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.