Based on the provided scientific article, here's how the pathway enrichment analysis was conducted:

1. **Tool Used for Pathway Enrichment Analysis**: 
   - Ingenuity and Webgestalt (Web-based Gene-set Analysis Toolkit) were used for pathway enrichment analyses.
   - GSEA (Gene Set Enrichment Analysis) from the Molecular Signature Database (MSigDB) was also utilized.

2. **Tool Version Number Provided**:
   - Not described. The article does not specify version numbers for Ingenuity, Webgestalt, or GSEA.

3. **Gene Set Library Queried**:
   - Global Canonical Pathways in Ingenuity.
   - Various tools within Webgestalt were used (not specified which libraries).
   - Oncogenic and immunologic signatures from MSigDB in GSEA.

4. **Background Gene List Defined for Pathway Enrichment Analysis**:
   - For the 16k protein microarray analyses, all annotated proteins on the array were used as background.
   - For cytogenetic mapping (GSEA), the whole human genome was applied as gene positions.

5. **Statistical Test Used for Enrichment Analysis**:
   - Right-tailed Fisher’s exact test in Ingenuity.
   - Hypergeometric test in Webgestalt.
   - Not explicitly stated for GSEA, but typically uses methods like Kolmogorov-Smirnov statistics or permutation tests.

6. **False Discovery Rate Correction Used**:
   - False discovery rates (FDR) were mentioned as part of the results output in some analyses (e.g., Ingenuity).
   - The article does not explicitly state if FDR correction was applied for controlling false positives across all analyses, but it is commonly used in these contexts.

Here's how this information can be collated into a table:

| Question                                                                 | Answer                                |
|--------------------------------------------------------------------------|---------------------------------------|
| Tool Used for Pathway Enrichment Analysis                                | Ingenuity, Webgestalt, GSEA (MSigDB)  |
| Tool Version Number Provided                                             | Not described                         |
| Gene Set Library Queried                                                 | Global Canonical Pathways, MSigDB     |
| Background Gene List Defined                                             | Annotated proteins on the array, Human genome for GSEA |
| Statistical Test Used for Enrichment Analysis                            | Fisher’s exact test (Ingenuity), Hypergeometric test (Webgestalt) |
| False Discovery Rate Correction Used                                     | Not explicitly stated across all tools |

This table provides a structured summary of how pathway enrichment analysis was conducted in the study.