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Sample Size Selection for Microarray based Gene Expression Studies

Sample Size Selection for Microarray based Gene Expression Studies. Gregory R. Warnes, Pfizer Global R&D. Fasheng Li Smith Hanley Consulting Group. Outline. What is the context? What is the problem? What are possible approaches? What approach was chosen and why?

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Sample Size Selection for Microarray based Gene Expression Studies

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  1. Sample Size Selection for Microarray based Gene Expression Studies Gregory R. Warnes, Pfizer Global R&D Fasheng Li Smith Hanley Consulting Group

  2. Outline • What is the context? • What is the problem? • What are possible approaches? • What approach was chosen and why? • How was the approach implemented? • What do the results look like? • Future plans? • References Industry/FDA Statistics Workshop: September 18-19, 2003

  3. What is Pfizer Global R&D? • What do we do? Lots! • Pharmaceutical research and development • Associated basic science, medical, and technological research • How are we doing? Very Well • 2003 R&D budget: $7.1 billion • 33 major research projects across 10 major therapeutic categories • 12,000 employees • 6 Major Research Sites Industry/FDA Statistics Workshop: September 18-19, 2003

  4. How are we using Gene Expression Technologies? • Determine regulatory and metabolic pathways • Identify potential biomarkers • Identify potential targets • Determine mechanism of action (desired and undesired) • Evaluate / predict safety • Determine mechanism of toxicity Industry/FDA Statistics Workshop: September 18-19, 2003

  5. What is the problem? • Gene expression assays are expensive • ~ $2,000 per samplefor Affymetrix experiments • Good experimental design is important • A huge number of variables measured on each experimental unit • 9,300 variables the Affymetrix S98 Yeast Genechip™ • 16,000 variables for Affymetrix RAE230a Rat Genechip™ • 23,000 + 23,000 = 46,000 variables for the Affymetrix U133A and U133B Human Genechips™ • Sample size calculations are hard Industry/FDA Statistics Workshop: September 18-19, 2003

  6. Standard sample size calculation For a single outcome variable, given • simple design (e.g., two-sample t-test) • effect size (ideally, minimum practical significance) • population variance ², • significance level(probability of a false positive when no true effect) • power(probability of a true positive given the defined effect size) It is straightforward to compute the required sample size n (see e.g. Cochrain & Cox (1957)) Industry/FDA Statistics Workshop: September 18-19, 2003

  7. Gene expression sample size calculation When there are thousands of outcome variables which are not independent, many problems arise: • How to handle multiple comparison? • How to deal with dependencies? • One effect size or many? • One power or many? • Many variables, how to get a single answer? Industry/FDA Statistics Workshop: September 18-19, 2003

  8. What are possible approaches? Two extremes: • Treat each variable (gene) as a separate and independent problem, then summarize + easy to set up, understand, explain + available data can be used - may not be sufficiently realistic, hence accuracy may suffer • Model the entire system, including realistic error structure and interdependencies +may be more accurate (if model is good) - more initial work to set up / compute - may require substantial new data to be realistic - May be hard to understand, explain Industry/FDA Statistics Workshop: September 18-19, 2003

  9. What approach was chosen and why? • We chose to treat each variable (gene) as a separate and independent problem, then summarize • Why? • First approximations usually yield a useful information with minimal effort. • Answers were needed immediately. • At best, results would only be used for general guidance • A more realistic error model didn’t work: We tried fitting the model from Zien, et al (2002), which requires high-dimensional numerical integration via MCMC or equivalent. However, the model appears to be non-identifiable. Industry/FDA Statistics Workshop: September 18-19, 2003

  10. How was the approach implemented? • Compute variance of each gene (variable) from existing studies • Assume a two sample t-test on log(expression) • Bonferonni adjust significance value: i =  / #variables • Generate plots of cumulative #genes : • Fixed I, , 1- vs. sample size (e.g. n=5/group,6/group,…) • Fixed I, , n vs. power (eg. 1-= 60%, 70%, 80%, …) • Fixed I, 1-, n vs. effect size (=1.5x, 2.0x, 2.5x, …) • Run twice: • ‘candidate’ genes ( less stringent Bonf. Adj.) • all genes • Implemented using R [Ross & Ihaka, 1996] using the power.t.test function. Industry/FDA Statistics Workshop: September 18-19, 2003

  11. What do the results look like? Standard Deviations: Focus Group Industry/FDA Statistics Workshop: September 18-19, 2003

  12. What do the results look like? Fixed I, , 1- vs. Sample Size:Focus Group Industry/FDA Statistics Workshop: September 18-19, 2003

  13. What do the results look like?Fixed I, , n vs. Power: Focus Group Industry/FDA Statistics Workshop: September 18-19, 2003

  14. What do the results look like?Fixed I, 1-, n vs. Fold Change: Focus Group Industry/FDA Statistics Workshop: September 18-19, 2003

  15. What do the results look like? Standard Deviations: All Genes Industry/FDA Statistics Workshop: September 18-19, 2003

  16. What do the results look like? Fixed I, , 1- vs. Sample Size:All Genes Industry/FDA Statistics Workshop: September 18-19, 2003

  17. What do the results look like?Fixed I, , n vs. Power: All genes Industry/FDA Statistics Workshop: September 18-19, 2003

  18. What do the results look like?Fixed I, 1-, n vs. Fold Change: All Genes Industry/FDA Statistics Workshop: September 18-19, 2003

  19. Future plans? • A web-applet backed by R to perform the calculations Industry/FDA Statistics Workshop: September 18-19, 2003

  20. Future plans? • Provide a web-applet backed by R to perform the calculations • Use a library of gene variation information in normal samples, (structured by organism, Affymetrix chip type, cell type, normalization/scaling method) • Extend to more complicated designs (2-way ANOVA, Repeated measures, etc) • Other types of multiple comparison adjustments (FDR) • Develop models that deal with correlations between genes. Industry/FDA Statistics Workshop: September 18-19, 2003

  21. References • Two-sample t-test sample size: • Cochrain WG, Cox GM (1953). Experimental Designs (2nd Ed). 17-28. • General sample size calculations: • Chow SC, Liu JP (1998). Design and Analysis of Clinical Trials : Concept and Methodologies. Wiley-Interscience. Chapter 10, 424 – 482 • Chow SC , Shao J, Wang H (2003). Sample Size Calculation in Clinical Research. Marcel Dekker [New, looks interesting] • Gene expression experiments sample size: • Zien A, Fluck J, Zimmer R, Lengauer T (2002). Microarrays: How Many Do You Need? RECOMB02, Meyers G, Hannenhalli S, Istrail S, Pevzner P, Waterman M, eds. 321-330. • Statistical analysis software: • Ihaka R, Gentleman R, et al (2003). http://www.r-project.org[web site] • Ross Ihaka and Robert Gentleman (1996). R: A Language for Data Analysis and Graphics, Journal of Computational and Graphical Statistics, Vol 5, Number 3: 299-314. • Web applet software: • Warnes GR, (2003). http://www.analytics.washington.edu/Zope/projects/RSessionDA/ [web site] • Me: • http://www.warnes.net Industry/FDA Statistics Workshop: September 18-19, 2003

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