t.opt

Genes with predominantly (but not homogeneously) high expression in the experimental group as compared to a control group exhibit a high difference between the average expression among highly expressed samples of the experimental group and the average expression in the control group. To estimate this difference, it is straightforward to compare trimmed means. One way to choose the trimming proportion adaptively is based on a series of comparisons of trimmed means. This is done using a t-statistic where trimmed empirical means and trimmed empirical variances of the two groups are plugged in. For this test statistic the trimming proportion is selected from a pre-determined set, e. g., {0.0, 0.1, 0.2, 0.3}. Raw P-values are computed for each trimming proportion by comparing the value of the test statistic to the t-distribution with appropriate degrees of freedom. We define that trimming proportion as the 'optimal' one which yields the smallest raw P-value. Of course, the optimization of the trimming proportion has to be accounted for when generating the permutation distribution of the test statistic: the same series of tests is performed for each permutation and the minimum of the obtained P-values is selected as the P-value corresponding to that permutation. Obviously, there is a trade-off between the number of tests to be corrected for and the chance of finding that trimming proportion that best detects PHE. Because of the inherent optimization with respect to the trimming proportion, we denote this test as the optimization test (Opt-test).
We have prepared an R package implementing the Opt-test and, for comparison purposes, the traditional t-test, suitable for application in microarray studies. The package takes a matrix of gene expression and a vector of group labels as input, and computes Opt-test and t statistics. Furthermore, q-values controlling the false discovery rate are computed for each gene. A constant can be added to the pooled within-group standard error estimate of each gene to stabilize the distribution of test statistic, similar to the approach used in the samr package (Chu et al, 2009). A utility function supplied with the package can be employed to optimize this constant.

Referenzen:
Gleiss, A., Sanchez-Cabo, F., Perco, P., Tong, D., Heinze, G. (2011): "Adaptive trimmed t-Tests for identifying predominantly high expression in a microarray experiment", Statistics in Medicine 30 (1), 52 - 61
doi:10.1002/sim.4093
Chu, G., Narasimhan, B., Tibshirani, R., Tusher, V.: "Significance Analysis of Microarrays - Users guide and technical document", available at http://www-stat.stanford.edu/~tibs/SAM/sam.pdf (accessed 3rd November 2009)

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