1. A Microarray-Based Screening Procedure for Detecting Differentially Represented Yeast Mutants Rafael A. Irizarry Department of Biostatistics, JHU rafa@jhu.edu http://biostat.jhsph.edu/~ririzarr

3. kanR A Transformation into deletion pool Select for Ura + transformants Genomic DNA preparation Circular pRS416 PCR Cy5 labeled PCR productsCy3 labeled PCR products Oligonucleotide array hybridization B EcoRI linearized PRS416 NHEJ Defective MCS CEN/ARS URA3 ttaa aatt CEN/ARS URA3 UPTAG DOWNTAG

4. Which mutants are NHEJ defective? Find mutants defective for transformation with linear DNA Dead in linear transformation (green) Alive in circular transformation (red) Look for spots with large log(R/G)

5. .

6. Data 5718 mutants 3 replicates on each slide 5 Haploid slides, 4 Diploid slides Arrays are divided into 2 downtags, 3 uptag (2 of which replicate uptags)

7. Average Red and Green Scatter Plot

8. Average Red and Green MVA plot

10. Improvement to usual approach Take into account that some mutants are dead and some alive Use a statistical model to represent this Mixture model? With ratio’s we lose information about R and G separately Look at them separately (absolute analysis)

11. Histograms

12. Using model we can attach uncertainty to tests For example posterior z-test, weighted average of z-tests with weights obtained using the posterior probability (obtained from EM) Is Normal(0,1)

13. QQ-Plot

14. Uptag/Downtag Z-Scores

15. Average Red and Green MVA Plot

16. Average Red and Green Scatter Plot

22. ResultsTable 1 YMR106C 9.5 47 69.2 a a 100 2 YOR005C 19.7 35 44.9 a d 100 3 YLR265C 6.1 32 35.8 a m 100 4 YDL041W 10.4 32 35.6 a m 100 5 YIL012W 12.2 31 21.7 a a 100 6 YIL093C 4.8 29 30.8 a a 100 7 YIL009W 5.6 29 -23.5 a a 100 8 YDL042C 12.9 29 32.1 a d 100 9 YIL154C 1.8 28 91.3 m m 82 10 YNL149C 1.7 27 93.4 m d 71 11 YBR085W 2.5 26 -15.8 a a 84 12 YBR234C 1.7 26 87.5 m d 75 13 YLR442C 6.1 26 -100.0 a a 100

23. Acknowledgements Siew Loon Ooi Jef Boeke Forrest Spencer Jean Yang

24. END

25. Summary Simple data exploration useful tool for quality assessment Statistical thinking helpful for interpretation Statistical models may help find signals in noise

26. Acknowledgements UC Berkeley Stat Ben Bolstad Sandrine Dudoit Terry Speed Jean Yang MBG (SOM) Jef Boeke Siew-Loon Ooi Marina Lee Forrest Spencer Biostatistics Karl Broman Leslie Cope Carlo Coulantoni Giovanni Parmigiani Scott Zeger Gene Logic Francois Colin Uwe Scherf’s Group PGA Tom Cappola Skip Garcia Joshua Hare WEHI Bridget Hobbs Natalie Thorne

31. Warning Absolute analyses can be dangerous for competitive hybridization slides We must be careful about “spot effect” Big R or G may only mean the spot they where on had large amounts of cDNA Look at some facts that make us feel safer

32. Correlation between replicates R1 R2 R3 G1 G2 G3 R1 1.00 0.95 0.95 0.94 0.90 0.90 R2 0.95 1.00 0.96 0.90 0.95 0.91 R3 0.95 0.96 1.00 0.91 0.92 0.95 G1 0.94 0.90 0.91 1.00 0.96 0.96 G2 0.90 0.95 0.92 0.96 1.00 0.97 G3 0.90 0.91 0.95 0.96 0.97 1.00

33. Correlation between red, green, haploid, diplod, uptag, downtag RHD RHU RDD RDU GHD GHU GDD GDU RHD 1.00 0.59 0.56 0.32 0.95 0.58 0.54 0.37 RHU 0.59 1.00 0.38 0.56 0.58 0.95 0.40 0.58 RDD 0.56 0.38 1.00 0.58 0.54 0.39 0.92 0.64 RDU 0.32 0.56 0.58 1.00 0.33 0.53 0.58 0.89 GHD 0.95 0.58 0.54 0.33 1.00 0.62 0.56 0.39 GHU 0.58 0.95 0.39 0.53 0.62 1.00 0.41 0.58 GDD 0.54 0.40 0.92 0.58 0.56 0.41 1.00 0.73 GDU 0.37 0.58 0.64 0.89 0.39 0.58 0.73 1.00

34. BTW The mean squared error across slides is about 3 times bigger than the mean squared error within slides

35. Mixture Model We use a mixture model that assumes: There are three classes: –Dead –Marginal –Alive Normally distributed with same correlation structure from gene to gene

36. Random effect justification Each x = (r1,…,r5,g1,…,g5) will have the following effects: Individual effect: same mutant same expression (replicates are alike) Genetic effect: same genetics same expression PCR effect : expect difference in uptag, downtag

37. Does it fit?

39. What can we do now that we couldn’t do before? Define a t-test that takes into account if mutants are dead or not when computing variance For each gene compute likelihood ratios comparing two hypothesis: alive/dead vs.dead/dead or alive/alive

40. QQ-plot for new t-test

41. Better looking than others

45. 1 YMR106C 9.5 47 69.2 a a 100 2 YOR005C 19.7 35 44.9 a d 100 3 YLR265C 6.1 32 35.8 a m 100 4 YDL041W 10.4 32 35.6 a m 100 5 YIL012W 12.2 31 21.7 a a 100 6 YIL093C 4.8 29 30.8 a a 100 7 YIL009W 5.6 29 -23.5 a a 100 8 YDL042C 12.9 29 32.1 a d 100 9 YIL154C 1.8 28 91.3 m m 82 10 YNL149C 1.7 27 93.4 m d 71 11 YBR085W 2.5 26 -15.8 a a 84 12 YBR234C 1.7 26 87.5 m d 75 13 YLR442C 6.1 26 -100.0 a a 100