Exploration and Analysis of DNA Microarray Data

Transcription

1 Exploration and Analysis of DNA Microarray Data Dhammika Amaratunga Senior Research Fellow in Nonclinical Biostatistics Johnson & Johnson Pharmaceutical Research & Development Javier Cabrera Associate Professor in Statistics Rutgers University A short course sponsored by the New Jersey Chapter of the American Statistical Association Piscataway, New Jersey, May

2 Agenda Morning session - Dhammika Amaratunga 1. A very brief intro to molecular biology 2. Microarrays: experimental procedure 3. Preprocessing microarray data 4. Finding differentially expressed genes Afternoon session - Javier Cabrera 5. Clustering genes and/or samples 6. Class prediction 7. Software 2

3 DNA An organism s genetic information is encoded in DNA stored in its cells. double-stranded molecule strand=backbone+bases nucleotide=backbone+base bases: A,T,G,C complementary bases on each strand (A T, G C) the sequence of bases contains the genetic info 3

4 The central dogma of molecular biology A gene is a segment of DNA whose sequence of bases (nucleotides) codes for a specific protein. AKAP6: CATCATGCAGCAGGTCAAACAAGG CATCTCCTAGTATTGCATCCTACA A gene is expressed via the process: DNA mrna protein transcription translation 4

5 Differential gene expression An organism s genome is the complete set of genes in each of its cells. Given an organism, every one of its cells has a copy of the exact same genome, but different cells express different genes different genes express under different conditions differential gene expression leads to altered cell states 5

6 Principal underlying gene expression studies Obtain gene expression profile information by measuring the levels of the various mrnas in a cell in a specific state information regarding what drives cell state Applications: biological pathways and disease processes functions of specific genes and proteins drug targets and toxicity mechanisms 6 medical diagnostics and prognostics

7 DNA microarrays DNA microarray technology is one of the most promising tools for obtaining gene expression data. A DNA microarray is a tiny glass slide on which genes (purified single-stranded cdna sequences in solution) have been robotically spotted in an (approximately) rectangular array. On a cdna microarray, each spot on the array corresponds to a single gene. 7

8 Experimental procedure Manufacture DNA microarray. Prepare labeled test sample. cellular contents mrna (isolate & purify) cdna sample (reverse (add flourescent transcription) dye) 8

9 Experimental procedure (continued) Disperse the labeled sample over the microarray. Whenever there is cdna in the array complementary to cdna (mrna) in the sample, the two will hybridize. Let hybridization take place, then wash and dry the array. Scan the array with a laser microscope. 9

10 Scanned image 10

11 Interpreting the scanned image High intensity spot the DNA at that spot corresponds to some mrna in sample. Low intensity spot no mrna in sample that corresponds to the DNA at that spot. Intensity ~ mrna abundance. For any gene, can compare intensities across different samples (but shouldn t compare intensities for different genes for the same sample). 11

12 Comparing two scanned images Control vs Treatment same genes on each slide 12

13 Paradigm dissimilar spot intensity pattern difference in mrna abundance in tissue genes differentially expressed within cell altered cell state 13

14 Objectives of microarray experiments (1) Identify those genes that are differentially expressed across two or more predefined classes (can compare gene expression patterns across classes multiple genes at a time): o Which genes are expressed in which cells and under what conditions. o Which genes are expressed differently in diseased cells compared to normal cells. o Which genes are expressed differently 14 when a patient is administered a drug.

15 Objectives of microarray experiments (2) Class prediction: Develop multi-gene predictor ( signature ) of class. o breast cancer patients - staging o toxicogenomics Pattern discovery: Discover clusters among samples or genes o breast cancer patients - subtypes o genes performing similar function 15

16 Processing steps Raw image Spotted image Preprocess Data analysis Biological inference 16

17 Convert scanned image to spotted image Run initial check of data quality Adjust for background Transform data Normalize data Deal with gross outliers and other anomalies Run final check of data quality Analyze data Interpret and report findings 17

18 Raw cdna microarray image speckles (B) (A) Light Background (C) Shape 18

19 Processing the raw image Gridding: where are the spots? Segmentation: which pixels correspond to the spot (signal) and which to background? Measurement: what is the intensity at each spot? Spot intensity = average pixel intensity within the spot Background intensity = average pixel intensity immediately around the spot 19

