Project R-10786

Nonparametric estimation of time-varying association measures for bivariate censored time-to-event data (Research)

The cross-ratio function (CRF) is a commonly used local dependence measure for the association between two variables, such as infection times in infectious disease epidemiology, failure times in survival analysis or lifetimes in reliability theory. Being a ratio of conditional hazards, the CRF can be rewritten in terms of (first and second order derivatives of) the joint survival function of these random variables. Parametric and nonparametric estimators for the CRF have been proposed in the literature in the context of bivariate right-censored time-to-event data. These existing estimators are, however, either based on very strong parametric assumptions regarding the underlying association structure (in terms of copula family or frailty distribution) for these variables, or these are of little practical use due to their rough behaviour. This project aims to (i) develop a novel flexible estimator of the CRF, based on penalized splines, and investigate its finite sample properties (in simulation studies) as well as its asymptotic properties (by proving, in particular, consistency/asymptotic distribution); (ii) propose a new goodness-of-fit measure to assess the choice of the bivariate copula function or frailty distribution in marginal and conditional models for bivariate right-censored time-to-event data, as well as (iii) (bivariate) interval-censored data. This project takes a new nonparametric look on estimation of the CRF and contributes with new statistical methodology.

01 October 2020 - 30 September 2024