Analysis of microarray data - VSN International

Analysis of Microarray Data in GenStat 39Empirical Bayes error estimationWith the large number of genes analysed in parallel on the same series of slides, the variation in the resultsfor each gene may be thought of as coming from a common error distribution. If all the results weregenerated from a normal error process, we would expect the distribution of standard deviations for eachgene to follow a Chi-squared distribution. If this was the case, considerable extra power could be obtainedif we model the genes together, borrowing information from the whole distribution of standard deviations.The empirical Bayes error estimation does this by modelling the distribution of the standard deviations ofthe results over all probes. The distribution of standard deviations has two components, a single commonstandard deviation of the uniform error process operating on all genes, and a specific component ofvariance unique to each gene. A prior distribution for the standard deviations, or equivalently, thevariances, is assumed. In this approach, it is assumed that the reciprocal of the variance is distributed witha multiple of a chi-squared distribution with d 0 degrees of freedom, i.e.1 1 2~ χ2 2 d0spd0s0If the parameters of this distribution, the prior degrees of freedom and standard deviation, d 0 and s 0 areestimated, more information can be gained on an individual probe, by shrinking it towards the priorstandard deviation, s 0 . The relative amount of information in the prior and individual standard deviationof a probe, (s 0 and s p respectively) is specified by their degrees of freedom, d 0 and d p . The modifiedstandard deviation,~sp , is then given by the weighted average of s0 and s p :~sp=d0sd200+ d0s+ dp2pA modified t-test can then be performed using the modified standard deviation with d 0 +d p degrees offreedom. The method can also produce the p values from a test of the differential expression beingdifferent from zero.Using the estimates from the 13-6 to 13-9 series (saved in13-6to9_Estimates), we can create modified t-statistics andp-values for the contrast effects of DM vs. Control.Opening the menu Stats | Microarrays | Analyse | EmpiricalBayes error estimation gives us the window to the right,when the fields are filled in with the appropriate columnnames. The Data Type dropdown list allows the data to begiven in 3 formats, means (as in this example),T values, or a Pointer to a set of columns from whichmeans and standard deviations are calculated from eachrow over the set of columns. Note: a pointer is a GenStatstructure that specifies a list of data structures to be treated as agroup, that can be defined using the View | Data View menu). Theresult columns are specified in the Save section, with the option ofadding these back to the source spreadsheet if it is still open.Clicking the Options button opens the dialog to the right, whichallows you to specify whether the output printed in the Outputwindow, which graphs are plotted, and the nature of the t-testperformed (two sided or either of the one sided tests). Here, a two-sided test is used with output of theresults to the Output window, and just the histogram of the t-values before and after adjustment using theestimated prior parameters. Clicking the Run button creates the following output and graphs: