# Molecular Subtyping and Outlier Detection in Human Disease Using the Paralique Algorithm
## 3 Experimental Results  
### Discussion  
We applied this novel analytical approach to a dozen sets of publicly available gene co-expression data obtained from the Gene Expression Omnibus (GEO). These data were selected because they provide a wide cross-section of human disease, and because each has both a case and a control group for the aforementioned filtering task. Table 1 provides an overview of the datasets we studied. Our investigation into the effectiveness of this proposed new methodology was focused on two guiding questions: (1) Are these tools capable of reliably and robustly identifying putative subtypes? (2) Are these subtypes appropriate to the associated disease as supported by biological evidence from clinical, published, analytical or other orthogonal information source(s)? The answer to the first question seems to be an unequivocal yes. As summarized in Table 2, our methods decomposed raw data into putative subtypes in ten of our datasets. In the case of asthma, for example, every patient sample fell into some paraclique. In other cases, patients were sometimes left unclassified, which is hardly surprising given the limitations on dataset sizes coupled with possible extremes in disease as well as sample heterogeneity. Only for Parkinson's disease and type 2 diabetes were no subtypes identified. It is probably no coincidence then that these two diseases also have by far the smallest datasets, especially in light of clinical subtyping evidence to the contrary [38; 39]. Figure 1: An illustration of the paraclique algorithm with glom term \(g=2\). (**a**) Starting with a maximum clique of size 4 as shown by red vertices, (**b**) paraclique first gloms onto vertex 5, (**c**) and then it gloms onto vertex 8 to form a paraclique of size 6. The second question is considerably more difficult to answer because it depends on the availability of alternate, non-transcriptomic data sources. We therefore followed a two-pronged approach in putative subtype comparisons. First, we calculated GO enrichments and their associated \(p\)-values for the top 100 differentially expressed genes in each paraclique. These results and their corresponding GO categories are summarized in Table 3. In every case, we found statistical evidence for biological significance among the genes separating samples into subgroups, with enrichment \(p\)-values ranging from \(1.1\,\times 10^{-4}\) for asthma to \(4.92\,\times 10^{-46}\) for prostate cancer. Next, we performed a literature search to check the top scoring genes for involvement in known subtypes. As such, this is at best a hit-or-miss proposition, and one depending for each disease on whether the research community has studied subtyping issues, found results, and published them in venues that we were able to search. Despite these obstacles, however, we found strong evidence in print to support our putative subtype decompositions for four of the diseases we studied. These are asthma, breast cancer, chronic lymphocytic leukemia, and colorectal cancer. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Disease**} & \multirow{2}{*}{
\begin{tabular}{c} **GEO** \\ **Accession** \\ \end{tabular} } & \multicolumn{2}{c}{**Patients**} & \multicolumn{2}{c}{**Probes**} \\ \cline{3-6}  & & **Case** & **Control** & **Initial** & **Filtered** \\ \hline Asthma & GSE4302 & 42 & 28 & 54,675 & 2322 \\ Breast Cancer & GSE10810 & 31 & 27 & 18,382 & 11,531 \\ Chronic Lymphocytic Leukemia & GSE8835 & 24 & 12 & 22,283 & 1338 \\ Colorectal Cancer & GSE9348 & 70 & 12 & 54,675 & 22,968 \\ Lung Cancer & GSE7670 & 27 & 27 & 22,283 & 7458 \\ Multiple Sclerosis & GD53920 & 14 & 15 & 54,674 & 9844 \\ Pancreatic Cancer & GD54102 & 36 & 16 & 54,613 & 23,711 \\ Parkinson’s Disease & GSE20141 & 10 & 8 & 54,674 & 6625 \\ Prostate Cancer & GSE6919 & 61 & 63 & 12,625 & 1531 \\ Psoriasis & GSE13355 & 58 & 58 & 54,675 & 29,407 \\ Schizophrenia & GSE17612 & 28 & 23 & 54,675 & 4250 \\ Type 2 Diabetes & GSE20966 & 10 & 10 & 61,294 & 93 \\ \hline \hline \end{tabular}
\end{table}