 Solution

Targeting the Neyman ratio asymptotically minimizes the standard error for a fixed total sample size, so it cannot be worse than a fixed 1:1 design when the target probabilities are known. Targeting the ethical ratio can increase the standard error because it optimizes failures rather than information, although it may still outperform 1:1 for some probabilities.

In response-adaptive randomization, the probabilities are estimated during the trial. Delayed outcomes, time trends, unstable early estimates, and random final arm sizes complicate logistics and inference; naive Wald standard errors may also ignore adaptation.