Preprocessing -- examples in microarrays

Transcription

1 Preprocessing -- examples in microarrays

2 I: cdna arrays Image processing Addressing (gridding) Segmentation (classify a pixel as foreground or background) Intensity extraction (summary statistic) Normalization Plate to plate By grid By print tip

3 FYI: Segmentation

4 FYI: Information extracting Calculating and summarizing background and foreground intensity for each channel Foreground Mean, median, or other quantile of spot area Local Background Often median intensity from background pixels All pixels within a square, but not in spot Area between two concentric circles Valleys - furthest pixels from real spots

5 FYI: Background adjusting

6 Data table header you might see in online data Data table header descriptions ID_REF VALUE CH1_Median CH1_MEAN CH1_SD CH1_BG_Median CH1_BG_Mean CH1_BG_SD CH2_Median CH2_MEAN CH2_SD CH2_BG_Median CH2_BG_Mean CH2_BG_SD AREA AREA_BG FLAGS Normalized log2 ratio of background subtracted medians defined by CH2/CH1 (LPS over Mock) CH1 (F635) median fluorescence intensity CH1 (F635) mean fluorescence intensity CH1 (F635) standard deviation of fluorescence intenisty CH1 (F635) background median fluorescence intensity CH1 (F635) background mean fluorescence intensity CH1 (F635) background standard deviation of fluorescence intensity CH2 (F532) median fluorescence intensity CH2 (F532) mean fluorescence intensity CH2 (F532) standard deviation of fluorescence intenisty CH2 (F532) background median fluorescence intensity CH2 (F532) background mean fluorescence intensity CH2 (F532) background standard deviation of fluorescence intensity Number of feature pixels Number of feature background pixels 0 found feature, -50 not found feature, -75 absent feature, -100 manually flagged bad feature.

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8 Analysis of cdna chip Data From each array, there are four vectors of length J

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10 Normalization Identify and remove the effects of systematic variation in the measured fluorescence intensities, other than differential expression, for example different labelling lli efficiencies i i of the dyes; different scanning parameters; print-tip, spatial, or plate effects, etc. The need for normalization can be seen most clearly in self-self hybridizations, where the same mrna sample is labeled with the Cy3 and Cy5 dyes. Q: In sequencing, how do we check if there is need for normalization?

11 Intensity log-ratio, M Boxplots by print-tip-group tip

12 Self-self hybridization There appears to be a non-linear dependence on intensity

13 Self-self hybridization Two-color platform

14 MA-plot by print-tip-group The smooth curves were created using loess. Splines work just as well

15 Nonlinear Normalization normalized log 2 R/G log 2 R/G L(intensity, sector, ) L depends on a number of predictor variables, such as spot intensity A, sector, plate origin. Intensity-dependent normalization. Intensity and sector-dependent normalization. 2D spatial normalization. Other variables: time of printing, plate, etc. Composite normalization. Weighted average of several normalization functions.

16 2D images of L values Global l median normalization Global loess normalization Within-print-tipgroup loess normalization 2D spatial normalization

17 2D images of normalized M-L Global l median normalization Global loess normalization Within-print-tipgroup loess normalization 2D spatial normalization

18 Boxplots of normalized M-L Global median normalization Global loess normalization Within-print-tip- p group loess normalization 2D spatial normalization

19 MA-plots of normalized M-L Global l median normalization Global loess normalization Within-print-tipgroup loess normalization 2D spatial normalization

20 Assumptions we made M does not depend on spot location M does not depend on A E[M]=0 for most genes, or symmetric differential expression What if we expect most genes are up and/or p g p down regulated? (to be continued)

21 Background subtraction: yes, no, when? Motivation: measured foreground intensity includes contribution other than target hybridization Yes: to remove bias. B x x B y y No: to avoid variance var[log{(r-rb)/(g-gb)}] >> var[log(r/g)] for many background measurements. What s the trade-off?

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24 References Empirical Evaluation of Methodologies for Microarray Data Analysis Lixuan Qinand Kathleen Kerr Analysis of cdna microarray images Yee Hwa Yang, Michael J Burckley and Terence P Speed Briefings in Bioinformatics, 2001 Comparison of methods for image analysis on cdna microarray data YH Yang, MJ Buckley, S Dudoit, TP Speed - Journal of Computational and Graphical Statistics, 2002 Improved Background Correction for Spotted DNA Microarrays C KOOPERBERG et al, Journal of Computational Biology

25 II. Preprocessing Oligonucleotide arrays Background adjustment Normalization Summarization Why and how?

26 GeneChip Feature Level Data Each gene represented by a set of probes, referred to as probesets More than 10, probesets Each probeset includes features (probes) Exon arrays may include on average 4 features for each exon

