B1587
Title: Nonparametric estimation of the cross ratio function under right censoring
Authors: Omer Sercik - Hasselt University (Belgium) [presenting]
Anneleen Verhasselt - Hasselt University (Belgium)
Steven Abrams - University of Antwerp and UHasselt (Belgium)
Abstract: The cross-ratio function (CRF) is a commonly used local dependence measure describing the strength of association between two time-to-event variables, such as infection times in infectious disease epidemiology, failure times in survival analysis or lifetimes in reliability theory. Being a ratio of conditional hazard functions, the CRF can be rewritten in terms of (first and second-order derivatives of) the joint survival function of these random variables. Parametric and non-parametric 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 (i.e., in terms of copula family or frailty distribution for marginal and conditional approaches, respectively), or these are of little practical use due to their rough behaviour yielding unsatisfying finite sample performance. Based on Bernstein polynomials, a new non-parametric estimator is proposed for the CRF under univariate right censoring. Its performance is discussed through simulation studies and its theoretical properties are shown. Moreover, the applicability of the proposed estimator is shown in the context of a real-life data application. Finally, some interesting topics and challenges for further research are highlighted.
