Dealing with noise in microarray analysis

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1 Dealing with noise in microarray analysis

2 Analysis flow Quantification Normalization Filtering Data analysis

3 Outline Systematic noise Between and within arrays Considerations of normalization in experimental design Stochastic noise Filtering: Absolute expression noise Differential expression noise Reduce: Multi-chip concept

4 Quantification Signal Background

5 Systematic noise Two-color experiment One-color experiment condition control condition control RNA extraction RNA labeling

6 Normalization: Types of Global Intensity Spatial Dye swap Hybridization Scanner Malfunction Tip and plate Labeling efficiency Between arrays Within arrays

7 Global Normalization Two views of the same data On the average the intensities of measurements between replicates should be the same Therefore, the ratio in most cases should be approximately 1. Namely, dots should fall on the green line.

8 Intensity-Dependent Normalization M Re d = log( ) Green = log( r) log( g) A = log( Re d * Green ) = log( r) + log( g) 2

9 Per-Tip Normalization }Sub-array Gene replicates Array

10 Per-Tip Normalization Y. H. Yang, et al., Normalization for cdna microarray data: a robust composite method addressing single and multiple slide systematic variation. Nucleic Acids Research, 30(4), 2002.

11 Per-Tip Normalization (pre-normalization) Down-regulated Up-regulated Spatial graph each colored squared represent a spot each black square represents a set of spots printed by a given tip. Green is a gene that were down-regulated in the 10 th percentile Red is a gene that were up-regulated in the 10th percentile

12 Per-Tip Normalization (post-normalization)

13 Dye-Swap Normalization Treated sample Control sample T C C T Average over colors! T/C T/C

14 Assumptions Most of the genes on the array do not differentially express - Global The number of differentially expressed genes do not depend on the level of expression Intensity dependent Differentially expressed genes do not located at a given sub-array of the array slide Spatial (Per-Tip) There is a reason to believe that the efficiency of gene labeling is different between Green labeling and Red labeling Dye Swap

15 Considerations of Experimental Design Biological question Correction the systematic noise Correction the stochastic noise How much RNA

16 Normalization: Experimental design There are two type of normalizations: Between arrays Within array Each time we one do not estimate correctly the normalization factor you might increase the bias rather than decrease it Using the right design we can do only one normalization instead of two

17 Type of Design Direct Common reference Pooled reference Loop design

18 Direct comparisons C1 C2 T1 T2 Cy3 Cy5 T1 C1 T2 C2 T C Churchill GA, volume 32 supplement pp Nat. Gent. Note: [n*(n-1)]/2 We should use within and between arrays normalization Graph Scheme

19 Common Reference Within normalization is enough RNA quantity for each sample is 1; for the reference is N (N number of treatments) T1 T2 Tn C RNA quantity is defined for non dye swap experiment

20 Pooled Reference Within normalization is enough RNA quantity for each sample is 2 T1 T2 T1+T2+T3..Tn Tn Note: The reference cover the entire spots on the microarray slide; reduce the fold change range Caveat:: If one of the RNA extraction is failed the entire reference may fail as well

21 Filtering

22 Filtering To find differentially expressed genes we should filter out genes which are do not expressed over all conditions To find patterns of expression profiling we should filter out uninformative changes in the pattern Control Expressed genes Expressed Gene Treatment Expressed genes Expressed gene Non-Expressed gene Non-Expressed Gene Differentially expressed genes Induction Suppression Non- Expressed Gene Non- Expressed Gene Nonexpressed genes

23 Filtering: types Absolute expression: Based on Value Based on Flags Based on Replicates Differential expression: Based on replicates

24 The noise is changed from sample to sample and is independent of the signal Filtering: based on value

25 Filtering: Spotted Flags Ratio=2 Dust Flagging done manually Example of spotted to be flagged

26 Flagging: Affymetrix EST Sequence GeneChip Expression Array Design 5 3 Multiple oligo probes Probe Pair { Perfect Match (PM) Mismatch (MM) Probe Set

27 Flagging: Affymetrix Calculating the normalized difference (as R) of probe pair replicates within a probe set Testing statistically the Rs of probe pairs replicates against the parameter Tau=0.05 Define the flag on basis of p-value p cutoff PM MM PM MM P R = (PM - MM) / (PM + MM) R = (PM - MM) / (PM + MM) M A

28 Flagging: Affymetrix flags The yellow dots are measurements that were flagged as absent for both sample replicates The red dots are measurements that were flagged as present for both sample replicates are in dependent of signal value

29 For each spot/probe set the standard deviation over the sample replicates is calculated and fitted by the following model: S(raw) 2 = a 2 +b 2 C 2 Where a is fixed error, b is the proportion error and C is the control signal. The cutoff C is calculated as a/b Filtering Absolute expression: base on Replicates

30 Filtering: replicates A word on analysis of variance Null hypothesis: the two samples comes from the same population/groups, i.e., that they have the same mean If the variance within the populations is less than the variance between the populations the samples won t t overlap Variance within populations Variance between populations Variance within populations

31 Filtering: A Single Factor Replicates have two usages: Experiment Replicates Reducing the noise by averaging Estimating the source of the noise Churchill GA, volume 32 supplement pp Nat. Gent.

