Gordon Smyth, WEHI Analysis of Replicated Experiments. January 2004 IMS NUS Microarray Tutorial. Some Web Sites. Analysis of Replicated Experiments

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1 Some Web Sites Statistical Methods in Microarray Analysis Tutorial Institute for Mathematical Sciences National University of Sinapore January, 004 Gordon Smyth Walter and Eliza Hall Institute Technical reports etc Statistical software: R - Packaes within R environment - Bioconductor - LIMMA - SPOT (cdna imae analysis) 1 Five Statistical Issues Desinin ene expression experiments Acquirin the raw data: imae analysis Summarizin and removin artefacts from the data Discoverin which enes are differentially expressed Discoverin which enes exhibit interestin expression patterns For a review see Smyth, Yan and Speed, Statistical issues in microarray data analysis, In: Functional Genomics: Methods and Protocols, Methods in Molecular Bioloy, Humana Press, March 003 Lots of other bioinformatics issues 3 Imae Analysis Yan, Buckley, Dudoit and Speed, Comparison of methods for imae analysis on cdna microarray data, Journal of Computational and Graphical Statistics, January Imae Analysis Software If you re usin Affymetrix arrays, the imae analysis will be done as part of the Affy system. If you re usin spotted arrays, you ll scan your arrays to produce TIFF imaes. The imaes will be processed by a proram such as SPOT, GenePix, Imaene or Quantarray to acquire intensity measurements 5 Printin custom library on lass slide Array Printin 6 1

2 Microarray Imae False-coloured imae with two channels overlaid: more hihly expressed in mutant equally expressed more hihly expressed in normal 6 x 6 spots in each pin roup Genes printed in duplicate pairs Arrows indicate print direction AGRF NIA 15k mouse array: 1 x 4 pin roups 7 8 Steps in Imae Processin Sementation 1. Addressin: locate centers. Sementation: divide pixels into foreround (part of spot) or backround 3. Information extraction: calculate sinal intensity pairs, backround and quality measures for each spot Seeded reion rowin SPOT Fixed circle method Genepix: adaptive circles 9 Foreround measured from pixels inside the circle backround measured from ambient intensity around spot 10 Local Backrounds Measures Morpholoical Backround One channel rey scale Genepix: reion includin pink diamonds 11 Measures SPOT estimates overall backround baseline backround usin a nonlinear level morpholoical filter a lower, less variable measure 1

3 Quantification of Expression: cdna Foreround red, reen Backround red, reen Backround corrected lo-ratio ( Minus ) Averae intensity ( Add ) Rf, Gf Rb, Gb R = Rf Rb, G = Gf Gb M = lo R lo G A= (lo R+ lo G) / Example of a quality weihtin: downweiht spots smaller or larer than nominal size Many other possibilities Spot Quality Weihts Lots of issues: which b is best, to subtract b or not, quality, filterin Quantification of Expression: Affymetrix 1-40,000 probe sets/chip, each consistin of 11-0 Perfect Match (PM) and MisMatch (MM) probe pairs. Consider one set: chips i=1,,.. probes j=1,,.. Affymetrix summary: lo(sinal Intensity) = TukeyBiweiht{lo(PM j -MM j *)} dchip model (Li, Schadt & Won): PM ij -MM ij = θ i ϕ j + ε ij Robust Multichip Analysis (RMA): Use median polish or robust reression to fit Exploratory Data Display lo (PM-*BG) ij = chip i effect + probe j effect + ε ij See Bioconductor packaes: affy, AffyPLM Spatial bias in cdna arrays Spatial Plots: Backround Intensities Lo-ratios Print-tip roups Boxplots of M = lo R/G by print-tip roup (1-16) Same slide Locations of spots with extreme 5% M: hih, low

4 MA Plot Backround Affects Variability 19 From Spot: note lack of fannin (not same data) From GenePix: note fannin out at low intensities 0 MA plots of 10 Affymetrix replicate chip pairs Normalization Each of the 5 chips was scanned on a different scanner. 1 Smyth and Speed Normalization of cdna microarray data, in: METHODS: Selectin Candidate Genes from DNA Array Screens, December 003 No Absolute Measurement Scale MA Plot The spotted DNA sequences differ in bindin efficiency, so absolute intensities are not directly comparable between enes The response of the dyes is subject to arbitrary rescalin for each dye on each array need to normalize the red/reen balance for each array (to make M-values unbiased) 3 M = lo R lo G A = 1 / ( lo R + lo G ) 4 4

5 Print-tip-loess Normalization 6 x 4 pin-roups M = lo R lo G 5 A = 1 / ( lo R + lo G ) 6 After Normalization Before normalization M = lo R lo G A = 1 / ( lo R + lo G ) 7 8 After normalization Which Genes are Differentially Expressed? Smyth, Linear models and empirical Bayes methods for assessin differential expression in microarray experiments, July

