A novel method for subgroup discovery in precision medicine based on topological data analysis.

Background: The Mapper algorithm is a data mining topological tool that can help us to obtain higher level understanding of disease by visualising the structure of patient data as a similarity graph. It has been successfully applied for exploratory analysis of cancer data in the past, delivering several significant subgroup discoveries. Using the Mapper algorithm in practice requires setting up multiple parameters. The graph then needs to be manually analysed according to a research question at hand. It has been highlighted in the literature that Mapper's parameters have significant impact on the output graph shape and there is no established way to select their optimal values. Hence while using the Mapper algorithm, different parameter values and consequently different output graphs need to be studied. This prevents routine application of the Mapper algorithm in real world settings.

Methods: We propose a new algorithm for subgroup discovery within the Mapper graph. We refer to the task as hotspot detection as it is designed to identify homogenous and geometrically compact subsets of patients, which are distinct with respect to their clinical or molecular profiles (e.g. survival). Furthermore, we propose to include the existence of a hotspot as a criterion while searching the parameter space, addressing one of the key limitations of the Mapper algorithm (i.e. parameter selection).

Results: Two experiments were performed to demonstrate the efficacy of the algorithm, including an artificial hotspot in the Two Circles dataset and a real world case study of subgroup discovery in oestrogen receptor-positive breast cancer. Our hotspot detection algorithm successfully identified graphs containing homogenous communities of nodes within the Two Circles dataset. When applied to gene expression data of ER+ breast cancer patients, appropriate parameters were identified to generate a Mapper graph revealing a hotspot of ER+ patients with poor prognosis and characteristic patterns of gene expression. This was subsequently confirmed in an independent breast cancer dataset.

Conclusions: Our proposed method can be effectively applied for subgroup discovery with pathology data. It allows us to find optimal parameters of the Mapper algorithm, bridging the gap between its potential and the translational research.