SEMINAR by Niels Richard Hansen (University of Copenhagen) on "The Local Covariance Measure in Survival Analysis"

Abstract :
The local covariance measure (LCM) quantifies deviations from conditional local independence (CLI) between two time-continuous stochastic processes. It is a function of time defined as the expectation of a suitably defined stochastic integral. Under CLI this integral is a martingale and LCM is constantly 0. The talk will focus on applications in survival analysis where one process is the indicator of death. In this case LCM can be used to test the hypothesis that survival time is conditionally independent of a baseline covariate even in the presence of censoring. More importantly, LCM can be used to define an assumption-lean additive hazard target parameter. The talk will cover aspects of implementation based on machine learning (ML) as well as asymptotic theory in the spirit of double/debiased ML and using cross-fitting techniques.