributed along 23 pairs of chromosomes. 22 autosomal pairs; the sex chromosome pair, XX for females and XY for males. In each pair, one chromosome is paternally inherited, the other maternally inherited. Chromosomes are made of compressed and entwined DNA. A (protein-coding) gene is a segment of chromosomal DNA that directs the synthesis of a protein.

5 Chromosomes and DNA

6 DNA A deoxyribonucleic acid or DNA molecule is a double-stranded polymer composed of four basic molecular units called nucleotides. Each nucleotide comprises a phosphate group, a deoxyribose sugar, and one of four nitrogen bases: adenine (A), guanine (G), cytosine (C), and thymine (T). The two chains are held together by hydrogen bonds between nitrogen bases. Base-pairing occurs according to the following rule: G pairs with C, and A pairs with T.

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8 Exons and introns Genes comprise only about 2% of the human genome; the rest consists of noncoding regions, whose functions may include providing chromosomal structural integrity and regulating when, where, and in what quantity proteins are made (regulatory regions). The terms exon and intron refer to coding (translated into a protein) and noncoding DNA, respectively.

9 Differential expression Each cell contains a complete copy of the organism's genome. Cells are of many different types and states E.g. blood, nerve, and skin cells, dividing cells, cancerous cells, etc. What makes the cells different? Differential gene expression, i.e., when, where, and in what quantity each gene is expressed. On average, 40% of our genes are expressed at any given time.

10 Functional genomics The various genome projects have yielded the complete DNA sequences of many organisms. E.g. human, mouse, yeast, fruitfly, etc. Human: 3 billion base-pairs, thousand genes. Challenge: go from sequence to function, i.e., define the role of each gene and understand how the genome functions as a whole.

11 Central dogma The expression of the genetic information stored in the DNA molecule occurs in two stages: (i) transcription, during which DNA is transcribed into mrna; (ii) translation, during which mrna is translated to produce a protein. DNA mrna protein Other important aspects of regulation: methylation, alternative splicing, etc. The correspondence between DNA's four-letter alphabet and a protein's twenty-letter alphabet is specified by the genetic code, which relates nucleotide triplets to amino acids.

12 Idea: measure the amount of mrna to see which genes are being expressed in (used by) the cell. Measuring protein might be better, but is currently harder.

13 RNA A ribonucleic acid or RNA molecule is a nucleic acid similar to DNA, but single-stranded; ribose sugar rather than deoxyribose sugar; uracil (U) replaces thymine (T) as one of the bases. RNA plays an important role in protein synthesis and other chemical activities of the cell. Several classes of RNA molecules, including messenger RNA (mrna), transfer RNA (trna), ribosomal RNA (rrna), and other small RNAs.

14 Affymetrix GeneChip Commericial mass produced high density oligonucleotide array technology developed by Affymetrix Some overview images courtesy of Affymetrix.

15 Probes and Probesets Typically 11 probe(pairs) in a probeset Latest GeneChips have as many as: 54,000 probesets 1.3 Million probes Counts for HG-U133A plus 2.0 arrays

16 Two Probe Types Reference Sequence TAGGTCTGTATGACAGACACAAAGAAGATG CAGACATAGTGTCTGTGTTTCTTCT CAGACATAGTGTGTGTGTTTCTTCT PM: the Perfect Match MM: the Mismatch

17 Constructing the Chip

18 Sample Preparation

19 Hybridization to the Chip

20 The Chip is Scanned

21 Chip dat file checkered board close up pixel selection

22 Chip cel file checkered board Courtesy: F. Colin

23 Levels of Analysis Probe level Unprocessed data (or minimal processing) Dataset is larger Often ignored or viewed as a black box. High level Processed data Dataset is smaller Most analysis seems to start here

24 High-Level Analysis Clustering/Classification Pathway Analysis Cell Cycle Gene function Anything where a more biological interpretation is desired These are important topics, but such matters will not be discussed further in today's talk.

25 Probe-Level Analysis What is Probe-level analysis? Analysis and manipulation of probe intensity data Expression calculation: Background, Normalization, Summarization Fitting models to probe intensity data Quality control diagnostics Why do we do it? Hopefully it will allow us to produce better, more biologically meaningful gene expression values We want accurate (low bias) and precise (low variance) gene expression estimates Is there additional information at the probe-level that we might otherwise throw away?

