New data science methods for precision medicine based on topological data analysis

However, the algorithm has numerous parameters, and its implementation is constrained by the subsequently large graph space which needs to be manually interrogated by the user.<br><br>This thesis aims to streamline applications of the Mapper algorithm for disease subgroup discovery and classification in precision medicine. First, I address the challenge of manual analysis of the Mapper graph by introducing a novel method to search for unique subgroups of patients within a Mapper graph.

In particular, I propose a novel algorithm that performs hotspot detection on a graph to locate anomalous and interconnected communities of nodes (i.e. a hotspot) representing homogenous subsets of patients. Simultaneously, I propose to address the problem of Mapper parameter selection by considering the presence of a hotspot as a parameter selection criterion. I explore artificial datasets using the novel algorithm and demonstrate the effectiveness of the hotspot detection method for subgroup discovery in Mapper.<br><br>As the second work of this thesis I apply the hotspot detection algorithm in a real world setting and demonstrate that it can extract a subset of patients with atypical survival outcomes from a larger cohort of breast cancer patients.

I investigate two publicly available gene expression datasets from oestrogen-receptor positive breast tumours, which are typically associated with a favourable prognosis. The hotspot detection algorithm uncovers a unique hotspot of patients with a shared gene signature and higher levels of tumour reoccurrence, who may benefit from modified interventions or treatment options in the future.<br><br>Finally, I address the challenge of classifying unseen patients as members of the hotspot group by proposing a novel Mapper-based classification algorithm.

The results show that standard machine-learning predictive algorithms produce inconsistent results in this task across five cancer gene expression datasets. The second proposed algorithm of this thesis, called ‘Mapper k-Nearest Neighbour’, extends the k-Nearest Neighbours algorithm for hotspot membership prediction. Mapper k-Nearest Neighbour is shown to achieve reliably high prediction performance, accommodating different hotspot scenarios produced from variable parameter selections in Mapper.<br><br>