32 cells Filtering: Replicates by Scatter-Plot RNA crna hyb. cocktail chip scan analyze

33 Filtering: Technical Replicate I cells RNA Same array, 2 scans (diff. scanners, days) crna hyb. cocktail chip scan scan analyze analyze

34 Filtering: Technical Replicate II cells RNA Same crna, 2 arrays (diff. days) crna hyb. cocktail chip chip scan scan analyze analyze

35 Filtering: Technical Replicate III cells RNA Same RNA, 2 preps crna crna hyb. cocktail hyb. cocktail chip chip scan scan analyze analyze

36 Filtering: Biological Replicate cells RNA cells RNA 2 RNAs, 2 preps crna crna hyb. cocktail hyb. cocktail chip chip scan scan analyze analyze

37 Filtering: Experiment Differential expression Different RNAs

38 Filtering: summary Cross- Gene error model Flags Analysis of Variance Absolute expression Differential expression - - +

39 Noise reduction

40 Noise reduction: Affymetrix Probeset organization EST Sequence GeneChip Expression Array Design 5 3 Multiple oligo probes Probe Pair { Perfect Match (PM) Mismatch (MM) Probe Set

41 Noise reduction: Quantification Matrix Samples 12,000 22,000 genes ~500,000 probes

42 Noise reduction: algorithms Algorithms MAS5 - Affymetrix dchip Li & Wong RMA Irizarry et al. (Speed group) The purpose of the algorithms is to summarize all probe pairs replicates in one probe set properly The concept: MAS5 uses the per-chip approach dchip and RMA use multi-chip approach

43 Noise reduction: MAS5 Summarize all probe pair using robust averaging which assure no negative value PM MM MM > PM

44 Noise reduction: dchip mrna G A G Perfect match (PM) MisMatch (MM) MM ij PM ij = = υ j υ j + + θ i α j + ε PM ij MM ij = θ i Ф j + ε θ i α j + θ i Ф j + ε

45 Noise reduction: Probe Set Matrix RNA level i Arrays j Probe quality Probe set Probe pair Measurement = RNA level * probe quality

46 Noise reduction: Outliers Detection Light line is fitted values Dark line is observed values

47 Noise reduction: Source Scratches Cross-hybridizations of Outliers p2 p2 p3

48 Noise reduction: robust multi-array averaging (RMA) RMA use the same probe matrix as an input but calculate the RNA level by non- model-based robust method

49 Noise reduction: Overall Precision of MAS5, dchip and RMA Reducing the noise of low signals

50 Calculating the standard deviation over 5 replicates for all genes for all concentrations of two tissues. Noise reduction: Signal Dependent Precision Gene specific precision Irizarry RA, et al. Summaries of Affymetrix GeneChip probe level data Nucleic Acids Res ; 31(4):e15

51 Noise reduction: Robustness (Precision) of Fold Change Orange squares 2-3 fold inconsistency Red circles >3 fold inconsistency Gene expression fold changes of Liver vs. CNS calculated for 1.25µg and 20µg using three summary algorithms 1223 >2fold inconsistency 302 >2fold inconsistency 22 >2fold inconsistency Irizarry RA, et al. Summaries of Affymetrix GeneChip probe level data Nucleic Acids Res ; 31(4):e15

52 Noise reduction: Summary and Recommendations dchip gives standard errors and finds outlier detection where RMA do not gives standard errors For 2 chips the only option is to use MAS5, for 4 or more chips use RMA, for 10 or more chips use dchip

53 Summary: step 1 Normalization: Correction of the systematic error Control Expressed genes Treatment Expressed genes Differentially expressed genes Non- Expressed Gene Expressed gene Induction Expressed Gene Non-Expressed gene Suppression Non-Expressed Gene Non- Expressed Gene Nonexpressed genes

54 Normalization: Correction of the systematic error Summary: step 2 (needs many probe replicates) Control Expressed genes Treatment Expressed genes Differentially expressed genes Reduce the noise Non-Expressed Gene Expressed gene Induction Expressed Gene Non-Expressed Gene Non-Expressed gene Non-Expressed Gene Suppression Nonexpressed genes

55 Summary: step 3 Normalization: Correction of the systematic error Control Expressed genes Treatment Expressed genes Differentially expressed genes Reduce the noise Non- Expressed Gene Expressed gene Induction Expressed Gene Non-Expressed gene Suppression Filtering out noise Non-Expressed Gene Non- Expressed Gene Nonexpressed genes

56 Thank You

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