Analysis of microarray data - VSN International

Analysis of Microarray Data in GenStat 41differentially expressed probes from the rest. There are two methods of estimating the FDR, one based ona mixture model, and another based on a non-parametric methods.False Discovery Rate using Bonferroni MethodThis menu can be used to estimate false discovery rates (defined in the table below) using a Bonferronitypeprocedure. This is a non-parametric approach, where for each value of lambda; the observedproportion of the sample that is not differentially expressed (π 0 ) is calculated. The procedure uses twomethods to get an overall measure of π 0 . The first uses bootstrapping to choose the value of π 0 whichminimises the mean squared error, and the second uses a spline smoother to smooth the values of π 0around the maximum value of lambda. Unadjusted q-values are then calculated from the estimate of π 0 asπ 0 *p*(Proportion of tests < p) (where p is the test probability) for each test value, and then the Bonferroniq values are defined as the minimum of the q values above each test value, stepping this procedure downthrough the sorted p values.The following table defines some random variables related to m hypothesis tests:Signficance Test # declared non-significant # declared significant Total# true null hypotheses U V m 0# non-true null hypotheses T S m 1 = m − m 0Total W = m − R R mm 0 is the number of true null hypotheses.m − m 0 is the number of false null hypotheses.U is the number of true negatives.V is the number of false positives.T is the number of false negatives.S is the number of true positives.H 1 ...H m are the null hypotheses being tested.In m hypothesis tests of which m 0 are true null hypotheses, R is an observable random variable, and S, T,U, and V are unobservable random variables. The proportion of tests that are truly null, π 0 , is m 0 dividedby m. The false discovery rate (FDR), also known as the q-value of a test, is a commonly used errormeasure in multiple-hypotheses, defined as FDR = E(V/R | R > 0) × Pr(R > 0), i.e. the expectedproportion of false positives findings among all the rejected hypotheses multiplied by the probability ofmaking at least one rejection; the FDR is zero when R = 0. Similarly the false rejection rate (FRR) isdefined as FRR = E(T/W | W > 0) × Pr(W > 0), i.e. the expected proportion of false negatives findingsamong all the accepted hypotheses times the probability of accepting at least one test. We also define thepower to be equal to E(S/m 1 | m 1 > 0) ×Pr(m 1 > 0).Opening the Stats | Microarray | Analyse |False Discovery Rate by Bonferronimenu gives the menu to the right. Usingthe F probability values in the file ‘Hyb-ANOVA.gwb’ in the Empirical Bayessection above, we can fit obtain theesimated false discovery rates toFProb[1].