Response adaptive designs intend to allocate more patients to better treatments without undermining the validity and the integrity of the trial. The immediacy of the primary response (e.g. deaths, remission) determines the efficiency of the response adaptive design, which often requires outcomes to be quickly or immediately observed. This presents difficulties for survival studies, which may require long durations to observe the primary endpoint. Therefore, we introduce auxiliary endpoints to assist the adaptation with the primary endpoint, where an auxiliary endpoint is generally defined as any measurement that is positively associated with the primary endpoint. Our proposed design (referred to as bivariate adaptive design) is based on the classical response adaptive design framework. The connection of auxiliary and primary endpoints is established through Bayesian method. We extend parameter space from one dimension to two dimensions, say primary and auxiliary efficacies, by implementing a conditional weigh function on the loss function of the design. The allocation ratio is updated at each stage by optimization of the loss function subject to the information provided for both the auxiliary and primary outcomes. We demonstrate several methods of joint modeling the auxiliary and primary outcomes. Through simulation studies, we show that the bivariate adaptive design is more effective in assigning patients to better treatments as compared with univariate optimal and balanced designs. As hoped, this joint-approach also reduces the expected number of patient failures and preserves the comparable power as compared with other designs.