Algorithm 1 PRANA: Pseudo-value Regression Approach in Network Analysis

Input:

\(n_z\) samples (in rows) × p expression levels of genes (in columns) RNA-Seq expression data and \(n_z\) × q phenotype data for each group z = 1, 2.

Output:

A vector of adjusted p-values (and coefficient estimates and p-values) of the group variable for each gene k with a covariate adjustment.

1:

Estimate p × p association matrix (a matrix form of a network) via ARACNE [27] from the \(n_z\) × p expression data for each group z = 1, 2.

2:

Obtain the group-specific degree centrality by taking the marginal sums of association matrix of each taxa k ∈ {1, · · · , p}.

3:

Repeat the first two steps above but using the association matrix that is re-estimated from the expression data without the i ∈ {1, · · · , \(n_z\)} individual of \(n_z\) × p data.

4:

Calculate a group-specific jackknife pseudo-value for each gene k and individual i based on summary measures of degree centrality from Steps 2 and 3.

5:

For each gene k, a robust regression is fitted with a binary group variable and additional covariates to obtain the p-values of the group variable. In the regression, a binary group variable is the main predictor to declare a gene is DC between two groups under different conditions (or phenotypes).

6:

Lastly, a vector of gene-specific adjusted p-values [28] of the group variable is returned. See the Results section for more demonstration.