Bernstein-based estimation of the cross ratio function

Abstract

Local association measures provide useful insights in time-varying changes in association, especially between time-to-event variables. Such local dependence between two correlated random variables can be measured using the cross ratio function. The cross ratio function is defined as the ratio of conditional hazard functions which have been estimated using Bernstein polynomials before. Alternatively, the cross ratio function can be expressed in terms of (derivatives of) the joint survival function of the two random variables. In this paper, we discuss an alternative Bernstein-based plug-in estimator of the cross ratio function in which each of the ingredients is estimated separately. Next to asymptotic normality of the nonparametric estimator, a simulation study is used to assess its finite-sample performance. Finally, the novel estimator is applied to a real-life data application.

Keywords:

• Bernstein polynomials
• copula functions
• local association
• time-to-event data
• survival functions

Acknowledgments

The authors express their gratitude to access and use the hospital data collected in Ziekenhuis Oost Limburg to illustrate the novel methodology presented in this paper.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

SA and OS gratefully acknowledge support of the Research Foundation - Flanders (FWO) (grant nr. G011022N).