Maximizing power and minimizing treatment failures in clinical trials

Response-adaptive randomization procedures have a long history in the theoretical statistics literature over the past four decades. The main idea historically was to develop randomization procedures that place fewer patients on the inferior treatment. More recent research has changed the main focus to that of usual considerations in typical clinical trials: power, sample size, expected treatment failures, maintaining randomization, among others.

We describe response-adaptive randomization procedures for simple clinical trials comparing two binomial success probabilities, including the randomized play-the-winner rule, the drop-the-loser rule, and a modification of the doubly-adaptive biased coin design. We treat as our principal goal minimizing expected treatment failures while preserving power and randomization. Based on some recent theoretical literature, the basic guidelines for selecting an appropriate procedure include targeting optimal allocation, having small variability, and preserving randomization. We use simulation to compare power and expected treatment failures according to these guidelines.

When the two treatments had high probabilities (> 0.5) of success, the randomized play-the-winner rule was less powerful than complete randomization and the drop-the-loser rule by 1-3 percent with slightly larger expected number of treatment failures than the drop-the-loser rule. For all the success probabilities we examined, the drop-the-loser rule was within 1 percent of the power of complete randomization with a modest reduction of treatment failures. The doubly-adaptive biased coin design was as powerful or slightly more powerful than complete randomization in every case and expected treatment failures were always less, with modest reductions of the order of 0.3 percent to 8.3 percent.

We conclude that the drop-the-loser rule and a modification of the doubly-adaptive biased coin design are the preferred procedures, and simulations show that these procedures yield a modest reduction in expected treatment failures while preserving power over complete randomization.