Comparing three regularization methods to avoid extreme allocation probability in response-adaptive randomization.

We examine three variations of the regularization methods for response-adaptive randomization (RAR) and compare their operating characteristics. A power transformation (PT) is applied to refine the randomization probability. The clip method is used to bound the randomization probability within specified limits. A burn-in period of equal randomization (ER) can be added before adaptive randomization (AR). For each method, more patients are assigned to the superior arm and overall response rate increase as the scheme approximates simple AR, while statistical power increases as it approximates ER. We evaluate the performance of the three methods by varying the tuning parameter to control the extent of AR to achieve the same statistical power. When there is no early stopping rule, PT method generally performed the best in yielding higher proportion to the superior arm and higher overall response rate, but with larger variability. The burn-in method showed smallest variability compared with the clip method and the PT method. With the efficacy early stopping rule, all three methods performed more similarly. The PT and clip methods are better than the burn-in method in achieving higher proportion randomized to the superior arm and higher overall response rate but burn-in method required fewer patients in the trial. By carefully choosing the method and the tuning parameter, RAR methods can be tailored to strike a balance between achieving the desired statistical power and enhancing the overall response rate.