20 Data from the image Gene Row Col Signal Background G G G G G G G G G G

21 Image plot of a good array Signal Background

22 Image plot of a defective array Signal Background

23 Technology differences pin spotting or photolithography multi-channel or single-channel almost-complete or sequences (cdna) subsequences (oligonucleotides) cdna array Affymetrix chip 23

24 Two-channel cdna microarrays Take two mrna samples, label each with a different fluorescent dye, then disperse composite sample over microarray. The two spot intensities at a spot are very different the gene at that spot is differentially expressed. Advantage: Natural matching of samples - reduces spot-related bias. Disadvantage: intensity-dependent dye 24 effect, gene-specific dye effect, logistics.

25 Designs for two-channel experiments Simple Dye-swap Reference Dye A 1 A 2 A 1 A 2 A 1 A 2 R G A A A B Ref Ref B B B A A B larger studies simple but treatment effects confounded with dye effects extra effort needed but intensity-dependent dye effects can be separated out 25

26 Oligonucleotide arrays Each gene is represented by a probe set of 20 or so 25bp-oligonucleotides called perfect matches (PM). Each PM is paired with a mismatch (MM) formed by switching the middle base of PM - MM acts as a (imperfect) control. CTGATGATCTCGAATAGCGTGCGCGAATGAT PM: ATGATCTCGAATAGCGTGCGCGAAT MM: ATGATCTCGAATTGCGTGCGCGAAT 26

27 Oligonucleotide arrays (contd) Interpretation: PM>>MM gene expressed PM MM gene not expressed. Gene expression level: Ave(PM-MM) or RobustAve(PM-MM) or Ave(PM) or, with replicates, Li-Wong or RMA or Affymetrix: Array manufactured by synthesizing oligonucleotides directly onto the surface of a silicon chip. 27

28 A comparative experiment Data: Gene expression profiles for genes in 6 mice (= 3 Control + 3 Test). Question: Which genes are differentially expressed in C vs T? Or: Could ask whether the differential gene expression profiles discriminate between C and T (class prediction). 28

29 Single-channel spot intensity data Gene C1 C2 C3 T1 T2 T3 G G G G G G G G G G G G G G *

30 Convert scanned image to spotted image Run initial check of data quality Adjust for background Transform data Normalize data Deal with gross outliers and other anomalies Run final check of data quality Analyze data Interpret and report findings 30

31 Check array quality Check consistency across arrays Spearman correlation coefficient (measures the degree of monotonicity, preservation of rank order) Concordance correlation coefficient (measures the degree of agreement) ρ S

32 Convert scanned image to spotted image Run initial check of data quality Adjust for background Transform data Normalize data Deal with gross outliers and other anomalies Run final check of data quality Analyze data Interpret and report findings 32

33 Signal The signal at a particular spot is taken to be or or X g SpotIntensity X g SpotIntensity - Background X g SpotIntensity - SmoothedBackground LOG SIGNAL LOG BACKGROUND 33

34 Thresholding Sometimes the signal may be thresholded if low intensity values are considered unreliable: X g median(t Lower,X g,t Upper ) or X g MISSING if X g is considered unreliable 34

35 Convert scanned image to spotted image Run initial check of data quality Adjust for background Transform data Normalize data Deal with gross outliers and other anomalies Run final check of data quality Analyze data Interpret and report findings 35

36 Transformation Take logs (makes the range of the data more manageable, symmetrizes the withingene distribution but does not eliminate the heterogeneity of variances across genes, reduces but does not eliminate the skewness of the across-gene distribution). X log(x+λ) with λ=

37 Convert scanned image to spotted image Run initial check of data quality Adjust for background Transform data Normalize data Deal with gross outliers and other anomalies Run final check of data quality Analyze data Interpret and report findings 37

38 Normalization Often the signals on even identical microarrays tend to be on different scales (due to quality and quantity of RNA, labeling efficiency, laser setting, experimenter effects, etc) - this can be regarded as a sort of (nonlinear but monotone) array effect. The scales need to be normalized prior to further analysis, so that the arrays are on more directly comparable scales. 38

