Discussion of ‘Event history and topological data analysis’

Abstract

Because many statisticians may not yet be aware of topological data analysis and, as the underlying mathematical theory of persistent homology is rather technical, the example-based introduction to topological data analysis provided by Garside et al.(2021) is appreciated; alternatively, see Biscio & Møller (2019, § 1.1). In topological data analysis, a nested sequence of subcomplexes is used to determine the birth and death times of topological features, and often these birth and death times are represented in a persistence diagram, such as Fig. 3 in Garside et al.(2021). Garside et al.’s idea of adapting this approach to the context of event history analysis is appealing. In particular, we like that it is easy to calculate confidence bounds for the Nelson–Aalen estimator in a nonparametric setting, and that it is possible to deal with censored trees and covariates. However, Garside et al.(2021) do not fully take their idea to …