Fig. 7

A case–control study that considers matrix-variate samples. a Data matrices stacked along the x-axis to form a data cubic. Each element in the data cubic is a real or discrete value, called the expression at the corresponding coordinate. Each matrix sample consisting of rows obtained from different conditions is arranged along the z-axis, while each row consisting of probes or called measurements is located along the y-axis. b Row-wise bi-partition of the data cubic with the control representing those normal (N) conditions and the case representing those abnormal or trouble (T) conditions. Test is made per a probe, aiming at differentiation expression (DE) cross conditions (N and T), shortly called NT test. Those with the p value below a threshold and the fold rate of T over N bigger than a threshold are selected as a set \(F_{NT}\) of significant DE probes. On the right side, the scatter plot consists of dots locating on a vertical line, with two dots per sample (T in red, N in green). c Column-wise bi-partition of the data cubic with the case and control representing two of targeted phenotypes (e.g. cancer stages I, II, III, & IV, 3-year survival, 5-year survival, etc). Only the T layer is considered. Similar to b but with T, N replaced by \(PT_1\), \(PT_2\), the test aims at a set \(F_{PT}\) of significant DE probes of targeted phenotypes (\(PT_1\), \(PT_2\)), shortly called PT test. d Both the T and N layers are jointly considered. We have two ways for getting \(F_{PT}\). One considers two steps, firstly getting \(F_{NT}\) in the same way as (b) and then getting \(F_{PT}\subseteq F_{NT}\) in the same way as (c), featured by two lines of scatters on its right side. The second considers T and N jointly in a 2D sample and makes a two-variate PT test to get a set \(F_{PT}\) of significant DE probes cross \(PT_1\), \(PT_2\). The right side is a 2D scatter plot with a dot representing two dots in (b)