27 EDA-I Specific Binding: Linear with concentration Background Additive Y=B+aC

28 Effect of Background: revisited B + ac B ac 1 C 1 B + ac 1 1 B +ac 2 B ac 2 C 2 B + ac 2 log(b ac 1 ) log(b ac 2 ) log(c 1 ) log(c 2 ) When a or C is small log(b ac) log(b) When C (concentration) is low

29 Why background correct

30 Distribution of Optical and NSB Noise

31 Can we do Y-B? Different probes have different background level Motivation for MM measurements

32 Direct Measurement Strategy Affymetrix s tries to measure non-specific binding directly Deterministic Model PM = O + N + S MM = O + N PM MM = S PM-MM is supposed to give us a good estimate of specific binding But it is not so simple

33 Sometimes MM larger than PM

34 Deterministic model is wrong Do MM measure non- specific binding? Look at Yeast DNA hybridized to Human Chip Look at PM, MM logscale scatter-plot R 2 is only 0.5

35 Stochastic Model (Additive background/multiplicative error) PM = O PM + N PM + S, MM = O MM + N MM E[ PM MM ] = S, but Var[ log( PM MM ) ] ~ 1/S 2 (can be very large) Note: Technically, var[ log(pm-mm) ] is not defined. We need to make sure we avoid taking logs of negative. Affymetrix s current default does this.

36 Simulation We create some feature level data for two replicate arrays Then compute Y=log(PM-kMM) for each array We make an MA using the Ys for each array We make an observed concentration versus known concentration plot We do this for various values of k. The following movie shows k moving from 0 to 1.

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38 Does this happen in practice? MAS 5.0

39 Introducing the Empirical Bayes Concept Is referred to as the prior distribution and the parameters describing the prior distribution ib ti are hyperparameters.

40 Toy example for Bayesian estimate Data:11110: 1,1,1,1,0: likelihood:

41 Toy example Data: c(rep(1,80),rep(0,20)):, )) likelihood: 80 (1- ) 20

42 When sample size increases the estimates moves from prior location towards MLE

43 R code for making the previous figures pi0=seq(0,1,.01) ### note "pi" is a reserved name for the pi= ################## prior distribution beta(50,50) and beta(5,5) ########## plot(pi0,dbeta(pi0,50,50),type="l",col=1,lwd=3, xlab=expression(pi),ylab="density", main=expression(paste("prior distribution of ",pi))) lines(pi0,dbeta(pi0,5,5),col=2,lty=2,lwd=3) legend(0.7,6,legend=c("beta(50,50)","beta(5,5)"),lty=1:2,col=1:2,lwd=3) abline(v=.5) ################## posterior distribution ########## ################## prior: beta(50 50) and beta(5 5) ########## ################## prior: beta(50,50) and beta(5,5) ########## ################## data: 4 "1"s and 1 "0" ########## plot(pi0,dbeta(pi0,50,50)*pi0^4*(1-pi0),type="l",col=1,lwd=3, xlab=expression(pi),ylab="density", main=expression(paste("posterior distribution of ",pi))) lines(pi0,dbeta(pi0,5,5)*pi0^4*(1-pi0),,col=2,lty=2,lwd=3) legend(0.7,0.2,legend=c("prior","beta(50,50)","beta(5,5)"),lty=0:2,col=0:2,lwd=3) text(.8,.12,"data=1,1,1,1,0") abline(v=c(.5,.8))

44 ################## posterior distribution ib ti ########## ################## prior: beta(50,50) and beta(5,5) ########## ################## data: 80 "1"s and 20 "0" par(mfrow=c(2,1)) plot(pi0,dbeta(pi0,50,50)*pi0^80*(1-pi0)^20,type="l",col=1,lwd=3,,, p ( p ),,,, xlab=expression(pi),ylab="density", main=expression(paste("posterior distribution of ",pi))) abline(v=c(.5,.8)) text(.2,2e-26,"data=80(1) and 20(0)") text(.2,3e-26,"strong t( 26 t prior beta(50,50)") 50)") plot(pi0,dbeta(pi0,5,5)*pi0^80*(1-pi0)^20,,col=2,lty=2,lwd=3) legend(0.7,0.2,legend=c("prior","beta(50,50)","beta(5,5)"),lty=0:2,col=0:2,lwd=3) text(.8,.12,"data=80(1) and 20(0)") text(.8,.12, data 80(1) and 20(0) ) abline(v=c(.5,.8)) text(.2,2e-43,"data=80(1) and 20(0)") text(.2,3e-43,"week prior beta(5,5)")

45 How do you set prior? If the hyper parameters are estimated from data, it is an Empirical Bayes method. This only works well when you have a large amount of data, such as in genomics borrow information : data on a particular feature may not be directly affected by other features, but data on other features help setting the prior distribution

