January 2004 IMS NUS Microarray Tutorial. Gordon Smyth, WEHI Analysis of Complex Experiments

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1 nalsis of Complex Experiments Januar 4 nalsis of Complex Experiments Statistical Methods in Microarra nalsis Tutorial Institute for Mathematical Sciences National Universit of Sinapore Januar, 4 Gordon Smth Walter and Eliza Hall Institute What s Your Question? What are the tarets enes for m knock-out ene? Gene discover, differential expression Is a specified roup of enes all up-reulated in a specified condition? Gene set differential expression Can I use the expression profile of cancer patients to predict chemotherap outcome? Class prediction, classification re there tumour sub-tpes not previousl identified? Do m enes roup into previousl undiscovered pathwas? Class discover, clusterin This talk covers first question - differential expression Tpes of microarras in this talk inear modellin approach in this talk applies to both sinle channel (ffmetrix) and two-colour arras Need to cover some special features of two-colour arras The examples are two-colour Two colour with common reference is virtuall equivalent to sinle channel from an analsis point of view inear Models nalse all arras toether combinin information in optimal wa Combined estimation of precision Extensible to arbitraril complicated experiments Desin matrix: specifies RN tarets used on arras Contrast matrix: specifies which comparisons are of interest 4 o-ratios or Sinle Channel Intensities? Tradition analsis, as here, treats lo-ratios Mlo(R/G) as the primar data, i.e., ene expression measurements are relative lternative approach treats individual channel intensities R and G as primar data, i.e., ene expression measures are absolute (Wolfiner, Churchill, Kerr) Sinle channel approach makes new analses possible but - make stroner assumptions - requires more complex models (mixed models in place of ordinar linear models) to accommodate correlation between R and G on same spot inear Models for Differential Expression - requires absolute normalization methods 6 Ref C lo ( R) lo ( G) β β β β β β β Ref β β β C llows all comparisons to be estimated simultaneousl

2 nalsis of Complex Experiments Januar 4 Matrix Multiplication Slihtl larer example: Ref C β β β β β β β β+ β β β β+ β β β β β Ref β β β C Contrast β β C 7 WT. µ MT. µ + b WT. µ + a 4 MT. µ +a+b+a.b WT. µ + a + a 7 MT. µ + (a + a) + b + (a + a)b a a b ab ab 8 inear Model Estimates Obtain a linear model for each ene var( ) W σ E( ) Xβ Estimate model b robust reression, least squares or eneralized least squares to et coefficients standard deviations standard errors ˆj β s ˆ se( β j) cjs arallel Inference for Genes,-4, linear models Curse of dimensionalit: Need to adjust for multiple testin, e.., control famil-wise error rate (FWE) or false discover rate (FDR) oon of parallelism: Can borrow information from one ene to another 9 Hierarchical Model Normal Model rior ˆ (, ) j N j cj β β σ s σ χ d ( β ) p j β β σ j j N(, c j ) σ s Generalization of önnstedt and Speed ( χd d ) osterior Statistics osterior variance estimators sd + sd s d + d Moderated t-statistics t j βˆj s c j ~ t d + d under null Normalit, independence assumptions are wron but Eliminates lare t-statistics merel from ver small s convenient, resultin methods are useful

3 nalsis of Complex Experiments Januar 4 osterior Odds Within-rra Replicate spots osterior probabilit of differential expression for an ene is + d+ d / p c c c + c + c p( β βˆ, s ) p c t + d + d p( β βˆ, s ) t + d + d Monotonic function of t for constant d Replicate spots of each ene on same arra, assume duplicates at reular spacin ssume spatial component of correlation between duplicates is same for each ene Estimate spatial correlation from consensus estimator across enes Greatl improves estimation of precision Generalization of önnstedt and Speed 4 Implications for Desin Comparin RN Sources I (a) Common reference I (b) Common reference II Direct comparison Given linear modellin approach, can compute efficienc of various experimental desins Need to specif which RN sources are to compared and which contrasts are of interest Number of Slides ve. variance Units of material w N w N6 N.67 ve. variance For k, efficienc ratio (Desin I(a) / Desin II) In eneral, efficienc ratio k / (k-) 6 Comparin RN Sources I (a) Common reference I (b) Common reference II Direct comparison Desin Choices in Time Series TT t vs t+ TT TT4 t vs t+ TT TT4 TT4 ve w w N ) T as common reference T T T T4 ) Direct Hbridization T T T T4..67 Number of Slides ve. variance N N6 N.67 N4 C) Common reference T T T T4 Ref D) T as common ref + more Units of material ve. variance C C For k, efficienc ratio (Desin I(b) / Desin II). In eneral, efficienc ratio k / (k-) C.67 7 T T T T4 E) Direct hbridization choice T T T T4 F) Direct Hbridization choice T T T T

4 nalsis of Complex Experiments Januar 4 Desin Choices for x Factorial Indirect balance of direct and indirect # Slides I) C II). C III) C. N 6 IV) C.. Case Stud: Cell ineae Commitment Main effect Main effect N. Interactio n. Table entr: variance 9 Cell ineae Commitment How Does ax Work? ax is a critical ene for cell development Enables development alon the cell lineae and simultaneousl inhibits other pathwas Desin a microarra experiment to identif enes downstream from ax in the molecular pathwas Halted Development cell development can be halted at the pro stae b - bsence of the ax ene - bsence of the Ra ene (which activates recombination) - Withdrawal of the reulator ctokine I-7 (essential rowth factor) RN Sources Compare RN from 4 sources: - ax-/- (knock-out cell line) - Ra-/- (knock-out cell line) - Wt ( wild tpe, i.e., normal) - Wt cells with I-7 removed after initial development commenced Ra-/- and I-7 removal identif enes turned on or off b halted development rather than b ax 4 4

