Optimal Cohort Staircase Designs
Staircase cluster randomized trials restrict outcome collection to a limited window around each cluster's transition from control to intervention. This can reduce the burden of repeated measurement, but the allocation of clusters and participants across treatment sequences requires careful consideration. We develop an optimal design framework for closed-cohort staircase trials with continuous outcomes, allowing cluster sizes to differ across sequences. Under a linear mixed model, we express treatment-effect precision through sequence-specific information contributions and establish convexity of the variance criterion in the cluster allocation proportions. An equivalence theorem characterizes optimal allocations, and reversal symmetry yields analytical solutions for several three- and four-sequence designs. We also consider joint optimization of sequence allocation and cluster sizes under a fixed participant total. Numerical investigations show that the value of unequal cluster sizes depends on the observation window and correlation structure: gains are often modest but can be substantial in selected settings. Comparisons with complete stepped-wedge designs demonstrate a trade-off between repeated measurements and additional clusters, with staircase designs achieving lower costs in some settings at comparable precision. Illustrations motivated by psychosocial cancer care and trial recruitment distinguish hypothetical design adaptations from the original studies. The results support choosing sequence allocation, cluster sizes, and observation windows jointly when repeated measurement is a major constraint.