Identifying the Null Region Sample Clauses

Identifying the Null Region. As mentioned earlier, a majority of proteins will not be differentially expressed in any given SILAC experiment. These null proteins have an expected log-2 relative expression ratio of zero and are tightly packed around the center of the distribution of z. A simplistic method of identifying this central ‘null’ region is to use a cutoff such as ±1 SD or |z| ≤ 2. Xxxxxxxx (2007)[118], developed a method of optimally calculating this center region that produces consistent FDR estimates under the weak zero assumption. This assumption states that there exists an optimal cutoff t such that f1(z) = 0 for z ∈ [−t, t]. We adopt the same strategy in our work since this approach minimizes the MSE of the estimator f^+(z) and is asymptotically unbiased, when f0(z) is assumed to be N (µ0, σ2). Under this approach, the optimal cutoff rule, as a function of the total number of proteins, m, is t∗ ≈ µˆ0 + bσˆ0 (3.13) where µˆ0 = median(z), σˆ0 = IQR(z)/1.349, and b = max(1 , 4.3 m−0.112966). In the following sections, let, z0 = {z : z ∈ [−t∗, t∗]}, l0 = 2bσˆ0, and m0 = # (proteins in z0), denote the assumed null protein set, the length of the null region of z, and the number of assumed null proteins, respectively.