PMC:4979051 / 9443-10983 JSONTXT

{"target":"https://pubannotation.org/docs/sourcedb/PMC/sourceid/4979051","sourcedb":"PMC","sourceid":"4979051","source_url":"https://www.ncbi.nlm.nih.gov/pmc/4979051","text":"2. Methodology\nThe standard t-test is scale- and location-invariant, i.e., the results of the test do not change if x is replaced by ax+b, where a and b are constants. Because of that, according to the model described in Equation (1), applying the t-test to the normalized intensity data is equivalent to applying the test on the concentration variable θ, as illustrated in the following manipulations:tjg=〈Yijg〉i∈A−〈Yijg〉i∈Bs(Yijg)=〈Bjg〉i∈A+ϕjg〈θig〉i∈A−〈Bjg〉i∈B−ϕjg〈θig〉i∈Bϕjgs(θig)=ϕjg〈θig〉i∈A−〈θig〉i∈Bϕjgs(θig)=〈θig〉i∈A−〈θig〉i∈Bs(θig)j      (4)\nNote that no log transform was performed in the data and that for each gene g a set of t variables (one for each probe) is obtained. In order to select the differentially expressed genes, we propose to take the median t-values, since the median is more robust than the average in the presence of outliers. Then, the genes can be ranked according to its relevance by the median t-values, which often is enough for selecting a subset of genes as biomarkers candidates.\nTo estimate the statistical significance of the median t-values of each gene, we define F(t) and f(t) to be respectively the cdf and pdf distribution of a t-variable. Then, for the case of a number of probes equal to n, the pdf distribution of the median t-value g(t) is given by [21]:(5) g(t)=Cn[F(t)]n/2[1−F(t)]n/2f(t)ifnisevenandCn=n!(n/2)!(n/2)!Cn[F(t)](n−1)/2[1−F(t)](n−1)/2f(t)ifnisoddandCn=n!(n−1)/2!(n−1)/2!\nNow, for a given t-median value tm, a p-value can be estimated by integrating the pdf g(t) function for t\u003ctm.","divisions":[{"label":"Title","span":{"begin":0,"end":14}}],"tracks":[]}