26 RMA Background Approach Convolution Model = + Observed O 2 a o, b Signal S ( ) a o a φ E( ) b φ b SO= o = a+ b a o a Φ 1 b +Φ b = μ σ α = σ Noise N ( 2 ) Exp α N μ, σ

27 Normalization Non-biological factors can contribute to the variability of data... In order to reliably compare data from multiple probe arrays, differences of non-biological origin must be minimized. 1 Normalization is a process of reducing unwanted variation across chips. It may use information from multiple chips 1 GeneChip 3.1 Expression Analysis Algorithm Tutorial, Affymetrix technical support

28 Non-Biological Variability 5 scanners for 6 dilution groups

29 Quantile Normalization Normalize so that the quantiles of each chip are equal. Simple and fast algorithm. Goal is to give same distribution to each chip. Original Distribution Target Distribution

30 It works!! Unnormalized Scaled Quantile Normalization

31 General Probe Level Model y kij = f( X) + ε kij Where f(x) is function of factor (and possibly covariate) variables (our interest will be in linear functions) y kij is a pre-processed probe intensity (usually log scale) Assume that E = 0 ε kij = 2 Var εkij σ k

32 Parallel Behavior Suggests Multi-chip Model

33 Probe Pattern Suggests Including Probe-Effect

34 Also Want Robustness

35 Summarization Problem: Calculating gene expression values. How do we reduce the probe intensities for each probeset on to a gene expression value? Our Approach: RMA

36 What is RMA? 1. Convolution Background 2. Quantile Normalization 3. Probe Level Linear model on the log2 scale fit robustly. Software Bioconductor affy package RMAExpress Also available in some commercial software eg S+ ArrayAnalzyer, Iobian GeneTraffic

37 The RMA model y = m + α + β + ε kij k ki kj kij where y kij α ki ( ( )) = log 2 N B PMkij is a probe-effect i= 1,,I is chip-effect ( m + β is log2 gene expression on array j) j=1,,j k=1,,k is the number of probesets βkj k kj

38 RMA mostly does well in practice Detecting Differential Expression Not noisy in low intensities RMA MAS 5.0

39 One Drawback RMA MAS 5.0 Some fixes for this are being developed see GCRMA (Irizarry and Wu, JHU)

40 Median Polish Algorithm y11 L y1 J 0 M O M M yi1 L yij 0 0 L 0 0 Imposes Constraints Sweep Columns Iterate medianα = median β = 0 i Sweep Rows median ε = median ε = 0 i ij j ij j ˆ ε L ˆ ε αˆ 11 1J 1 M O M M ˆ ε ˆ ˆ I1 L ε α IJ I ˆ ˆ β L β mˆ 1 J

41 Advantages Fast Very robust Disadvantages Median Polish No algorithmic flexibility to fit alternative models No standard error estimates

42 An Alternative Method for Fitting a PLM Robust regression using M-estimation In this talk, we will use Huber s influence function ψ. The software handles many more. Fitting algorithm is IRLS with weights dependent on current residuals ( r ) Software for fitting such models is part of BioConductor package affyplm ψ r kij kij

43 Variance Covariance Estimates Suppose model is Y = Xβ + ε Huber (1981) gives three forms for estimating variance covariance matrix 2 κ 1/ ( n p) ψ ( r) 1/ n i i ψ ( r) i i 2 2 ( T X X ) 1 1/( n p) ψ ri i κ 1/ n ψ r i ( ) ( ) i 2 W 1 1 1/ ( ) ( ) ( T n p ψ r ) i W X X W κ i We will use this form T ' W = X Ψ X

44 We Will Focus on the Summarization PLM Array effect model Array Effect y = α + β + ε kij ki kj kij Pre-processed Log PM intensity With constraint I i= 1 α ki = Probe Effect 0

45 Detecting Differential Expression Problem: Given an experiment with two treatment groups correctly identify the differential genes without incorrectly choosing non differential genes. Question 1: How do different methods for DDE compare? Question 2: Can we do better using PLM s?

46 How Do We Know Which Genes are Differential? Spike-in datasets. Transcripts at known concentrations differing across arrays. Common background crna. Typically, Latin Square design

47 Affymetrix Spike-in Data 59 chips. All but 1 of the rows are done as triplicates A B C D E F G H I J K L M N O P Q R S T

48 X Testing for Differential Expression On a probeset by probeset basis compute a test statistic Should include something related to observed FC and some variability estimate l A t statistic: something of the form = β Ind( j group l) j Ind( j group l) t = X SE ie Average expression measures across arrays in group

49 Expression Values Based Statistics Fold Change X l X m FC Two Sample T-statistic s + n ( X l X m ) 2 2 l m l s n m T.std Simple Moderation 2 2 sl sm X X + + s nl nm ( l m) med T.mod Limma Ebayes T.ebayes Robust % s s % % % + n n ( X ) l Xm 2 2 l m l m T.robust

50 Probe Level Model Test Statistics Σ Suppose that is component of the variancecovariance matrix related to β Let c be the contrast vector defined such that the j th element of c is T 1 c β t n if array j is in group l PLM.1 = l J 2 1 if array j is in group m c jσ jj n m j= 1 0 otherwise T t PLM.2 = c β T c Σc

51 A First Comparison 8 chips from Affymetrix HG-U95A spike-in dataset 4 arrays for each of two concentration profiles Fit an array effect model to all 8 chips Compare the performance of the different methods by looking at all 3 vs 3 comparisons

