73 – Alternative Designs and Related Topics
Big Stick Design Within Arbitrary Boundaries Minimizes the Selection Bias in an Open-Label Trial
Olga Kuznetsova
Merck & Co., Inc.
The investigator in a randomized open-label single-center trial knows the treatment assignments of all randomized subjects and based the knowledge of the allocation procedure used in the trial can often make a guess regarding the treatment to be assigned to the next subject. This allows the investigator to introduce the selection bias in the study results by allocating subjects with a better prognosis to a specific treatment group. Blackwell and Hodges (1957) demonstrated that the truncated binomial design of the size N (an even number), where subjects are allocated at random with probability ½ until one of the treatment arms reaches the full size of N/2 subjects and the remaining subjects are allocated to the opposite arm, minimizes the selection bias among all 1:1 allocation procedures that assign N/2 subjects to each treatment. We expand this fact to allocation spaces other than an N×N square by demonstrating that among all two-arm equal allocation procedures with an arbitrary allocation space the selection bias is minimized with the procedure that allocates subjects at random with probability ½ as long as allocation to both treatments is allowed.