Topological Data Analysis and its usefulness for precision medicine studies

Precision medicine allows the extraction of information from complex datasets to facilitate clinical decision-making at the individual level. Topological Data Analysis (TDA) offers promising tools that complement current analytical methods in precision medicine studies. We introduce the fundamental concepts of the TDA corpus (the simplicial complex, the Mapper graph, the persistence diagram and persistence landscape). We show how these can be used to enhance the prediction of clinical outcomes and to identify novel subpopulations of interest, particularly applied to understand remission of depression in data from the GENDEP clinical trial.