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Statistical Tools

Statistical Tools. Balasubramanian Narasimhan, Data Coordinating Center Joint with Division of Biostatistics Stanford University. Microarray Data Analysis. Number of features greater than number of samples (p >> n) Traditional statistical algorithms cannot be used

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Statistical Tools

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  1. Statistical Tools Balasubramanian Narasimhan, Data Coordinating Center Joint with Division of Biostatistics Stanford University

  2. Microarray Data Analysis • Number of features greater than number of samples (p >> n) • Traditional statistical algorithms cannot be used • Simple, easily understood approaches are preferable • Goal is to extract a small number of meaningful features • Need a way to quantify errors in deciding which features are significant

  3. Signficance Analysis of Microarrays • Relies on a permutation distribution as a reference distribution • Compared observed t-like statistic with expected statistic values from the permutation distribution to decide which genes are significantly differentially expressed • Unified theory handles all kinds of response: two-class, multi-class, censored data, paired data • Provides False Discovery Rates (FDR) to quantify errors in genes called significant

  4. False Discovery Rate • Traditional approach to multiple hypothesis testing is a Bonferroni-type adjustment • FDR tells you what proportion of your genes called significant might actually be false positives. An FDR is 5% means out of 100 genes called significant, 5 of them could be false positives. • Just as p-values measure false positive rates, q-values (J. Storey) measure FDRs.

  5. SAM and FDR • A p-value of 5 % means that among all null features, 5% will will meet the rejection criterion • A q-value of 5% means that among all features called significant, 5% will be false positives • SAM provides q-values

  6. Prediction Analysis of Microarrays • Predict phenotype based on expression values • Algorithm is more general than the name implies • Utilizes shrunken centroids to select genes that characterize each class • Best illustrated with an example

  7. Peak Probability Contrasts • Data arising from Time-of-Flight Mass spectrometry for measuring relative abundance of different sized proteins in a blood sample, a useful technological complement to microarrays • Several popular systems including MALDI (matrix assisted laser desorption/ionization) and SELDI (Surface enhanced laser desorption/ionization) • Existing algorithms: svm, trees ,boosting, genetic algorithms • Focuses on peaks in the spectra at least for initial analysis • Accounts for variation in the horizontal position and peak heights for the same biological peak • Gives a measure of importance for each peak • Filters out less significant peaks in a simple way • Provides FDR estimates

  8. Software • We firmly believe that easily available and usable software is important • We therefore develop tools that are embedded in very common applications like Excel as many people seem to like the idea • Many of our tools are freely available on the web for download. (PPC will soon be on the list).

  9. References • J. Storey & R. Tibshirani. Statistical significance for genome-wide studies, PNAS 100: 9440-9445 • R. Tibshirani, B. Narasimhan, T. Hastie, G. Chu. Diagnosis of multiple cancer types by Shrunken Centroids of Gene Expression, PNAS 2002 99:6567-6572 (May 14) • PPC paper to appear in Bioinformatics.

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