Implementations | Applications |
---|---|

1. Make the two-variate PT test by the method given in Table 3 (a), which provides an improvement on making the two-variate PT test by Hotelling test as suggested in Table 8(1)(a) of Ref. Xu (2015a) | (a) Identify mRNA and lncRNA biomarkers for tumour vs normal in expression analysis |

2. Make the FDA-based PT test by Table 3 (b), especially one-tailed z-test or one-tailed t-test by Eq. (32), which is a complementary to the FDA-based PT test listed in Table 2(1) of Ref. Xu (2015a), where a univariate two-tailed t test is made
| (b) Identify mRNA and lncRNA biomarkers for 3-year & 5-year survival in expression analysis |

3. Find probes that significantly differentiate not only phenotypes but also abnormal vs normal, as well as their common part |
(c) Identify mRNA and lncRNA biomarkers for cancer grades I, II, III, & IV in expression analysis (d) For each of the above cases (a)(b)(c), we use the FDA projection \(s_u(f)= \mathbf{s}^T {\mathop{ {\beta}}\limits^{\rightarrow}}\) to replace the original expression value for painting heatmaps and making the corresponding clustering analysis |