Practical Issues in Microarray Data Analysis Mark Reimers National Cancer Institute Bethesda Maryland

Overview Scales for analysis Systematic errors Sample outliers & experimental consistency Useful graphics Implications for experimental design Platform consistency Individual differences

Distribution of Signals Most genes are expressed at very low levels Even after log-transform the distribution is skewed NB: Signal to abundance ratio NOT the same for different genes on the chip

Explanation of Distribution Shape Left hand steep bell curve probably due to measurement noise Underlying real distribution probably even steeper += abundances + noise = observed values

Variation Between Chips Technical variation: differences between measures of transcript abundance in same samples Causes: Sample preparation Slide Hybridization Measurement Individual variation: variation between samples or individuals Healthy individuals really do have consistently different levels of gene expression!

Replicates in True Scale Signals vary more between replicates at high end Level of ‘noise’ increases with signal mean signal chip 1 chip 2 Comparison of chips (Affy) Std Dev as a function of signal across all chips SD Red line is lowess fit

Replicates on Log Scale Measures fold-change identically across genes Noise at lower end is higher in log transform SD vs signal after log transform chip 1 vs chip 2 after log transform

Ratio-Intensity (R-I) plots Log scale makes it convenient to represent fold- changes up or down symmetrically R = log( Red/Green ); I = (1/2)log( Red*Green ) aka. MA (minus, add) plots (log) Ratio (log) Intensity

Simple power transforms (Box-Cox) often nearly stabilize variance Durbin and Huber derived variance-stabilizing transform from a theoretical model: y =  (background) + m e  (mult. error) +  static error) m is true signal;  and  have N(0,  ) distribution Transform: Could estimate  (background) and     empirically In practice often best effect on variance comes from parameters different from empirical estimates Huber’s harder to estimate Variance Stabilization

Box-Cox Transforms Simple power transformations (including log as extreme case), eg cube root Often work almost as well as variance- stabilizing transform

Should you use Transforms? Transforms change the list of genes that are differentially regulated The common argument is that bright genes have higher variability However you aren’t comparing different genes Log transform expands the variability of repressed genes Strong transforms (eg log) most suitable for situations where large fold-changes occur (eg. Cancers) Weak transforms more suited for situations where small changes are of interest (eg. Neurobiology)

Graphical methods Aims: Exploratory analysis, to see natural groupings, and to detect outliers To identify combinations of features that usefully characterize samples or genes Not really suitable for quantitative measures of confidence Principal Components Analysis (PCA) Standard procedure of finding combinations with greatest variance Multi-dimensional scaling (MDS) Represent distances between samples as a two- or three-dimensional distance Easy to visualize

MDS Plots

Representing Groups Cluster diagram Multi-dimensional scaling Day 1 Chips

Different Metrics – Same Scale 8 tumor; 2 normal tissue samples Distances are similar in each tree Normals close Tree topologies appear different Take with a grain of salt!

Volcano Plot Displays both biological importance and statistical significance log 2 (fold change) log 2 (p-value) or t-score

Quantile Plot Plot sample t- scores against t- scores under random hypothesis Statistically significant genes stand out Corresponding quantiles of t-distribution Sample t-scores

Systematic Variation Intensity-dependent dye bias due to ‘quenching’ Stringency (specificity) of hybridization due to ionic strength of hyb solution How far hybridization reaction progresses due to variation in mixing efficiency Spatial variation in all of the above

Relevance for Experimental Designs Balanced designs with several replicates built in have smaller standard errors than reference design with same number of chips – Kerr & Churchill Assuming error is random! Sample 2 Sample 1 Sample 5 Sample 4Sample 3 In practice very hard to deal with systematic errors in a symmetric design No two slides with comparable fold- changes

Critique of Optimal Designs Optimal for reduction of variance, if All chips are good quality No systematic errors – only random noise In fact systematic error is almost as great as random noise in many microarray experiments With loop designs single chip failures cause more loss of information than with reference designs

Individual Variation Numerous genes show high levels of inter- individual variation Level of variation depends on tissue also Donors, or experimental animals may be infected, or under social stress Tissues are hypoxic or ischemic for variable times before freezing

Frequent False Positives Immuno-globulins, and stress response proteins often 5-10X higher than typical in one or two samples Permutation p-values will be insignificant, even if t-score appears large gene levels frequency Group 1 Group 2