Estimation of covariate effects in proportional cross-ratio model of bivariate time-to-event outcomes

• Published in: Communications in statistics. Simulation and computation Vol. 51; no. 12; pp. 7472 - 7486
• Main Authors: Ran, Liao, Hu, Tianle, Gao, Sujuan
• Format: Journal Article
• Language: English
• Published: Philadelphia Taylor & Francis 01.12.2022; Taylor & Francis Ltd
• Subjects: Bivariate analysis; Bivariate survival; Clayton copula; Cross-ratio; Estimation; Proportional cross-ratio model; Statistical methods; Survival
• ISSN: 0361-0918; 1532-4141
• DOI: 10.1080/03610918.2020.1839093

Medical studies often collect bivariate survival data including time to the same type of disease in twins or time to two different diseases from the same individuals. Cross-ratio, defined as the ratio of conditional hazard functions for one event given the other, is often used as a measure of dependency between the two survival outcomes. Statistical methods have also been proposed to estimate the effect of covariates on cross-ratio in order to identify common factors influencing both survival outcomes. There are currently three estimation approaches for cross-ratio, namely, a parametric approach using the Clayton copula, a semi-parametric two-stage approach proposed by Shih and Louis, and a nonparametric pseudo-partial likelihood approach proposed by Hu et al. In this paper, we compare the three estimation approaches on estimating covariates' effect on the cross-ratio in simulation studies. We found that the nonparametric pseudo-partial likelihood estimation approach performed well and that the method was also robust under various model assumptions. Data from a longitudinal cohort of elderly African Americans were used to illustrate the three estimation approaches.