A topological approach for cancer subtyping from gene expression data

Gene expression data contains key information which can be used for subtyping cancer patients. However, computational methods suffer from 'curse of dimensionality' due to very high dimensionality of omics data and therefore are not able to clearly distinguish between the discovered subtypes in terms of separation of survival plots.

To address this we propose a framework based on Topological Mapper algorithm. The novelty of this work is that we suggest a method for defining the filter function on which the mapper algorithm heavily depends. Survival analysis of the discovered cancer subtypes is carried out and evaluated in terms of minimum pairwise separation between the Kaplan-Meier plots. Furthermore, we present a method to measure the separation between the discovered subtypes based on hazard ratios.

Five cancer genomics datasets obtained from The Cancer Genome Atlas portal have been used for comparisons with Robust Sparse Correlation-Otrimle (RSC-Otrimle) algorithm and Similarity Network Fusion(SNF). Comparisons show that the minimum pairwise life expectancy difference (in days) between the discovered subtypes for lung, colon, breast, glioblastoma and kidney cancers is 107, 204, 20, 88 and 425 days, respectively, for the proposed methodology whereas it is only 69, 43, 6, 61 and 282 days for RSC-Otrimle and 9, 95, 18, 60 and 148 days for SNF. Hazard ratio analysis also shows that the proposed methodology performs better in four of the five datasets. A visual inspection of Kaplan-Meier plots reveals that the proposed methodology achieves lesser overlap in Kaplan-Meier plots especially for lung, breast and kidney cases. Furthermore, relevant genetic pathways for each subtype have been obtained and pathways which can be possible targets for treatment have been discussed.

The significance of this work lies in individualized understanding of cancer from patient to patient which is the backbone of Precision Medicine.