Proportional cross-ratio model

Abstract

Cross-ratio is an important local measure of the strength of dependence among correlated failure times. If a covariate is available, it may be of scientific interest to understand how the cross-ratio varies with the covariate as well as time components. Motivated by the Tremin study, where the dependence between age at a marker event reflecting early lengthening of menstrual cycles and age at menopause may be affected by age at menarche, we propose a proportional cross-ratio model through a baseline cross-ratio function and a multiplicative covariate effect. Assuming a parametric model for the baseline cross-ratio, we generalize the pseudo-partial likelihood approach of Hu et al. (Biometrika 98:341-354, 2011) to the joint estimation of the baseline cross-ratio and the covariate effect. We show that the proposed parameter estimator is consistent and asymptotically normal. The performance of the proposed technique in finite samples is examined using simulation studies. In addition, the proposed method is applied to the Tremin study for the dependence between age at a marker event and age at menopause adjusting for age at menarche. The method is also applied to the Australian twin data for the estimation of zygosity effect on cross-ratio for age at appendicitis between twin pairs.

Association measure of doubly interval censored data using a Kendall’s τ estimator

“…Furthermore, when such an association varies over time, a suitable measure such as the cross ratio function can be applied. Recently, Hu et al (2011Hu et al ( , 2019) considered a proportional cross ratio model to reflect both time dependent association and covariate effect simultaneously and analyzed the association between age at menopause and and age at menarche which are sequential events controlled by right censoring. We have extended their approach to doubly interval censored data as a related study (Lee and Kim, 2020).…”