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Summer Inst. Of Epidemiology and Biostatistics, 2008: Gene Expression Data Analysis 8:30am-12:30pm in Room W2017 Carlo Colantuoni – [email protected] http://www.biostat.jhsph.edu/GenomeCAFE/GeneExpressionAnalysis/GEA2008.htm Class Outline • Basic Biology & Gene Expression Analysis Technology • Data Preprocessing, Normalization, & QC • Measures of Differential Expression • Multiple Comparison Problem • Clustering and Classification • The R Statistical Language and Bioconductor • GRADES – independent project with Affymetrix data. http://www.biostat.jhsph.edu/GenomeCAFE/GeneExpressionAnalysis/GEA2008.htm Class Outline - Detailed • Basic Biology & Gene Expression Analysis Technology – – – • Data Preprocessing, Normalization, & QC – – – – – – – • Bonferroni False Discovery Rate Analysis (FDR) Differential Expression of Functional Gene Groups – – – – – – • Basic Statistical Concepts T-tests and Associated Problems Significance analysis in microarrays (SAM) [ & Empirical Bayes] Complex ANOVA’s (limma package in R) Multiple Comparison Problem – – • Intensity Comparison & Ratio vs. Intensity Plots (log transformation) Background correction (PM-MM, RMA, GCRMA) Global Mean Normalization Loess Normalization Quantile Normalization (RMA & GCRMA) Quality Control: Batches, plates, pins, hybs, washes, and other artifacts Quality Control: PCA and MDS for dimension reduction Measures of Differential Expression – – – – • The Biology of Our Genome & Transcriptome Genome and Transcriptome Structure & Databases Gene Expression & Microarray Technology Functional Annotation of the Genome Hypergeometric test?, Χ2, KS, pDens, Wilcoxon Rank Sum Gene Set Enrichment Analysis (GSEA) Parametric Analysis of Gene Set Enrichment (PAGE) geneSetTest Notes on Experimental Design Clustering and Classification – – – Hierarchical clustering K-means Classification • • • LDA (PAM), kNN, Random Forests Cross-Validation Additional Topics – – – The R Statistical Language Bioconductor Affymetrix data processing example! DAY #3: Measures of Differential Expression: Review of basic statistical concepts T-tests and associated problems Significance analysis in microarrays (SAM) (Empirical Bayes) Complex ANOVA’s (“limma” package in R) Multiple Comparison Problem: Bonferroni FDR Differential Expression of Functional Gene Groups Notes on Experimental Design Slides from Rob Scharpf Fold-Change? T-Statistics? Some genes are more variable than others Slides from Rob Scharpf Slides from Rob Scharpf Slides from Rob Scharpf Slides from Rob Scharpf distribution of distribution of Slides from Rob Scharpf Slides from Rob Scharpf X1-X2 is normally distributed if X1 and X2 are normally distributed – is this the case in microarray data? Slides from Rob Scharpf Problem 1: T-statistic not t-distributed. Implication: p-values/inference incorrect P-values by permutation • It is common that the assumptions used to derive the statistics are not approximate enough to yield useful pvalues (e.g. when T-statistics are not T distributed.) • An alternative is to use permutations. p-values by permutations We focus on one gene only. For the bth iteration, b = 1, , B; 1. Permute the n data points for the gene (x). The first n1 are referred to as “treatments”, the second n2 as “controls”. 2. For each gene, calculate the corresponding two sample t-statistic, tb. After all the B permutations are done: 3. p = # { b: |tb| ≥ |tobserved| } / B 4. This does not yet address the issue of multiple tests! Another problem with t-tests The volcano plot shows, for a particular test, negative log p-value against the effect size (M). Remember this? Problem 2: t-statistic bigger for genes with smaller standard error estimates. Implication: Ranking might not be optimal Problem 2 • With low N’s SD estimates are unstable • Solutions: – Significance Analysis in Microarrays (SAM) – Empirical Bayes meothods and Stein estimators Significance analysis in microarrays (SAM) • A clever adaptation of the t-ratio to borrow information across genes • Implemented in Bioconductor in the siggenes package Significance analysis of microarrays applied to the ionizing radiation response, Tusher et al., PNAS 2002 SAM d-statistic • For gene i : yi xi di si s0 yi xi si mean of sample 1 mean of sample 2 Standard deviation of residuals for gene i s0 Exchangeability factor estimated using all genes Scatter plots of relative difference (d) vs standard deviation (s) of repeated expression measurements Random fluctuations in the data, measured by balanced permutations (for cell line 1 and 2) Relative difference for a permutation of the data that was balanced between cell lines 1 and 2. Selected genes: Beyond expected distribution SAM produces a modified T-statistic (d), and has an approach to the multiple comparison problem. eBayes: Borrowing Strength • An advantage of having tens of thousands of genes is that we can try to learn about typical standard deviations by