46 Borrow information from all other probes on the same array Robust Multiarray Analysis (RMA) Y=B+S B ~ Normal (, 2 ) All probes exchangeable S ~ Exp(a) Estimate a,, 2 using all probes ( borrow strength across all probes ) Estimated Signal: E [ S Y ] Irizarry et al (2003)

47 Does it help? MAS 5.0 RMA

48 Aclose-up

49 II: Borrow information from other Rational: similar probes (GCRMA) identity of probes are determined by their sequences. predict affinity to non-specific binding based on sequence probes sharing similar affinity are expected to have similar background level

50 Which are the similar probes 0.6 C C C C C C C C C C C C 0.4 C C C C C C 0.2 C C C C C 0.0 GC A G G G G G G G T G C T G T T G T T T T T T T GT GT GT GT T T T T T T T T G G G G A G G G G A A A A A A A G A T G A T A A A A A A A A A A A A A A j, k1 1 k 1 j { A, T, G, C} b k j µ j,k ~ smooth function of k

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52 Normalization Normalization is needed to ensure that differences in intensities are indeed due to differential expression, and not some printing, hybridization, or scanning artifact. Normalization is different in spotted/two-color and highdensity-oligonucleotides (Affy) technologies No dye bias (hence no within-array normalization to remove dye effect) No print-tip issue

53 Normalization density log (PM) These are from replicate RNA Left are empirical density These are from replicate RNA. Left are empirical density estimates for 5 GeneChip arrays.

54 Non-linear dependency on intensity again These are two technical replicates. Only the red are differentially expressed

55 Nonlinear normalization Proposed solutions Force distributions (not just medians) to be the same: Amaratunga and Cabrera (2001) Bolstad et al. (2003) Use curve estimators such as splines to adjust for the effect: Li and Wong (2001) Note: they also use a rank invariant set Colantuoni et al (2002) Dudoit et al (2002) Use adjustments based on additive/multiplicative model: Rocke and Durbin (2003) Huber et al (2002) Cui et al (2003)

56 Quantile normalization All these non-linear methods perform similarly Quantile normalization is easy and fast Basic idea: order value in each array take average across probes Substitute probe intensity with average Put in original order

57 Example of quantile normalization Original Ordered Averaged Re-ordered

58 How does it work Before After But does it force everything to be the same and remove real differences?

59 After quantile normalization We say more later..

60 Assumption Either the majority of genes are not differentially expressed Or the differentially expression is symmetric

61 Dilution Experiment crna hybridized to human chip (HGU95) in range of proportions and dilutions Dilution series begins at 1.25 g crna per GeneChip array, and rises through 2.5, 5.0, 7.5, 10.0, to 20.0 g per array. 5 replicate chips were used at each dilution A few control genes were spiked in at same concentration across all arrays. Notice we can only make usual assumption within groups of 5

62 Raw Data

63 If you can t normalize your conclusions will likely l be wrong! 1.25 g, g 2.5 g,1g st 5 th scanner scanner

64 Normalize with control genes Looks almost as bad!

65 We can not median normalize We wash out real biological effects

66 Or quantile normalize

67 But we can quantile normalize and then use controls

68 Look at the improvement

69 Look at the improvement

70 Summarization Robust average Median polish (rma, gcrma) For a matrix X, assumes X ij =X 0 +R i +C j Estimates row effects (probe) and column effects (sample). Tukey, J. W. (1977). Exploratory Data Analysis R function medpolish (package: stat) Tukey biweight (MAS 5.0) R function tukey.biweight (package: affy)

71 Influence function How one observation changes the statistic Sample Mean can be sensitive to the change of any one data point Change x i to x *, the new sample mean changes by (x * /n-x i /n) The influence function is a straight line

72 FYI

73 summary Preprocessing is a common problem for many technologies Always keep in mind what is expected in the data. This is useful for quality control and normalization Where to look for pseudo-control when real controls are not available Robustness is important Empirical Bayes is particularly useful in bioinformatics

74 Exercise For those in Biostat PhD: Consider the model Y=B+S, where B ~ Normal (, 2 ) and S~ Exp(a). Suppose, 2 and a are known parameters. Derive the conditional expectation E[S Y] The code for plotting the prior and posterior distributions is provided in the lecture notes. For each of the two priors, Plot the posterior distributions of pi in the toy example, suppose the data is now 8 success out of 10 trials. Plot the posterior distributions of pi in the toy example, suppose the data is now 80 success out of 100 trials. (For better visual effect you may have to plot the two posterior distributions separately rather than in the same figure as shown in the lecture notes.) how would you explain to a non-statistician the role of prior and likelihood in Bayesian inference?