Abstract
One of the main questions in the design of a trial is how many subjects should be assigned to each treatment condition. Previous research has shown that equal randomization is not necessarily the best choice. We study the optimal allocation for a novel trial design, the sequential multiple assignment randomized trial, where subjects receive a sequence of treatments across various stages. A subject's randomization probabilities to treatments in the next stage depend on whether he or she responded to treatment in the current stage. We consider a prototypical sequential multiple assignment randomized trial design with two stages. Within such a design, many pairwise comparisons of treatment sequences can be made, and a multiple-objective optimal design strategy is proposed to consider all such comparisons simultaneously. The optimal design is sought under either a fixed total sample size or a fixed budget. A Shiny App is made available to find the optimal allocations and to evaluate the efficiency of competing designs. As the optimal design depends on the response rates to first-stage treatments, maximin optimal design methodology is used to find robust optimal designs. The proposed methodology is illustrated using a sequential multiple assignment randomized trial example on weight loss management.
Highlights
In many randomized controlled trials, participants are allocated to intervention arms
We focus on sample sizes to be used when comparing two Adaptive treatment strategies (ATSs) that start with different first-stage treatments
Before we focus on the prototypical sequential multiple assignment randomized trial (SMART), we rehearse some general ingredients for arbitrary SMART
Summary
In many randomized controlled trials, participants are allocated to intervention arms. Such a design is consistent with the view of clinical equipoise that must exist before the start of the trial.[1] it may be preferable to allocate more participants to one arm than to another, for instance, when variances and/or costs vary across the treatment arms,[1,2,3,4,5] or when outcomes are categorical rather than quantitative.[6,7,8,9,10] The derivation of the optimal allocation of units to treatment conditions has been done for individually randomized trials, and for more complex trial designs such as cluster-randomized trials,[11,12,13,14,15,16] and trials with partially nested data.[17,18,19] From a statistical point of view, it is more efficient to assign more subjects to the condition with the lowest costs and highest variance. More practical, reasons to use unequal allocation over equal allocation include resource constraints, administrative, political or ethical concerns or when the aim is to gain experience from an intervention and to study its feasibility.[5,20]
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