Implementation of Persistent Homology in Survival Analysis for Correlated and Longitudinal Data : A case study of COVID-19 Spread in Indonesia
Utih Amartiwi, Yaroslav A. Kholodov

Innopolis University

Abstract

Most survival models assume no autocorrelation between objects and time-independence. However, in many cases of disease spread, an object can potentially affect its neighbors, and the feature may change over time. To address these issues, we implemented persistent homology, a topological data analysis (TDA) approach, to handle the problems of correlated and longitudinal data. We applied this to the case of the first infection time of COVID-19 in each province in Indonesia, using the human mobility index as a feature. The results show that survival models with persistent homology achieved a higher C-Index than those without persistent homology.

Keywords: topological data analysis, persistent homology, survival analysis, correlated data, longitudinal data, Covid-19

Topic: Probability and Stochastic Analysis