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

Abstract

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.

Keywords:

• Bivariate survival
• Cross-ratio
• Clayton copula
• Proportional cross-ratio model

Additional information

Funding

This research is supported by funding from the National Institute of Health Grants R01 AG019181, R01 AG045350, and P30 AG10133.