Optimal Participant Allocation in Individually‐Randomized Stepped‐Wedge Clinical Trials With One or More Treatments: Extensions to Realistic Settings

ABSTRACT In stepped‐wedge clinical trials the patients are randomized into separate groups. Each group transitions from no treatment to treatment at a different time period. The designs are useful when limited resources or geographical constraints make it impossible to treat all patients at the same time. In applications of the design to individuals, it is typical that there is a single treatment and that equal numbers of patients are randomized to each sequence. Results from the methods of optimal experimental design indicate that this equal allocation is not optimal. Building on an information‐theoretic framework for this problem, we optimize participant allocation to maximize the trial's information yield. We formulate the problem as a semidefinite programming optimization and extend it to incorporate: (i) differential attrition rates between treatment and control groups, (ii) budget constraints where treatment costs increase over time, (iii) fairness constraints, and (iv) multiple treatments with different switching policies. While the first three challenges are addressed by introducing additional constraints, the systematic treatment of the last represents a novel contribution.