  In most clinical trials, patients are randomized with equal probability among treatments to obtain an unbiased estimate of the treatment effect. Response-adaptive randomization (RAR) has been proposed for ethical reasons, where the randomization ratio is tilted successively to favor the better performing treatment. However, the substantial disagreement regarding bias due to time-trends in adaptive randomization is not fully recognized. The type-I error is inflated in the traditional Bayesian RAR approaches when a time-trend is present. In our approach, patients are assigned in blocks and the randomization ratio is recomputed for blocks rather than traditional adaptive randomization where it is done per patient. We further investigate the design with a range of scenarios for both frequentist and Bayesian designs. We compare our method with equal randomization and with different numbers of blocks including the traditional RAR design where randomization ratio is altered patient by patient basis. The analysis is stratified if there are two or more patients in each block. Small blocks should be avoided due to the possibility of not acquiring any information from the $\mu_i$. On the other hand, RAR with large blocks has a good balance between efficiency and treating more subjects to the better-performing treatment, while retaining blocked RAR's unique unbiasedness. 
Robust Blocked Response-Adaptive Randomization Designs