Various Bayesian adaptive randomization (AR) methods have been proposed to assist clinicians in tailoring treatments. In order to assess the performance of the different designs, researchers usually compare each active treatment with a common control. However, when the covariate is a predictive factor, the comparison of different designs becomes difficult. The best treatment differs across individuals makes defining the power of a trial difficult. Our solution was to look at two criteria: the probability of selecting each individual's own best treatment by the final model and the proportion of individuals who received their best treatment during the trial. These two criteria are not used by previous researchers. Therefore, we conducted simulations to evaluate the performance of different allocation methods under Bayesian framework: AR by response rate; AR by superiority confidence; AR by covariate-adjusted response rate; AR by covariate-adjusted superiority confidence. Under four scenarios, in terms of the total number of responses and proportion of getting the best treatment, AR by covariate-adjusted superiority confidence outperformed the other allocation methods.