5 nalsis of Complex Experiments Januar 4 Saturated Desin Reression nalsis Wt 4 I-7 removed 9 6 ax-/- 8 7 Ra-/- Choose comparisons between the 4 RN sources to be the coefficients of the linear model, e.., - W: ax-/- vs Wt - RW: Ra-/- vs Wt - IW: I-7 withdrawn vs Wt For each ene, fit a linear model with a coefficient for each contrast n other comparisons of interest can be extracted from the linear model as contrasts 6 m m m m4 m m6 E m7 m 8 m9 m m m W RW IW ˆ β ( X' X) X' M Full desin matrix with duplicate spots is double this 7 What about Duplicate Spots? ρ between duplicate M values on the same slide ρ ρ ρ Gene X: M M M M M M ρ.8 Use ls procedure in R to fit linear model allowin for correlated spots 8 -fold up-reulation after removal of I-7 - ax-/- Ra-/- I-7 removed RT-CR Confirmation of DE Genes cdn -/- +/+ -/- +/+ controls Thmosinβ CD9 embiin NK snx He CD4(HS) IGF tulp4 HRT controls fold up-reulation in ax-/- 9 / arra positives confirmed b RT-CR standard

6 nalsis of Complex Experiments Januar 4 -fold up-reulation after removal of I-7 - o o o ax-/- Ra-/- I-7 removed known up known even known down reement with CR Observe averae rank of known DE enes relative to known non-de enes Moderated t-statistic and ordinar t- statistic do virtuall the same on this data oth do better than fold chane fold up-reulation in ax-/- Experiment with Transcription Factors Case Stud: Transcription Factor Tarets Transduction Hea cells denovirus EGF M CFb aload ERG ETS TE TEM 4 Experimental Desin I Experimental Desin II - Controls TEM arras M.CFb.ERG arras M.CFb.ETS arras Serum Effects Virus Effects TE arras M arras M.CFb 7 arras CFb 4 arras ll arras use reference EGF ERG 4 arras ETS arras M.CFb vs EGF w/o serum arras M viruses vs viruses arras M vs EGF w/o serum arras No Virus vs EGF 4 arras EGF viruses vs viruses arras Two G files 6 6

7 nalsis of Complex Experiments Januar 4 Comparisons of Interest Ordinar comparisons with EGF: N,, C, R, T, C, RC, TC, TE, TEM Comparisons with no virus condition: -N, C-N, R-N, T-N, C-N, RC-N, TC-N, TE-N, TEM-N Interaction comparisons: C-, C-C, RC-R, RC-C, TC-T, TC-C, TEM-TE, TEM-C Control comparisons: Cwos, wos, wos-, Cwos-C, G-G, - inear Models Desin matrix is straihtforward here because of use of common reference ots of contrasts of interest Raises question of simultaneous inference across the contrasts, as well as across enes 7 8 If then Moderated F-tests Can combine several t-tests toether in an F-test to test several hpotheses simultaneousl ˆT T β XWXβˆ β s F kd, + d Non-null prior on β doesn t enter 9 Classifin Genes n method of classifin enes as up, down or neutral for each transcription factor individuall will underestimate the number of enes co-reulated b two or more transcription factors Classifin F-test method classifies each ene over an number of comparisons arisin from a linear model More realistic idea of co-reulation 4 True Group Group onferroni Group Group F-Tests as Classification roblem Simulated Data 49 Group 96 Holm Group Group Group 9866 Classifin F Group Group t-stat -4-4 both up one up 4 Group Group t-stat 4 7

8 nalsis of Complex Experiments Januar 4 Composite Classification Method F-test classification is not ver powerful for detectin enes which respond to one condition (TF) onl when there are man comparisons Final classification method was a composite of classifin F and individual t No virus response (N) Filterin of EGF Responders Include TF vs EGF differences onl if the are not reproduced b the no virus vs EGF comparison M response () M vs no virus contrast (-N) Keep? Yes Yes No 4 44 Stemmed Heat Diaram are scale experiments allow differential expression results to be compared across conditions: Summar nalse data all at once Use standard deviances not just fold chanes Use ensemble information to shrink variances ssess differential expression for all comparisons toether 4 46 nalsis Strateies Stable backround estimation Intensit/spatial normalization Robustness utomatic spot qualit weihts Estimate variabilit Smoothin across enes inear modellin Duplicate spots Differential expression as classification IMM ackae for R inear models for microarra data. software packae for the R prorammin environment. Focus is differential expression includin - moderated t-statistics - methods for duplicate spots - classifin F-tests - stemmed heat diarams vailable from llows hih-throuh put analsis

9 nalsis of Complex Experiments Januar 4 cknowledements WEHI ioinformatics Terr Speed Matt Ritchie Natalie Thorne James Wettenhall WEHI Scott ab Joelle Michaud Catherine Carmichael Robert Escher Hamish Scott GRF Steve Wilcox Cath Jensen Melanie O Keefe WEHI Immunolo Steve Nutt UC San Francisco Jean Yan 49 9