Efficient Adaptive Randomization and Stopping Rules in Multi-arm Clinical Trials for Testing a New Treatment

Abstract

Motivated by applications to confirmatory clinical trials for testing a new treatment against a placebo or active control when the new treatment has k possible treatment strategies (arms)—for example, k possible doses for a new drug—we develop an asymptotic theory for efficient outcome-adaptive randomization schemes and optimal stopping rules. Our approach consists of developing asymptotic lower bounds for the expected sample sizes from the k treatment arms and the control arm and using generalized sequential likelihood ratio procedures to achieve these bounds. Implementation details of our design and analysis and comparative simulation studies are also provided.

Adaptive enrichment designs for confirmatory trials

“…Other randomization ratios have been used, eg, the 2:1 ratio used by the Interventional Management of Stroke (IMS) III trial described in the next section. Lai and Liao and Lai et al developed a theory of asymptotically optimal sampling ratios in 2012, as a frequentist alternative to Bayesian adaptive randomization (AR) schemes for enrichment designs introduced earlier and summarized by Berry et al (which may fail to maintain the type I error probability as discussed in Section 2.3 in the work of Lai et al). Although Lai and Liao did not actually consider patient subgroups and focused on different treatment strategies (arms) for the new treatment, their work can provide an extension to the case where these strategies are customized for different subgroups of the population.…”

“…Lai and Liao and Lai et al developed a theory of asymptotically optimal sampling ratios in 2012, as a frequentist alternative to Bayesian adaptive randomization (AR) schemes for enrichment designs introduced earlier and summarized by Berry et al (which may fail to maintain the type I error probability as discussed in Section 2.3 in the work of Lai et al). Although Lai and Liao did not actually consider patient subgroups and focused on different treatment strategies (arms) for the new treatment, their work can provide an extension to the case where these strategies are customized for different subgroups of the population. Moreover, while Lai and Liao and Lai et al focused only on maintaining the type I error under the intersection null hypothesis , Lai et al subsequently used the closed testing principle for multiple testing to show that α ( θ ) ≤ α for all θ ∈Θ 0 .…”

“…Although Lai and Liao did not actually consider patient subgroups and focused on different treatment strategies (arms) for the new treatment, their work can provide an extension to the case where these strategies are customized for different subgroups of the population. Moreover, while Lai and Liao and Lai et al focused only on maintaining the type I error under the intersection null hypothesis , Lai et al subsequently used the closed testing principle for multiple testing to show that α ( θ ) ≤ α for all θ ∈Θ 0 . Although Lai et al used equal randomization, the results can be readily extended to AR.…”

“…Following up on the works of Lai et al and Berry et al, Lai et al gave a review of adaptive enrichment designs, “briefly for clinical trials in new drug development and in more detail for comparativeness effectiveness trials involving approved treatments.” They also used the ideas of Lai and Liao and multiarm bandit theory, developed by Lai and Robbins and Lai, to introduce a new group sequential enrichment design, which uses AR and GLR statistics to “fulfill multiple objectives, which include (i) treating accrued patients with the best (yet unknown) available treatment, (ii) developing a treatment strategy for future patients, and (iii) demonstrating that the strategy developed indeed has better treatment effect than the historical mean effect of SOC plus a predetermined threshold.” They note that, because of the need for informed consent, the clinical trial needs to use randomization in a double blind setting, and the “randomization probability , determined at the l th interim analysis, of assigning a patient in group j to treatment k cannot be too small to suggest obvious inferiority of the treatments being tried, that is for some 0 < ϵ < 1/ K .” Using this constraint, they derive an AR scheme, called ϵ ‐greedy scheme in reinforcement learning, from multiarmed bandit theory. This randomization scheme is easy to implement, in contrast with the Thompson sampling scheme in the Bayesian approach that requires Markov chain Monte Carlo to implement and is also less efficient than ϵ ‐greedy sampling schemes.…”

Group sequential designs for developing and testing biomarker-guided personalized therapies in comparative effectiveness research

“…The adaptive randomization rule that uses randomization probabilities proportional to truep^jk(i) between interim analyses i and i + 1, denoted AR2, is also considered for comparison. In addition, we follow [19] and choose δij=nij−2/5 so that nijδij→∞ for biomarker class j at interim analysis i .…”