Two-Stage Estimation in Copula-Based Bivariate Survival Models with Cox Marginals

Abstract

This study is motivated by the presence of dependence between event times in bivariate survival data, which cannot be adequately captured by univariate Cox models. A copula-based bivariate survival model with Cox Proportional Hazards marginals is considered. The estimation procedure follows a two-stage approach, where marginal parameters are first obtained using partial likelihood and the baseline survival function is estimated via the Breslow method. In contrast to conventional approaches that treat marginal estimates as final or impose shared parameter structures, this study introduces a modification in the second stage by performing simultaneous joint estimation of marginal and dependence parameters using the BHHH algorithm. This allows the marginal parameters to be estimated while explicitly accounting for the dependence between event times. Simulation results show that the proposed method produces stable and reliable parameter estimates while preserving the interpretability of marginal effects, providing a flexible framework for modeling dependent bivariate survival data.