Gene Expression Data Analysis (I)

Transcription

1 Gene Expression Data Analysis (I) Bing Zhang Department of Biomedical Informatics Vanderbilt University

2 Bioinformatics tasks Biological question Experiment design Microarray experiment Image analysis Pre-processing Data Mining Experimental verification Data storage Data integration Data visualization Differential expression Clustering Classification Biological interpretation Hypothesis

3 Experiment design: well begun is half done A clearly defined biological question Well control of potential sources of variation (biological and technical) Statistically sound microarray experimental arrangement (replicates) Compliance with the standard of microarray information collection (MIAME)

4 Image analysis Analysis of the image of the scanned array in order to extract an intensity for each spot or feature on the array. Gridding: align a grid to the spots Segmentation: identify the shape of each spot Intensity extraction: extract intensity for each spot and potentially for each surrounding background Fixed circle Adaptive circle Seeded region growing

5 Data preprocessing Background correction: subtract background signal from the spot intensity to get a more accurate estimate of the biological signal from the spot Local subtraction: MM probe or local background Model-based correction: signal component + noise component Usually leads to an increased level of noise for low-expressing probe sets Normalization: remove systematic variation in a microarray experiment which affects the measured gene expression levels Experimenter bias Variability in experimental conditions Sample collection and preparation Machine parameters Summarization: combine the multiple probe intensities for each probe set to produce an expression value estimate (for affymetrix arrays) RMA model: y kij = β kj + α ki +ε kij k, j, i refer to probe set, array and probe, respectively

6 Normalization (within array, two-channel arrays) Remove systematic differences due to intensity and location dependent dye biases MA-plot M=log2(Cy5/Cy3) A=(log2(Cy5)+log2(Cy3))/2 Normalization Before normalization Global lowess normalization Global lowess (Locally weighted scatter plot smoothing) normalization: a non linear regression of log2(ratio)s against the average log2(intensity). It computes local linear regressions that are joined together to form a smooth curve. This normalization takes into account intensity artifacts. Print-tip lowess normalization: local linear regression computation are limited to a single print-tip group Before normalization Print-tip lowess normalization

7 Normalization (between arrays) Adjust the arrays using some control or housekeeping genes that you would expect to have the same intensity level across all of the samples Adjust using spike control Multiply each array by a constant to make the mean (median) intensity the same for each individual array (Global normalization) Match the percentiles of each array (Quantile normalization) No normalization Global normalization Quantile normalization

8 Get to know your data matrix Genes Samples Sample_1 Sample_2 Sample_3 Sample_4 Sample_5 Sample_6 TNNC DKK ZNF CHST FABP MGST DEFA VIL AKAP HS3ST

9 Bioinformatics tasks Biological question Experiment design Microarray experiment Image analysis Pre-processing Data Mining Experimental verification Data storage Data integration Data visualization Differential expression Clustering Classification Biological interpretation Hypothesis

10 Differential expression Genes Samples Sample_1 Sample_2 Sample_3 Sample_4 Sample_5 Sample_6 TNNC DKK ZNF CHST FABP MGST DEFA VIL AKAP HS3ST Case Control

11 Fold change n-fold change Arbitrarily selected fold change cut-offs Pros Usually 2 fold Intuitive and easily visualised Simple and rapid Cons Statistically inefficient Magnitude does not necessarily indicate importance Often too restrictive MA-plot M: log ratio ( log 2 (A/B) ) A: average log intensity ( log 2 (A*B)/2 )

12 Statistical analysis Genes Samples Sample_1 Sample_2 Sample_3 Sample_4 Sample_5 Sample_6 TNNC DKK ZNF CHST FABP MGST DEFA VIL AKAP HS3ST Case Control Null hypothesis Alternative hypothesis H 0 : µ 1 = µ 2 H 1 : µ 1 µ 2

13 Planning experiments for case-control studies Simulation of the dependency of fold change detection on the sample size. Experimental error is assumed to be 20%, i.e., CV of replicated control and treatment series equals 0.2. Samples are drawn from Gaussian distributions with mean equal to 1 for the control series and mean equal to 1.5 (black), 2 (red), 2.5 (green), 3 (blue), 5 (yellow), and 10 (magenta) for the treatment samples, respectively, in order to simulate the fold changes. Sampling is repeated 1000 times and the proportion of true positive test results (P < 0.05) is plotted (Y-axis) over the sample size (X-axis).

