Sample Size Calculation for the ROCI Design

The Response Over Continuous Intervention (ROCI) design offers a number of potential benefits over conventional non-inferiority trials in studies focused on the late-phase optimization of a continuous aspect of treatment intervention. One possible application of this design is in de-escalation trials, which aim to reduce the dose, duration, or frequency of an established treatment. In the absence of an alternative method, sample size requirements for the ROCI design are currently estimated through simulation, which is often time-consuming and computationally intensive. We propose a normal approximation approach to sample size calculation and evaluate alternative methods for deriving nuisance parameter estimates (e.g., treatment effect variance), considering both the reliability of results and the computational resources required to generate them. Our analysis demonstrates that adopting sample size methodology based on normal approximation is well-founded for the ROCI design and significantly reduces computational demands, though reliable estimation of distribution parameters typically requires methods that account for model selection uncertainty. The sample size estimation framework outlined in this paper follows previous recommendations for the ROCI design and employs fractional polynomial regression to model the intervention-response curve; however, it generalizes beyond this and has potential utility for designs implementing alternative flexible modeling approaches.