6 Replicate Arrays Need replication to do statistical analysis of differential expression. Most basic possible is series of arrays all comparin the same two RNA sources: A A A } B B B n arrays 31 Gene-wise Summaries Each ene ives a series of lo-ratios Summarize lo-ratios by averae and standard deviation for each ene, or robust versions of these: M,, 1 Mn M = ave M s = std.dev M 3 Rankin Criteria Moderated t-statistics Averae lo fold chane. Problem: non DE enes with lare variances have too much chance of bein selected. t-statistics Problem: enes with very small sample variances are suspect Moderated t-statistics. We use a happy compromise between the two M t t M = s n M = s n 33 Shrunk standard deviations sd + sd 0 0 s = d + d0 Moderated t-statistics t M = s c Eliminates lare t-statistics merely from very small s 34 Shrinkae of Standard Deviations Posterior Odds s 1 s 1 s s s 0 The data decides whether t,pooled or to s n s n fold chane t t t should be closer to d d 0 Posterior probability of differential expression for any ene is 1+ d+ d0 1/ 0 = c c + c 0 p( β 0 M, s ) p c t + d + d p( β = 0 M, s ) 1 p c + c t d d Monotonic function of t 35 Reparametrization of Lönnstedt and Speed t for constant d 6

7 Estimatin Hyper-Parameters Simulations Closed form estimators with ood properties are available: for s 0 and d 0 in terms of the first two moments of lo s for c 0 in terms of quantiles of the t N False Discoveries Fold Chane SMA Efron t Moderated t Ordinary t N False Discoveries Fold Chane SMA Efron t Moderated t Ordinary t N Genes Selected N Genes Selected 37 σ similar σ very different 38 How many enes are differentially expressed? Rankin Easier Than Testin Assinin absolute sinificance levels on the basis of probability models is problematic: Lo-ratios don t appear to be normally distributed, hard to check Lo-ratios for different enes are correlated in unknown way Hih level of multiple testin means that very small p-values are required distributional assumptions must hold in extreme tail Little opportunity for usual CLT results to apply 39 If there was only one ene, a t-test would ive a reliable P-value for judin whether the true lo-ratio was zero With many enes, computed P-values cannot be trusted (unless have > 16 arrays) It is more realistic to rank the enes in order of evidence for differential expression 40 In Search of Truth We treat moderated t and posterior odds as rankin criteria rather than as providers of absolute sinificance or posterior odds To riorously estimate type I or type II error rates or to compare competin analysis methods, need to construct microarray data with known truth Spike-Ins Spike-in artificial RNA cocktail to induce known fold chanes in control enes Spike-ins can ive an objective basis for choosin cut-off for differential expression

8 Spike-In Controls MA-Plot with spike-in controls hihlihted Print artificial enes on microarray, then add spike-ins of correspondin RNA in known quantities to sample RNA before labellin and hybridization ScoreCard and SpotReport are commercial systems in use at the AGRF Scorecard Controls 40 How well do moderated t- statistics distinuish ratio (DE) controls from calibration (non- DE) controls? Moderated t-statistics Calib01 Calib0 Calib03 Calib04 Calib05 Calib06 Calib07 Calib08 Calib09 Calib10 Ratio 3/1 Low Ratio 1/3 Low Ratio 3/1 Hih Ratio 1/3 Hih Ratio 10/1 Low Ratio 1/10 Low Ratio 10/1 Hih Ratio 1/10 Hih 46 Empirical Cut Off t > 4 appears a conservative rule for differential expression with very small false discovery rate for this data 47 Other Data with Constructed Truth Assessin Precision: Replicate arrays Same vs same hybridizations Whole library pool titration series dynamic rane but not differentially expressed Assessin Bias: Independent measurement of differential expression PCR, independent arrays Spike-in ratio and calibration controls Mixture and dilution experiments 48 8

9 LIMMA Packae for R limma GUI Linear models for microarray data. A software packae for the R prorammin environment. Focus is differential expression includin - moderated t-statistics - methods for duplicate spots - classifyin F-tests - stemmed heat diarams Available from Acknowledements WEHI Bioinformatics Terry Speed Matt Ritchie Natalie Thorne James Wettenhall everyone else WEHI Scott Lab Joelle Michaud Catherine Carmichael Robert Escher Hamish Scott AGRF Steve Wilcox Cathy Jensen Melanie O Keefe WEHI Immunoloy Steve Nutt Lynn Corcoran Mirielle Lahoud Melissa Holmes Berkeley Jean Yan Speed Lab Nai Lab 51 When the chips are done WEHI Bioinformatics 5 9