Analysis of (cdna) Microarray Data: Part I. Sources of Bias and Normalisation

Transcription

1 Analysis of (cdna) Microarray Data: Part I. Sources of Bias and Normalisation MICROARRAY ANALYSIS My (Educated?) View 1. Data included in GEXEX a. Whole data stored and securely available b. GP3xCLI on each hybridisation 2. Relaxed data acquisition criteria a. Signal to Noise > 1.00 (relaxer (sp?) exist) b. Mean to Median > 0.85 (Tran et al. 2002) 3. Data Normalisation 4. Mixed-Model Equations a. Check Residuals (plot Residuals vs Predicted) b. Check REML estimates of Variance Components c. Proportion of Total Variance due to Gene x Variety 5. Process Gene x Treatment BLUPs Differentially Expressed Genes a. t-statistics Z-score P-value b. Mixtures of Distributions Posterior Probabilities 6. Process Differentially Expressed genes a. Hierarchical clustering b. Gene ontology analysis 1

2 MICROARRAY ANALYSIS BASIC PIECES FOR SIGNAL DETECTION Foreground RED and GREEN R f G f Background RED and GREEN R b G b Background-corrected RED R = R f R b GREEN G = G f G b True Signals! Log-transformed Difference: Minus Mean: Average Log 2 (R) Log 2 (G) M = Log 2 (R) Log 2 (G) = Log 2 (R/G) A = 0.5 * ( Log 2 (R) + Log 2 (G) ) = 0.5 * Log 2 (R*G) MA-Plots to come Data Acquisition Criteria The Red/Green Intensities can be spatially biased 2

3 Data Acquisition Criteria The Red/Green Intensities can be intensity-biased MA-Plot Values should scatter around zero Data Acquisition Criteria Background Correction: Why bother? 3

4 Data Acquisition Criteria Background Correction: Why bother? Data Acquisition Criteria RED versus GREEN Log-transformation: Why bother? 4

5 Data Acquisition Criteria MA-Plots: All versus only valid signals Data Acquisition Criteria Signal to Noise Ratio Fg Bg S2N = σ Bg Mean to Median Correlation Min M 2 M = Max { Mean, Median} { Mean, Median} 5

6 Data Normalisation Normalisation is an attempt to correct for systematic bias. Normalisation allows you to compare data from one array to another. Systematic Bias can be introduced into microarray experiments at all stages. Need to: Avoid it (as much as possible) Recognize it Correct for it Discard unrecoverable data In practice we do not always understand the data - inevitably some biology will be removed too (or at least not revealed). Pool of Cell Lines Data Normalisation Tumor Source: Catherine Ball (Stanford) Different amounts of Differential starting material. labeling efficiency of dyes Different amounts of Differential RNA in efficiency each channel of scanning Differential in each efficiency channel. of hybridization over slide surface. 6

7 Sources Different labeling efficiencies or dye effects Scanner malfunction Differences in concentration of DNA on arrays (plate effects) Printing or tip problems Uneven hybridization Batch bias Experimenter issues Systematic Bias and Dealing with it Detect and recognize the effect Note something odd Determine magnitude and effect on data Try a few methods Identify source of bias Think big! Eliminate or reduce contributing factors Correct data Discard uncorrectable data Systematic Bias Labeling Efficiencies Cause Bias One channel of a twochannel array has higher intensity than the other (usually GREEN). Most common source of recognizable bias. Solution: Most easy to addressed (eg. dyeswaps, balanced loops). 7

8 Systematic Bias Scanning (operator?) Bias Mis-aligned lasers can cause big problems In this case, the two channels are slightly out of register Solution: fix the scanner and repeat Systematic Bias Printing (operator?) Bias Irregular shaped spots are often observed (printing error) Slides from the same printing batch cluster together Solution: Probably limited to better printing technique and image analysis, rather than normalization 8

9 Systematic Bias Probe Bias Different concentrations of probes might produce patterns in arrays Biological role of probes can produce patterns in arrays These patterns can create a spatial bias that are not artificial, but biological Systematic Bias Probe Bias Probes arranged on the array based on biological function cause spatial bias Solution: avoid arranging reporters based on function, know your experimental design Coding regions Intergenic regions 9

10 Systematic Bias Hybridisation (operator?) Bias Poor technique during hybridisation can cause a spatial bias Operator is one of the largest sources of systematic bias Experiments done by the same operator often cluster together more tightly than warranted by the biology Solution: Consistent methods, successful techniques Data Normalisation and other beautifying techniques Technique Choices Aim (Real) Aim (Ideal) Transformation To Near Normality Log 2 Lin-Log Numerically tractable Gaussian Normalisation Location Location Parameter: 1. Mean 2. Median 3. Regression(s) (LOWESS) Account for systematic effects Gaussian Standardisation Scale Scale Parameter Stabilise variance Gaussian 10

11 Data Normalisation Transformation to near normality Solution: Explore the entire Box-Cox family of power transformations: x ( λ) λ x 1 = λ ln( x) λ 0 λ= l( λ) = ln 2 n + ( λ 1) n j= 1 n j= 1 ( x ( λ) j ln( x ) x j ( λ) ) 2 Maximum at λ 0, hence use the log-transformation Data Normalisation Transformation to near normality Raw Data exponential-like Log2 Transformed normal-like 11

