Practical Considerations for Adaptive Trial Design and Implementation by Weili He José Pinheiro & Olga M. Kuznetsova

Author:Weili He, José Pinheiro & Olga M. Kuznetsova
Language: eng
Format: epub
Publisher: Springer New York, New York, NY

2.Determine the posterior distribution each time a patient’s response becomes available.

3.By comparing posterior distributions or means of different arms, update the randomization probability for each treatment arm.

4.Randomize the next patient and go back to step 2.

5.Repeat steps 2–4 until some stopping rule is satisfied or until the maximum sample size is attained.

In the following, we illustrate this idea by considering a trial comparing two treatments with binary responses and a maximum sample size N. Suppose responses of patients assigned to treatments A and B have a Bernoulli distribution with parameters θ A and θ B , respectively. We follow the steps listed above. Step 1 is to choose a prior distribution and a conjugate prior in this situation is a beta distribution. Since we assume there is no information to compare these two treatments at the beginning, a noninformative prior of Beta distribution with parameters 0.5 and 0.5 or Beta(0.5, 0.5) is used for both treatment arms. In step 2, suppose N A and N B patients have been assigned to treatments A and B with s A and s B successes, respectively. It is straightforward to determine that the posterior distributions for θ A and θ B are and . In Step 3, we need to generate a metric representing the treatment difference using the two posterior distributions. An intuitive metric, as in Thall and Wathen (2007) and traced back to Thompson (1933), is Prob(θ A  > θ B ), denoted by P A > B . Although this metric is not necessarily the optimal one, as will be commented shortly, we will use it in the following discussion for demonstration. The randomization probability for the next patient to treatment A, ρ A , is defined by

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