Statistical Methods for Identifying Differentially Expressed Genes in DNA Microarrays
In this chapter we discuss the problem of identifying differentially expressed genes from a set of microarray experiments. Statistically speaking, this task falls under the heading of “multiple hypothesis testing.” In other words, we must perform hypothesis tests on all genes simultaneously to determine whether each one is differentially expressed. Recall that in statistical hypothesis testing, we test a null hypothesis vs an alternative hypothesis. In this example, the null hypothesis is that there is no change in expression levels between experimental conditions. The alternative hypothesis is that there is some change. We reject the null hypothesis if there is enough evidence in favor of the alternative. This amounts to rejecting the null hypothesis if its corresponding statistic falls into some predetermined rejection region. Hypothesis testing is also concerned with measuring the probability of rejecting the null hypothesis when it is really true (called a false positive), and the probability of rejecting the null hypothesis when the alternative hypothesis is really true (called power).
- 2.Westfall, P. H. and Young, S. S. (1993) Resampling-Based Multiple Testing: Examples and Methods for p-Value Adjustment, Wiley, New York.Google Scholar
- 3.Benjamini, Y. and Hochberg, Y. (1985) Controlling the false discovery rate: a practical and powerful approach to multiple testing. J. Roy. Stat. Soc. B 85, 289–300.Google Scholar
- 4.Storey, J. D. A direct approach to false discovery rates, submitted. Available at http://www-stat.stanford.edu/~jstorey/.
- 5.Storey, J. D. and Tibshirani, R. Estimating false discovery rates under dependence, with applications to DNA microarrays, submitted. Available at http://www-stat.stanford.edu/~jstorey/.
- 7.Benjamini, Y. and Yekutieli, D. The control of the false discovery rate in multiple testing under dependency, in press.Google Scholar
- 8.Dudoit, S., Yang, Y., Callow, M., and Speed, T. Statistical methods for identifying differentially expressed genes in replicated cdna microarray experiments. Available at http://www.stat.berkeley.edu/users/sandrine.
- 9.Storey, J. D. The positive false discovery rate: a Bayesian interpretation and the q-value, submitted. Available at http://www-stat.stanford.edu/~jstorey/.
- 11.Efron, B., Tibshirani, R., Storey, J. D., and Tusher, V. Empirical Bayes analysis of a microarray experiment. J. Am. Stat. Assoc., in press.Google Scholar
- 12.Efron, B., Storey, J., and Tibshirani, R. Microarrays, empirical Bayes methods, and false discovery rates, submitted.Google Scholar