looking at all genes • Empirical Bayes gives us a formal way of doing this • “Shrinkage” of variance estimates toward a “prior”: moderated t-statistics • Implemented in the limma package in R. In addition, limma provides methods for more complex experimental designs beyond simple, two-sample designs. The Multiple Comparison Problem (some slides courtesy of John Storey) Hypothesis Testing • Test for each gene: Null Hypothesis: no differential expression. • Two types of errors can be committed – Type I error or false positive (say that a gene is differentially expressed when it is not, i.e., reject a true null hypothesis). – Type II error or false negative (fail to identify a truly differentially expressed gene, i.e.,fail to reject a false null hypothesis) Hypothesis testing • Once you have a given score for each gene, how do you decide on a cut-off? • p-values are most common. • How do we decide on a cut-off when we are looking at many 1000’s of “tests”? • Are 0.05 and 0.01 appropriate? How many false positives would we get if we applied these cut-offs to long lists of genes? Multiple Comparison Problem • Even if we have good approximations of our p-values, we still face the multiple comparison problem. • When performing many independent tests, p-values no longer have the same interpretation. Bonferroni Procedure a = 0.05 # Tests = 1000 a = 0.05 / 1000 = 0.00005 or p = p * 1000 Bonferroni Procedure Too conservative. How else can we interpret many 1000’s of observed statistics? Instead of evaluating each statistic individually, can we assess a list of statistics: FDR (Benjamini & Hochberg 1995) FDR • Given a cut-off statistic, FDR gives us an estimate of the proportion of hits in our list of differentially expressed genes that are false. Null = Equivalent Expression; Alternative = Differential Expression False Discovery Rate • The “false discovery rate” measures the proportion of false positives among all genes called significant: # false positives # called significan t • This is usually appropriate because one wants to find as many truly differentially expressed genes as possible with relatively few false positives • The false discovery rate gives an estimate of the rate at which further biological verification will result in dead-ends Distribution of Statistics Distribution of Observed (black) and Permuted (red+blue) Correlations (r) N=90 2 1 Observed 0 Density 3 Permuted -0.4 -0.2 0.0 Statistic Correlation (r) 0.2 0.4 Correlation of Age with Gene Expression False Pos. FDR = Total Pos. 0.10 Permuted = Observed 0.05 Observed Permuted 0.00 Density 0.15 0.20 Distribution of Observed (black) and Permuted (red+blue) Correlations (r) -0.45 -0.40 Correlation (r) Correlation (r) -0.35 -0.30 Distribution of p-values Distribution of p-values from Observed (Black) and Permuted Data 2.0 N=90 0.5 1.0 Permuted 0.0 Density 1.5 Observed 0.0 0.2 0.4 p-value p-value 0.6 0.8 1.0 FDR = False Positives/Total Positive Calls This FDR analysis requires enough samples in each condition to estimate a statistic for each gene: observed statistic distribution. And enough samples in each condition to permute many times and recalculate this statistic: null statistic distribution. What if we don’t have this? FDR = 0.05 Beyond ±0.9 FDR = 0.05 Beyond ±0.9 False Positive Rate versus False Discovery Rate • False positive rate is the rate at which truly null genes are called significant # false positives FPR # truly null • False discovery rate is the rate at which significant genes are truly null # false positives FDR # called significan t False Positive Rate and P-values • The p-value is a measure of significance in terms of the false positive rate (aka Type I error rate) • P-value is defined to be the minimum false positive rate at which the statistic can be called significant • Can be described as the probability a truly null statistic is “as or more extreme” than the observed one False Discovery Rate and Q-values • The q-value is a measure of significance in terms of the false discovery rate • Q-value is defined to be the minimum false discovery rate at which the statistic can be called significant • Can be described as the probability a statistic “as or more extreme” is truly null Power and Sample Size Calculations are Hard • Need to specify: – – – – – a (Type I error rate, false positives) or FDR s (stdev: will be sample- and gene-specific) Effect size (how do we estimate?) Power (1-b, b=Type II error rate) Sample Size • Some papers: – Mueller, Parmigiani et al. JASA (2004) – Rich Simon’s group Biostatistics (2005) – Tibshirani. A simple method for assessing sample sizes in microarray experiments. BMC Bioinformatics. 