Nonparametric estimation of risk ratios for bivariate data

Inspired by the cross-ratio proposed Clayton, we study a new risk ratio to describe relation between components of random vector (T1,T2). It is conditional hazard rate function T1 at t1, given that T2≥t2 and T2<t2. A nonparametric estimator its asymptotic distribution obtained using Bernstein smoothing for survival copula (T1,T2) derivatives. The finite sample performance studied via simulations. practical use illustrated in two real datasets, one on food expenditure net income maximum heart age, patients suffering from disease versus control (no disease). Extensions are discussion section.