Past exam of the mathematics course of the University of Cambridge 2024 iii Paper 207 2 f Solution Created 2026-09-24 Updated 2026-09-25
Response-adaptive randomization can assign a larger proportion of later participants to the treatment currently estimated to be better, improving outcomes for participants within the trial. Its allocation probabilities depend on earlier outcomes, which complicates statistical inference; delayed responses and calendar-time trends can also make adaptation ineffective or biased, and an allocation aimed at patient benefit need not maximize power.
Past exam of the mathematics course of the University of Cambridge 2026 iii Paper 207 3 c Solution Created 2026-09-24 Updated 2026-09-25
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.