14 Differential Gene Expression: DNA arrays (continuous data) Statistical tests Student s t-test: a two sample location test of the null hypothesis that the means of two normally distributed populations are equal (equal variance). Welch s t-test: unequal variance Mann Whitney U test (also called Wilcoxon rank-sum test): nonparametric t-test vs U-test Robustness: U-test is more robust to outliers Efficiency: When normality holds, the efficiency of the U-test is about 0.95 when compared to the t-test. For distributions sufficiently far from normal and for sufficiently large sample sizes, the U-test can be considerably more efficient than the t-test. GeneX GeneX t-test: p=0.06; U test: p=0.1 t-test: p=0.32; U test: p=0.1

15 Differential Gene Expression: sequencing-based technologies (count data) 2 x 2 contingency table Counts in case Counts in control Total Counts for gene X a b a+b Counts for all other genes c d c+d Total a+c b+d a+b+c+d Statistical tests Chi-square test Fisher s exact test Poisson regression

16 Correction for multiple testing Why? In an experiment with a 10,000-gene array in which the significance level p is set at 0.05, 10,000 x 0.05 = 500 genes would be inferred as significant even though none is differentially expressed The probability of drawing the wrong conclusion in at least one of the n different test is P(wrong) =1 (1 α s ) n = α g α s Where is the significance level at single gene level, and is the global significance level. α g

17 Correction for multiple testing Methods Control the family-wise error rate (FWER), the probability that there is a single type I error in the entire set (family) of hypotheses tested. e.g. Standard Bonferroni Correction. uncorrected p value x no. of genes tested Control the false discovery rate (FDR), the expected proportion of false positives among the number of rejected hypotheses. e.g. Benjamini and Hochberg correction. Ranking all genes according to their p value Picking a desired FDR level, q (e.g. 5%) p i Starting from the top of the list, accept all genes with m q, where i is the number of genes accepted so far, and m is the total number of genes tested.

18 Gene list interpretation Microarray data Differential expression 92546_r_at 92545_f_at 96055_at _f_at _at _s_at 92202_g_at _at _at _s_at _at _at... Normalization Clustering Lists of genes with potential biological interest

19 Bioinformatics tasks Biological question Experiment design Microarray experiment Image analysis Pre-processing Data Mining Experimental verification Data storage Data integration Data visualization Differential expression Clustering Classification Biological interpretation Hypothesis

20 Over-representation analysis HSPA1A HSPA1B HSPA1L HSPA8 HSPB1 HSPB2 HSPB8 HSPC138 HSPD1 HSPE1 HSPH1 HYPB HYPK IBRDC2 ID4 IGFBP5 IL1F5 IL6ST compare PNRC1 GADD45B RRAGC DDIT3 ASNS FOSB UBE2H EPC1 HDAC9 JMJD1C RRAGC RIT1 PURA... Input gene list (152 genes) Observed total total Expected Predefined functional category (339 genes) Enrichment ratio: 6.08 p value: 9.34E-9

21 Over-representation analysis Significant genes Non-significant genes Total Genes in the category k j-k j Other genes n-k m-n-j+k m-j Total n m-n m Hypergeometric distribution: given a total of m genes where j genes are in the functional category, if we pick n genes randomly, what is the probability of having k or more genes from the category? p = min(n, j ) i= k m j n i j i m n Zhang et.al. Nucleic Acids Res. 33:W741, 2005

22 Commonly used functional categories Gene Ontology ( ) Structured, precisely defined, controlled vocabulary for describing the roles of genes and gene products Three organizing principles: molecular function, biological process, and cellular component Pathways KEGG ( ) Pathway Commons ( ) WikiPathways ( ) Common targets of transcription factors TRANSFAC ( Cytogenetic bands

23 WebGestalt: Web-based Gene Set Analysis Toolkit 8 organisms 132 ID types webgestalt 73,986 functional categories Zhang et.al. Nucleic Acids Res. 33:W741, 2005 Duncan et al. BMC Bioinformatics. 11:P10, 2010

24 WebGestalt: over-represented GO biological processes

25 WebGestalt: over-represented pathway

26 Limitation of the over-representation analysis Does not account for the order of genes in the significant gene list Arbitrary thresholding leads to the lose of information Assumes genes are independent

27 Gene Set Enrichment Analysis (GSEA) Subramanian et.al. PNAS 102:15545, 2005 Test whether the members of a predefined functional category are randomly distributed throughout the ranked gene list Calculation of an Enrichment Score, modified Kolmogorov Smirnov test Estimation of Significance Level of ES, permutation test Adjustment for Multiple Hypothesis Testing, control False Discovery Rate Leading edge subset: genes contribute to the significance

28 Summary Biological question Experiment design Microarray experiment Image analysis Pre-processing Data Mining Experimental verification Data storage Data integration Data visualization Differential expression Clustering Classification Biological interpretation Hypothesis