Abstract
This manuscript derives the allocation predictability measured by the correct guess probability and the probability of being deterministic for individual treatment assignments, as well as the averages of a randomization sequence, based on the treatment imbalance transition matrix and the conditional allocation probability. The methods described are applicable to restricted randomization designs that satisfy the following criteria: (1) two-arm equal allocation, (2) restriction of maximum tolerated imbalance, and (3) conditional allocation probability fully determined by the observed current treatment imbalance. Analytical results indicate that, for two-arm equal allocation trials, allocation predictability alternates by the odd/even sequence order of the treatment assignment. Additionally, the sequence average allocation predictability converges to its asymptotic value significantly more slowly than the allocation predictability for individual assignment does. Consequently, comparisons of allocation predictability between different randomization designs based on sequence averages are sensitive to sequence length. Using sequence average allocation predictability may underestimate the risk of selection bias for individual assignment. This discrepancy is particularly pronounced for short sequence lengths, where individual assignment predictability can be substantially higher than the sequence average.