12 Data Normalisation Transformation to near normality Lin-Log Transformation x ( δ ) log2 ( x) x δ 1 = x log ( δ) 1+ x< δ 2 δ x = background corrected = Fg - Bg Data Normalisation Transformation to near normality The Edwards transformation as well as the Lin-Log transformation are an attempt to use the entire data, not only those for which foreground is greater than background. The reasoning is that errors are linear and multiplicative for small and large signals, respectively. The search for and choice of δ could be rather unconvincing (eg. Different for different array slides). Solution: Use Log 2 if Foreground > Background Otherwise, use a small arbitrary value (say 0), Or simply disregard. Alternatively: Use only Foreground and Log 2 it 12

13 Log 2 (R/G) c = M - c Location Parameter GLOBAL: Mean: c = Mean of M s Median: c = Median of M s Assumption: Changes roughly symmetric around Mean or Median LOWESS: c = Weighted Regress of M on A Assumption: Changes roughly symmetric at all intensities LOCAL: LOWESS: c = c(i) = Weighted Regression of M on A within print-tip-group i LOWESS = Locally WEighted Regression and Smoothing Scatterplots LOWESS = Locally WEighted Regression and Smoothing Scatterplots Source: G Rosa

14 LOWESS = Locally WEighted Regression and Smoothing Scatterplots SAS Code Source: G Rosa Genetic analysis of complex traits using SAS ISBN Normalised Intensities LOWESS = Locally WEighted Regression and Smoothing Scatterplots Source: G Rosa

15 LOWESS = Locally WEighted Regression and Smoothing Scatterplots Source: G Rosa None Source: Yang et al

16 After Global Median Source: Yang et al 2002 Global Lowess Source: Yang et al

17 Print-in-Group Lowess Source: Yang et al 2002 After Print-in-Group Lowess Source: Yang et al

18 Additional Assumption (other than symmetry of changes): The proportion of genes that are Differentially Expressed (DE) is minimal Question: Answer: Comment: Which genes to use? Only the ones (housekeeping) that we know are not DE Boutique arrays become a nuisance Scale Normalisation (Standardisation) Some scale adjustments may be required so that the relative expression levels from one particular experiment (slide) do not dominate the average relative expression levels across replicate experiments. Log 2 (R/G) c(i) a(i) Notes: 1. The scaling a(i) is such that Var(M) = a(i) 2 σ 2 2. The estimation requires an approximation ( robust ) to the geometric mean: MAD where MAD is the Median Absolute Deviation. 3. It doesn t get any more heuristic (funnier?) than this I I i =1 Yang et al 2002 i MAD i 18

19 Data Normalisation and other beautifying techniques Notes: 1. Except Log2, everything else applies only to Ratios: M = log2(r/g) 2. Except Log2, everything else applies only within slide 3. Everything is beautified to identify DE genes straight from MA-plot, either from a single slide or from a function of M s across slides. 4. The uncertainty in measurements increases as intensity decreases 5. Measurements close to the detection limit are the most uncertain (cf. Sensitivity) 6. Fold-change measurements ignore these effects 7. We can calculate an intensity-dependent z-score that measures the ratio relative to the standard deviation in the data Data Normalisation and other beautifying techniques Corrected Log10 ( Ratio ) 2 2 Locally estimated standard deviation of positive ratios Z= 5 Corrected Log10 ( Ratio ) 1 2-fold Z= 1 0 Z= -1 2-fold -1 Locally estimated standard deviation of negative ratios Z= 2 1 Z= 1 2-fold 0 2-fold Z= -1-1 Z= -5 Z= -2 Z= Mean ( Log10 ( Intensity ) ) Mean ( Log10 ( Intensity ) ) Local Log10 ( Ratio ) Z-Score 10 5 Z > 2 is at the ~ 95% confidence level Source: J Pevsner 2004 Z= Mean ( Log10 ( Intensity ) ) 19

20 Normalisation: References Bilban M, Buehler LK, Head S, Desoye G, Quaranta V. Normalizing DNA microarray data. Curr Issues Mol Biol Apr;4(2): Durbin BP, Hardin JS, Hawkins DM, Rocke DM. A variance-stabilizing transformation for gene-expression microarray data. Bioinformatics Jul;18 Suppl 1:S Kepler TB, Crosby L, Morgan KT. Normalization and analysis of DNA microarray data by self-consistency and local regression. Genome Biol Jun 28;3(7):RESEARCH0037. Schuchhardt, J., D. Beule, et al. Normalization Strategies for cdna Microarrays. NAR (10): E47-e47. Tran PH, Peiffer DA, Shin Y, Meek LM, Brody JP, Cho KW. Microarray optimizations: increasing spot accuracy and automated identification of true microarray signals. Nucleic Acids Res Jun 15;30(12):e54. Tseng GC, Oh MK, Rohlin L, Liao JC, Wong WH. Issues in cdna microarray analysis: quality filtering, channel normalization, models of variations and assessment of gene effects. Nucleic Acids Res Jun 15;29(12): Tsodikov A, Szabo A, Jones D. Adjustments and measures of differential expression for microarray data. Bioinformatics Feb;18(2): Yang MC, Ruan QG, Yang JJ, Eckenrode S, Wu S, McIndoe RA, She JX. A statistical method for flagging weak spots improves normalization and ratio estimates in microarrays. Physiol Genomics Oct 10;7(1): Yang YH, Dudoit S, Luu P, Lin DM, Peng V, Ngai J, Speed TP. Normalization for cdna microarray data: a robust composite method addressing single and multiple slide systematic variation. Nucleic Acids Res Feb 15;30(4):e15. 20