Statistical Analysis of Microarray Data

1. Statistical Analysis of Microarray Data By H. Bjørn Nielsen

2. Question Experimental Design The DNA Array Analysis Pipeline Array design Probe design Sample Preparation Hybridization Buy Chip/Array Image analysis Normalization Expression Index Calculation Comparable Gene Expression Data Statistical Analysis Fit to Model (time series) Advanced Data Analysis Clustering PCA Classification Promoter Analysis Meta analysis Survival analysis Regulatory Network

3. Example: alcohol dehydrogenase is expressed at a higher level when alcohol is added to the media alcohol dehydrogenase without alcohol with alcohol What's the question? Typically we want to identify differentially expressed genes

4. He’s going to say it However, the measurements contain stochastic noise There is no way around it Statistics

5. statistics Noisy measurements p-value You can choose to think of statistics as a black box But, you still need to understand how to interpret the results

6. The output of the statistics P-value The chance of rejecting the null hypothesis by coincidence ---------------------------- For gene expression analysis we can say: the chance that a gene is categorized as differentially expressed by coincidence

7. The statistics gives us a p-value for each gene We can rank the genes according to the p-value But, we can’t really trust the p-value in a strict statistical way!

8. Why not! For two reasons: We are rarely fulfilling all the assumptions of the statistical test We have to take multi-testing into account

9. The t-test Assumptions 1. The observations in the two categories must be independent 2. The observations should be normally distributed 3. The sample size must be ‘large’ (>30 replicates)

10. Multi-testing? In a typical microarray analysis we test thousands of genes If we use a significance level of 0.05 and we test 1000 genes. We expect 50 genes to be significant by chance 1000 x 0.05 = 50

11. P-value log2 fold change (M) Volcano Plot

12. What's inside the black box ‘statistics’ t-test or ANOVA

13. The t-test Calculate T Lookup T in a table

14. Density Intensity of gene x The t-test II The t-test tests for difference in means () mut mutant wt wt

15. The t-test III The t statistic is based on the sample mean and variance t

16. Conclusion • Array data contains stochastic noise • Therefore statistics is needed to conclude on differential expression • We can’t really trust the p-value • But the statistics can rank genes • The capacity/needs of downstream processes can be used to set cutoff • FDR can be estimated • t-test is used for two category tests • ANOVA is used for multiple categories