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53 What Happens as the Number of Arrays Increases? Expand comparison to all 24 Arrays with same concentration profiles from Affymetrix HG-U95A spike-in dataset Fit an array effect model to all 24 arrays Look at comparisons between equal number of chips

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57 How About With More Real Data? GeneLogic Dilution/Mixture Dataset Learning Set Liver 30x VS CNS 30x 400 top genes truth 75:25 5x VS 25:75 5x Test Set Mixture Data Dilution Series Data

58 Mixture Data Results Method 3 vs 3 4 vs 4 5 vs 5 0% FP 5% FP AUC 0% FP 5% FP AUC 0% FP 5% FP AUC FC Std Robust Mod PLM PLM Ebayes

59 Moderation for the PLM test statistic Method 5 vs 5 0% FP 5% FP AUC PLM Ebayes PLM Moderated Σ = (1 p) Σ+ pλ mod λ is Σ averaged over all probesets

60 Quality Assessment Problem: Judge quality of chip data Question: Can we do this with the output of the Probe Level Modeling procedures?

61 Chip Pseudo-images

62 An Image Gallery Crop Circles Ring of Fire Tricolor

63 NUSE Plots Normalized Unscaled Standard Errors

64 RLE Plots Relative Log Expression

65 Discordant Probes

66 Discordant Arrays

67 Morals for Today s Talk The black box that is low-level processing is important. Your processing can have a significant effect on your final expression values and resulting conclusions. Testing for differential expression at the probe level can improve upon probeset-level testing. There is interesting quality assessment information at the probe-level

68 Ongoing Work in this Area Technology changes: What still works? What doesn t? Other probe-level models (eg Introduce sequence information, MM s) Tweaking the model fitting procedure to down weight poor performing probes across all chips Can we introduce the biology into the process (gene families? GO? etc)

69 Acknowledgements Terry Speed (UC Berkeley) Francois Colin Julia Brettschneider (UC Berkeley) Rafael Irizarry (Johns Hopkins) Bioconductor Core

70 Additional Slides

71 Background/Signal Adjustment A method which does some or all of the following Corrects for background noise, processing effects Adjusts for cross hybridization Adjust estimated expression values to fall on proper scale Probe intensities are used in background adjustment to compute correction (unlike cdna arrays where area surrounding spot might be used)

72 E Correction is given by ( ) SO= o = a+ b a= o, b= 2 μ σ α σ φ a o a φ b b a o a Φ +Φ 1 b b

73 Sort Sort columns of of original matrix Take averages across rows Take averages across rows Set Set average as as value for for All All elements in in the the row row Unsort columns of of matrix to to original order

74 It Reduces Variability Expression Values Fold change Also no serious bias effects. For more see Bolstad et al (2003)

75 Summarization Problem: Calculating gene expression values. How do we reduce the probe intensities for each probeset on to a gene expression value? Our Approach RMA a robust multi-chip linear model fit on the log scale Some Other Approaches Single chip AvDiff (Affymetrix) no longer recommended for use due to many flaws Mas 5.0 (Affymetrix) use a 1 step Tukey-biweight to combine the probe intensities in log scale Multiple Chip MBEI (Li-Wong dchip) a multiplicative model on natural scale

76 How Do We Know Which Genes are Differential? Spike-in datasets. Transcripts at known concentrations differing across arrays. Common background crna. Typically, Latin Square design Affymetrix HG-U95A GeneLogic AML bacterial spike-ins GeneLogic Tonsil bacterial spike-ins

77 Quality Assessment using PLM PLM quantities useful for assessing chip quality Weights Residuals Standard Errors Expression values relative to median chip

78 Chip Pseudo-images Weights Residuals Positive Residuals Negative Residuals

79 NUSE Plots Normalized Unscaled Standard Errors

80 RLE Plots Relative Log Expression

81 Probes and Probesets

82 Two Probe Types Reference Sequence TAGGTCTGTATGACAGACACAAAGAAGATG CAGACATAGTGTCTGTGTTTCTTCT CAGACATAGTGTGTGTGTTTCTTCT PM: the Perfect Match MM: the Mismatch

83 Probe Level Model test statistics t PLM.1 = J j= 1 T c β c 2 j Σ jj PLM.2 T t = c β T c Σc

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85 A Larger Comparison Look at the entire 59 chips for Affymetrix HG-U95A spike-in dataset Examine two cases. After standard preprocessing Fit models for each pairwise comparison (individual models) Fit a model to all 59 chips (single model) There are 91 pairwise comparisions

86 Results Method Individual Models Single Model 0% FP 5% FP AUC 0% FP 5% FP AUC FC Std Robust Mod PLM PLM Ebayes

87 What is Going On Here? Examine residuals stratified by concentration group Spike-ins Randomly chosen non-differential probesets at low, medium and high average expression

88 Affymetrix Spike-ins

89 Low Non-Differential

90 Middle Non-Differential

91 High Non-Differential

92 Chip Pseudo-images