Using 2-way ANOVA to dissect the immune response to hookworm infection in mouse lung Using 2-way ANOVA to dissect the immune response to hookworm infection in mouse lung General microarry data analysis workflow From raw data to biological significance Comparison statistics Two-way ANOVA GeneSifter Overview The Gene Expression Omnibus (GEO) Microarray analysis of gene expression following hookworm infection Data overview Dissection of the immune response using 2-way ANOVA The Microarray Data Analysis Process Experimental Design Number of groups, factors, replicates Data management Data, sample annotation, gene annotation, databases Differential Expression Comparison statistics, Correction for multiple testing, Clustering Biological significance Individual genes, Biological themes Platform Selection One-color, two-color, platform comparisons System access Ease of you, accessibility Making data public and using public data MIAME, Journals, GEO, meta-analysis The Microarray Data Analysis Process Experimental Design Number of groups, factors, replicates Data management Data, sample annotation, gene annotation, databases Differential Expression Comparison statistics, Correction for multiple testing, Clustering Biological significance Individual genes, Biological themes Platform Selection One-color, two-color, platform comparisons System access Ease of you, accessibility Making data public and using public data MIAME, Journals, GEO, meta-analysis Experiment Design •Type of experiment – Two groups • Normal vs. cancer • Control vs. treated – Three or more groups, single factor • Time series • Dose response • Multiple treatment – Four or more groups, multiple factors • Time series with control and treated cells The type of experiment and number of groups and factors will determine the statistical methods needed to detect differential expression •Replicates – The more the better, but at least 3 – Biological better than technical Rigorous statistical inferences cannot be made with a sample size of one. The more replicates, the stronger the inference. Pavlidis P, Li Q, Noble WS. The effect of replication on gene expression microarray experiments. Bioinformatics. 2003 Sep 1;19(13):1620-7. Experimental Design and Other Issues in Microarray Studies - Kathleen Kerr - http://ra.microslu.washington.edu/learning/documents/KerrNAS.pdf Differential Expression The fundamental goal of microarray experiments is to identify genes that are differentially expressed in the conditions being studied. Comparison statistics can be used to help identify differentially expressed genes and cluster analysis can be used to identify patterns of gene expression and to segregate a subset of genes based on these patterns. •Statistical Significance – Fold change Fold change does not address the reproducibility of the observed difference and cannot be used to determine the statistical significance. – Comparison statistics • 2 group – t-test, Welch’s t-test, Wilcoxon Rank Sum, • 3 or more groups, single factor – One-way ANOVA, Kruskal-Wallis • 4 or more groups, multiple factors – Two-way ANOVA Comparison tests require replicates and use the variability within the replicates to assign a confidence level as to whether the gene is differentially expressed. Supporting material - Draghici S. (2002) Statistical intelligence: effective analysis of high-density microarray data. Drug Discov Today, 7(11 Suppl).: S55-63. t-test for comparison of two groups Calculate t statistic difference between groups Mean grp 1 – Mean grp 2 t = = difference within groups ((s 2/n ) + (s 2/n ))1/2 1 1 2 2 s = variance n = size of sample Determine confidence level for t (probability that t could occur by chance) df = n + n - 2 1 2 The larger the difference between the groups and the lower the variance the bigger t will be and the lower p will be Differential Expression 2 groups, 4 replicates each Mean, standard deviation, fold change and p-value calculated 8 18 7 16 6 al 14 n 5 g Si 12 4 n 10 a 3 Me 8 6 2 4 al 1 n 2 g Si 0 0 an Exp Con Exp Con e M Gene 2 Gene 1 Fold Change = 5.3 Fold Change = 5.3 p = 0.03 p = 0.19 Fold change vs. p value Analysis of Variance (ANOVA) •Like t-test, identifies genes with large differences between groups and small differences within groups •For use with 3 or more groups •One-way and two-way •One-way examines effects of one factor on gene expression •Two-way can examine effects of two factors on gene expression as well as the interaction of the two factors Pavlidis P. Using ANOVA for gene selection from microarray studies of the nervous system. Methods. 2003 Dec;31(4):282-9. Glantz S. Primer of Biostatistics. 5th Edition. McGraw-Hill. Glantz S, Slinker B. Primer of Regression and Analysis of Variance. McGraw-Hill. Two-way ANOVA Example Triple treatment in Huntington’s Disease model (R6/2 mice, GSE857, Affymetrix U74Av2) Treatment Disease effect - + n e r e s WT 3 3 t a at Treatment effect e p s n Di R6/2 3 3 o i s s e r Interaction p x e e n e G Disease and treatment effect (no Interaction) - + - + T T 2 2 W W 6/ 6/ R R