2006 Mar 2;7:106. Beyond Individual Genes: Functional Gene Groups • Borrow statistical power across entire dataset • Integrate preexisting biological knowledge • Beyond threshold enrichment Functional Annotation of Lists of Genes KEGG PFAM SWISS-PROT GO DRAGON DAVID/EASE MatchMiner BioConductor (R) Gene Cross-Referencing and Gene Annotation Tools In BioConductor (in the R statistical language) annotate package Microarray-specific “metadata” packages DB-specific “metadata” packages AnnBuilder package Annotation Tools In BioConductor: annotate package Functions for accessing data in metadata packages. Functions for accessing NCBI databases. Functions for assembling HTML tables. Annotation Tools In BioConductor: Annotation for Commercial Microarrays Array-specific metadata packages Annotation Tools In BioConductor: Functional Annotation with other DB’s GO metadata package Annotation Tools In BioConductor: Functional Annotation with other DB’s KEGG metadata package Functional Gene Subgroups within An Experiment 0 . 3 Swiss-Prot 0 . 2 EXP#1 0 . 1 PFAM 0 . 0 4 0 . 3 2 0 2 4 2 0 2 4 2 0 2 4 0 . 2 0 . 1 KEGG 0 . 0 4 0 . 3 0 . 2 0 . 1 0 . 0 4 Threshold Enrichment: One Way of Assessing Differential Expression of Functional Gene Groups Threshold Enrichment: One Way of Assessing Differential Expression of Functional Gene Groups Statistics for Analysis of Differential Expression of Gene Subgroups Is THIS … 0 . 3 … Different from THIS? 0 . 2 0 . 1 0 . 0 4 2 0 2 4 Over-Expression of a Group of Functionally Related Genes p<7.42e-08 T statistic Is THIS … 0 . 3 … Different from THIS? 0 . 2 Conceptually Distinct from Threshold Enrichment and the Hypergeometric test! 0 . 1 0 . 0 4 Statistical Tests: 2 0 2 4 c2 Kolmogorov-Smirnov Product of Probabilities GSEA PAGE geneSetTest (Wilcoxon rank sum) c2 All Genes c2 is the sum of D values where: (O-E)2 ______ D= E Subset of Interest histogram bins E O Kolmogorov-Smirnov All Genes Subset of Interest Product of Individual Probabilities All Genes Subset of Interest What shape/type of distributions would each of these tests be sensitive to? All statistics Statistics from gene subgroup Gene Set Enrichment Analysis (GSEA) Subramanian et al, 2005 PNAS Gene Set Enrichment Analysis (GSEA) Gene Set Enrichment Analysis (GSEA) Gene Set Enrichment Analysis (GSEA) Gene Set Enrichment Analysis (GSEA) Gene Set Enrichment Analysis (GSEA) Parametric Analysis of Gene Set Enrichment (PAGE) Kim et al, 2005 BMC Bioinformatics Parametric Analysis of Gene Set Enrichment (PAGE) Z = Sm-m 0.5 s/m A simple method in Bioconductor geneSetTest(limma) Test whether a set of genes is enriched for differential expression. Usage: geneSetTest(selected,statistics,alternative="mi xed",type="auto",ranks.only=TRUE,nsim=10000) The test statistic used for the gene-set-test is the mean of the statistics in the set. If ranks.only is TRUE the only the ranks of the statistics are used. In this case the pvalue is obtained from a Wilcoxon test. If ranks.only is FALSE, then the p-value is obtained by simulation using nsim random selected sets of genes. Wilcoxon test 0 . 3 0 . 2 0 . 1 0 . 0 4 2 0 2 4 Analysis of Gene Networks Large Protein Interaction Network Network Regulated in Sample #1 Large Protein Interaction Network Network Regulated in Sample #2 Network Regulated in Sample #1 Large Protein Interaction Network Network Regulated in Sample #3 Network Regulated in Sample #1 Network Regulated in Sample #2 Large Protein Interaction Network Network of Interest Network Regulated in Sample #1 Network Regulated in Sample #2 Network Regulated in Sample #3 Additional Notes on Experimental Design Replicates in a mouse model: Dissection of tissue Biological Replicates RNA Isolation Amplification Technical Replicates Probe labelling Hybridization Common question in experimental design • Should I pool mRNA samples across subjects in an effort to reduce the effect of biological variability (or cost)? Two simple designs • The following two designs have roughly the same cost: – 3 individuals, 3 arrays – Pool of three individuals, 3 technical replicates • To a statistician the second design seems obviously worse. But, I found it hard to convince many biologist of this. – 3 pools of 3 animals on individual arrays? Cons of Pooling Everything • You can not measure within class variation • Therefore, no population inference possible • Mathematical averaging is an alternative way of reducing variance. • Pooling may have non-linear effects • You can not take the log before you average: E[log(X+Y)] ≠ E[log(X)] + E[log(Y)] • You can not detect outliers *If the measurements are independent and identically distributed Cons specific to microarrays • Different genes have dramatically different biological variances. • Not measuring this variance will result in genes with larger biological variance having a better chance of being considered more important Higher variance: larger fold change We compute fold change for each gene (Y axis) From 12 individuals we estimate gene specific variance (X axis) If we pool we never see this variance. Remember this? Useful Books: “Statistical analysis of gene expression microarray data” – Speed. “Analysis of gene expression data” – Parmigianni “Bioinformatics and computational biology solutions using R” - Irizarry