39 Two arrays LOG SIGNAL INTENSITY LOG(C2) C1 C LOG(C1) ARRAY 39 ρ (Concordance) = 0.90, ρ (Spearman) = 0.97

40 Normalization To normalize arrays C(1),..., C(n): Calculate the median mock array M. Either use LOWESS (or spline) smoother to model the relationship between C(i) and M or fit a continuous monotone increasing function to the quantiles of C(i) vs the quantiles of M. Back-predict to obtain the normalized values of C(i). 40

41 Two arrays (after normalization) LOG SIGNAL INTENSITY LOG(C2) C1 C LOG(C1) ARRAY 41 ρ (Concordance) = 0.98, ρ (Spearman) = 0.97

42 Normalization issues The normalization procedure must be nonlinear (i.e., intensity dependent). Lowess or spline normalization could be used when corresponding values should match across arrays (e.g., across technical replicates). Quantile normalization can be used to ensure similar distributions of values across arrays (e.g., across biological replicates). 42

43 Normalization issues (contd) Normalization preserves the rank order of the genes within each array. Normalization does not (directly) affect gene-specific effects. The normalizability of a set of arrays can be assessed using Spearman s correlation coefficient. The success of a normalization can be judged by an increase in the concordance correlation coefficient. 43

44 Normalization issues (contd) Normalization is based on a function fitted to a gene set comprised mostly of constantly expressing genes - how to select this set? [all / housekeeping genes / spikein controls / rank invariant genes] Other issues: stagewise normalization (when there are multiple levels of effects), probe level normalization (for oligonucleotide arrays), spatial normalization (e.g., print tip, uneven hybridization). 44

45 Convert scanned image to spotted image Run initial check of data quality Adjust for background Transform data Normalize data Deal with gross outliers and other anomalies Run final check of data quality Analyze data Interpret and report findings 45

46 Outliers Find gross outliers among replicates: X gi = gene g on array i M g =median i {X gi } R gi = X gi - M g S g/ = lowess-predict{ R gi vsm g } FENCE g = (M g -τ S g/, M g +τ S g/ ) What to do with outliers? (1) ignore (2) exclude (3) winsorize (4) impute (5) robust analysis 46

47 Missing values Impute values for missing observations (reduces impact of missing values on downstream analysis). A k nearest neighbor procedure: For each gene with missing values, (1) find its k nearest neighbors based on Euclidean distances computed using just the columns for which that gene is not missing, (2) impute the missing elements by averaging the corresponding non-missing elements of its neighbors. 47

48 Convert scanned image to spotted image Run initial check of data quality Adjust for background Transform data Normalize data Deal with gross outliers and other anomalies Run final check of data quality Analyze data Interpret and report findings 48

49 Preprocessed data C1 C2 C3 T1 T2 T3 G G G G G G G G G G ok G G ρ S, ρ CC, G G *

50 Convert scanned image to spotted image Run initial check of data quality Adjust for background Transform data Normalize data Deal with gross outliers and other anomalies Run final check of data quality Analyze data Interpret and report findings 50

51 Identify differentially expressed genes Nonstatistical: Seek genes that exhibit a specified fold increase in mean intensity (e.g., 2-fold). Statistical: Seek genes that exhibit a statistically significant difference across the 2 groups (via e.g., t test, Welch s test, Wilcoxon test, robust t test, permutation test - or perhaps a modelbased test depending on the situation). 51

52 Analysis results Top 10 genes (sorted by t-test p-value) Gene Fold Dir p p(bonf) G D G U G U G U G D G U G D G D G D G D

53 The multiplicity issue Issue: # tests # false positives (# false discoveries ). Fix 0: Report all statistically significant genes with no multiplicity adjustment. Drawback: too many false positives. Fix 1: Control the probability of even one false positive (i.e., control the familywise error rate) using, e.g., Bonferroni (p BON i min(gp i,1)) or Holm (step-down). Drawback: too many false negatives. 53

54 The multiplicity issue (contd) Fix 2: Examine a qqplot of the test statistics. Fix 3: Model p ~ Uniform(0,1) vs p ~BetaMix Expected Observed 54 p-values

