1. 1 John R. Stevens Utah State University Notes 1. Case Study Data Sets Mathematics Educators Workshop 28 March 2009 1 Advanced Statistical Methods: Beyond Linear Regression http://www.stat.usu.edu/~jrstevens/pcmi

2. 2 Why this workshop? 2 Me … Outreach mission of USU Recruitment – undergraduate & graduate Too much fun You …

3. 3 Outline 3 Notes 1: Case Study Data sets 1. Challenger Explosion 2. Beetle Fumigation 3. T-cell Cancer Notes 2: Statistical Methods I Logistic Regression – incl. Separation of Points EM Algorithm Notes 3: Statistical Methods II Tests for Differential Expression Multiple hypothesis testing Visualization Machine Learning Notes 4: Computer Implementation (Notes 5): Bonus Material

4. 4 Case Study 1: Challenger January 18, 1986 explosion prompted the Presidential Commission on the Space Shuttle Challenger Accident Commission's 1986 report attributed the explosion to a burn through of an O-ring seal at a field joint in one of the solid- fuel rocket boosters After each of the previous 24 launches, the solid rocket boosters were inspected, and the presence or absence of damage to the field joint was noted

5. 5 Challenger Data Motivating question: What was so different on the 25th launch? ObsFlightTempDamage 1STS166NO 2STS970NO 3STS51B75NO 4STS270YES 5STS41B57YES 6STS51G70NO 7STS369NO 8STS41C63YES 9STS51F81NO 10STS480 11STS41D70YES 12STS51I76NO 13STS568NO 14STS41G78NO 15STS51J79NO 16STS667NO 17STS51A67NO 18STS61A75YES 19STS772NO 20STS51C53YES 21STS61B76NO 22STS873NO 23STS51D67NO 24STS61C58YES

6. 6 Case Study 2: Beetle Fumigation – Rhyzopertha Dominica (Image courtesy Clemson University – USDA Cooperative Extension Slide Series, www.insectimages.org)

7. 7 Motivation Beetle: lesser grain borer A primary pest of stored grain A year-round problem in moderate climates Australian grain industry: $6–8 billion Zero tolerance for insect-infested grain Phosphine fumigant for control Some beetles have developed resistance levels more than 235 times greater than normal (UQ News Online, 18 Oct. 1999)

8. 8 Experimental Background Two DNA markers linked to resistance rp6.79: two genotypes: –,+ rp5.11: three genotypes: B,H,A Motivating question: What contributes to the degree of resistance? Mixture of six beetle genotypes  exposure to various concentrations of fumigant (48 hours)

9. 9 Experimental Data

10. 10 Practical Considerations in Choosing Dosage Clearly a high dosage would kill all beetles, regardless of genotype Time more important than concentration Expense more time with lower dose Technical limitations maintain concentration in silos Safety spontaneous combustion at high conc.

11. 11 Case Study 3: T-cell Cancer Acute lymphoblastic leukemia (ALL) leukemia – cancer of white blood cells ALL – excess of lymphoblasts (immature cells that become white blood cells) Two types of interest here: T-cell – manage cell-mediated immune response (activation of cells, release of cytokines) B-cell – manage humoral immune response (secretion of antibodies) Researchers used gene expression technology

12. 12 Central Dogma of Molecular Biology

13. 13 General assumption of microarray technology Use mRNA transcript abundance level as a measure of the level of “expression” for the corresponding gene Proportional to degree of gene expression

14. 14 How to measure mRNA abundance? Several different approaches with similar themes: Affymetrix GeneChip Nimblegen array Two-color cDNA array more Representation of genes on slide Small portion of gene Larger sequence of gene oligonucleotide arrays

15. 15 Affymetrix Probes (Images courtesy Affymetrix, www.affymetrix.com) 25 bp

16. 16 Affymetrix Technology – GeneChip Each spot on array represents a single probe sequence (with millions of copies) Perfect match Mismatch Each gene is represented by a unique set of probe pairs (usually 12-20 probe pairs per probe set) These probes are fixed to the array (Image courtesy Affymetrix, www.affymetrix.com)

17. 17 Affymetrix Technology – Expression (Images courtesy Affymetrix, www.affymetrix.com) A tissue sample is prepared so that its mRNA has fluorescent tags; wait for hybridization

18. 18 Affymetrix GeneChip Image courtesy Affymetrix, www.affymetrix.com

19. 19 Cartoon Representations Animation 1: GeneChip structureGeneChip structure (1 min.) Animation 2: Measuring gene expressionMeasuring gene expression (2.5 min)

20. 20 Data: Spot Intensities Images courtesy Affymetrix, www.affymetrix.com Full Array ImageClose-up of Array Image

21. 21 Basic goal of microarray technology “Observe” gene expression in different conditions – healthy vs. diseased, e.g. Decide which genes’ expression levels are changing significantly between conditions Target those genes – to halt disease, e.g. Study those genes – to better understand differences at the genetic level

22. 22 “Preprocessed” gene expression data 12625 genes (hgu95av2 Affymetrix GeneChip) 128 samples (arrays) a matrix of “expression values” – 128 cols, 12625 rows phenotypic data on all 128 patients, including: 95 B-cell cancer 33 T-cell cancer Motivating question: Which genes are changing expression values systematically between B-cell and T-cell groups? ALL Data

23. 23 Next … Analysis for these case studies Build on known statistical methods Notice huge potential for additional methods