Sample size re-estimation for response-adaptive randomized clinical trials

Clinical trials usually take a period of time to recruit volunteers, and they become a steady accumulation of data. Traditionally, the sample size of a trial is determined in advance and data is collected before analysis proceeds. Over the past decades, many strategies have been proposed and rigorous theoretical groundings have been provided to conduct sample size re-estimation. However, the application of these methodologies has not been well extended to take care of trials with adaptive designs. Therefore, we aim to fill the gap by proposing a sample size re-estimation procedure on response-adaptive randomized trial. For ethical and economical concerns, we use multiple stopping criteria with the allowance of early termination. Statistical inference is studied for the hypothesis testing under doubly-adaptive biased coin design. We also prove that the test statistics for each stage are asymptotic independently normally distributed, though dependency exists between the two stages. We find that under our methods, compared to fixed sample size design and other commonly used randomization procedures: (1) power is increased for all scenarios with adjusted sample size; (2) sample size is reduced up to 40% when underestimating the treatment effect; (3) the duration of trials is shortened. These advantages are evidenced by numerical studies and real examples.