55 The multiplicity issue (contd) Fix 4: (1) Rank the genes or select a subset of genes according to their (individual) significance (test stats or p- values) for differential gene expression. (2) Associate a number with each gene (or with the selected subset) that tells us how confident one should be that including it in a list of potentially differentially expressing genes does not substantially increase the rate of false findings. (pfdr or q-values) 55

56 The positive False Discovery Rate pfdr = Average ( #FalsePositives / #Positives ) To calculate: Either Decision rule says reject if T>c h 0 permute h 1 permute h 2 h m average=h* pfdr=h*/h 0 refine Or use a recursive formula. 56

57 In the example, o o Results (contd) 9 genes with p< in 9 permutations, on average, 2.8 genes with p< o pfdr = 2.8/9 = 31% 57

58 The effect of small sample size Issue: Often the sample size per group is very small. unreliable variances (inferences) dependence between the test statistics (t g ) and the standard error estimates (s g ) 58

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60 Fixing the small sample size effect Borrow strength across genes (LPE/EB) σ g2 = f (µ g ) Regularize the test statistics (SAM) t= ( X X )/( s ) T C P t = ( X X )/( s + s ) SAM T C P 0 (assess significance by permutation) Work with t g s g (Conditional t). 60

61 Other issues Long-tailed within-gene distribution with small signal-to-noise ratio. Highly skewed gene-to-gene distribution. Gene variance related to gene mean. Genes co-dependent in clumps. 61

62 Model Let X gij denote the preprocessed intensity measurement for gene g in array i of group j. Model: X gij = µ gj + σ g ε gij Effect of interest: τ g = µ g2 - µ g1 Error model: ε gij ~ F(location=0, scale=1) Gene mean-variance model: (µ g1,σ g ) ~ F µ,σ 62

63 Possible approaches Parametric: Assume functional forms for F and F µ,σ and apply either a Bayes or Empirical Bayes procedure. Nonparametric: Estimate F µ,σ : edf, ˆF, of {( X, s 2 µσ, g1 g )} Estimate F : edf, ˆF, of { ( X X )/ s } gij gj g Proceed via a resampling procedure. 63

64 CT Procedure (1) Draw a gene, g, at random from {1,, G}. 2 Call it g*. ( X, s g * * ) ~ ˆF 1 g µσ,. (2) Take a random sample (with replacement) of size n 1 +n 2 from ˆF * : r ~ ˆ ij F (3) Combine these to form pseudo-data: X * X s r * = + ij g * * 1 g ij (4) Calculate the pooled standard error s* and t test statistic t* for the pseudo-data {X ij * }. 64

65 CT Procedure (contd) (5) Repeat steps (1)-(4) a large number ( 10,000) of times. (6) Given α, estimate the critical envelope, t α (s g ), as the (α/2) and (1-α/2) quantile curves in the t g vs s g relationship. (7) Genes that fall outside the critical envelope defined by t α (s g ) are deemed significant at level α. (Overall unconditional Type I error rate = α) 65

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67 Comments regarding CT The edf F is a biased estimator of F σ, ˆs particularly with small sample sizes. This can be fixed using target estimation. The overall unconditional probability of Type I error is α. Good efficiency in simulations. Implemented in DNAMR. 67

68 Linear model based approaches (1) Let X gij denote the preprocessed intensity measurement for gene g in array i of group j. Model: X gij = µ gj + τ gj + ε gij Gene-by-gene analysis by F or SAM-F, or Conditional F or Variations: Dunnett s, dose-response trend, time course, external effects. 68

69 Linear model based approaches (2) Let X gij denote the preprocessed intensity measurement for gene g in array i of group j. Model: X gij = µ + τ j + α i(j) + γ g + (γα) gi + ε gij Fit in two stages: X gij = µ + τ j + α i(j) + δ gij R gij = γ g + (γα) gi + ε gij Other effects (e.g., dye and external effects) can be incorporated into model. 69

70 Convert scanned image to spotted image Run initial check of data quality Adjust for background Transform data Normalize data Deal with gross outliers and other anomalies Run final check of data quality Analyze data Interpret and report findings 70

71 Assess biological significance Data analysis list of differentially expressed genes? Confirm by RT-PCR or similar technique. Assess relevance by incorporating known properties of genes (e.g., gene ontology (GO) information: structured vocabulary for gene annotation - biological process, molecular function, cellular component). 71

72 End of morning session 72