Survival Association Study in Metric Spaces

Igor Rodionov is a Senior Lecturer in Statistics at the University of Essex, UK; currently he is also an International Visiting Professor at the University of Science and Technology of China. He received his PhD in Probability and Statistics in 2014 and the Doctor of Sciences (Habilitation) degree in Probability and Statistics in 2021. Before joining Essex, he held research and academic positions at Lomonosov Moscow State University, the Russian Academy of Sciences, and EPFL (Switzerland). His research has been supported by competitive grants, including a Russian Science Foundation (RSF) Early-Career Research Grant for independent research. His research interests include extreme value theory, survival analysis and statistics in metric spaces. His work has been published in journals such as Bernoulli, Annales de l'Institut Henri Poincaré and Stochastic Processes and their Applications.

From high-throughput sequencing to neuroimaging, the clinical data for medical research become increasingly complex, challenging the statistical analysis in a great manner. During the past decades, Deep learning contributed vitally in utilizing image data and presented convincing performance in prediction tasks. However, its lack of interpretation is a major concern for the development of clinical diagnosis and intervention. In this work, we propose an analytical method for the association study between objects in the metric space and time-to-event survival outcome, where the predictor can be a vector of high-dimensional non-Euclidean elements with non-negligible interactions. We propose MRBCov and its sample estimator to measure the dependency between non-Euclidean object and the observed survival outcome. We study the properties of this measure as well as the asymptotic properties of the estimator. Simulation studies show the promising performance of our method in identifying the association between the complex predictor and survival outcome.