ABSTRACT
In an open-label single-center trial with restricted randomization, the investigator might try to guess the next treatment assignment and allocate a patient best suited for the guessed treatment. This introduces the selection bias in the study results by making the treatment groups incomparable. Selection bias is well studied for equal allocation procedures but is less studied for unequal allocation. For two-arm equal allocation, selection bias depends on the overall proportion of correct guesses, while for unequal allocation, it depends on the sum of expected proportions of correct guesses in each arm. In this chapter, the directional guessing strategy for trials with unequal allocation is justified. The selection bias with unequal allocation Permuted Block Randomization (PBR) is quantified under the directional strategy and the strategy where the investigator biases the randomization only when the expected payoff is sufficiently large. The chapter also demonstrates the advantage of using the Brick Tunnel Randomization in a study with unequal allocation when the investigator relies on the biasing strategy with a payoff threshold and expects the PBR to be used in the study.
