# 8.6 - "Play the Winner" Rule

8.6 - "Play the Winner" Rule

Another type of adaptive randomization scheme is called the "play the winner" rule. Suppose there is a two-armed clinical trial and the urn contains one "A" ball and one "B" ball for the first patient. Suppose that the patient randomly is assigned treatment A. Now you need to know if the treatment was successful with the patient that received this treatment. If the patient does well on treatment A, then the original "A" ball and another "A" ball are placed in the urn. If the patient fails on treatment A, then the original "A" ball and a "B" ball are placed in the urn. Thus, the second patient has probability of 1/3 or 2/3 of receiving treatment A depending on whether treatment A was a success or failure for the first patient. This process continues. If one treatment is more successful than the other, the odds are stacked in favor of that treatment.

The advantage of the "play the winner" rule is that a higher proportion of patients will be assigned to the more successful treatment. This seems to be an ethical approach.

The disadvantages of the "play the winner" rule are that:

1. sample size calculations are difficult, and
2. the outcome on each patient must be determined prior to the entry of the next patient.

Thus, the "play the winner" rule is not practical for most trials. The procedure can be modified, however, to be performed in stages. For example, if the target sample size is 200 patients, then the trial can be put on hold after each set of 50 patients to assess outcome and redefine the probability of treatment assignment for the patients yet to be recruited, i.e., "play the winner" after every 50 patients instead of every patient.

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