Fig 1.
Comparison of sequential designs for a one-arm trial to compare a null response rate of 10% and a target response rate of 30% to achieve 90% power and a 10% type I error rate under Simon’s two-stage minimax design, which enrolls a maximum sample size of 25.
Simon’s two-stage design assumes a single interim analysis after 16 participant outcomes are observed and would terminate for futility only if 0 or 1 response was observed. On the other hand, Bayesian designs with predictive probability monitoring may be more flexible. A 0.1 and 0.2 threshold are illustrated, where an arm could terminate for futility if no responses are observed within the first 6 participants for a threshold of 0.1 or 5 participants for a threshold of 0.2. Further, the Bayesian designs facilitate a continual evaluation of futility over the course of the study, with larger thresholds more aggressively terminating early for futility (e.g., after 10 participants are observed, the 0.1 threshold terminates if no responses are observed, whereas the 0.2 threshold terminates if 1 or fewer responses are observed.
Fig 2.
Comparisons of trial operating characteristics for global scenarios (all null or all alternative baskets).
Black coloring is for null baskets and gray coloring for alternative baskets. The dotted lines represent Simon’s two-stage minimax design, dashed lines represent a design with interim monitoring after each participant based on Bayesian predictive probability futility monitoring, dashed-dotted lines represent Simon’s (2016) design with information sharing with posterior probability futility monitoring, and the solid lines represent a Bayesian design that also facilitates information sharing across baskets based on exchangeability of the response rate with predictive probability futility monitoring. The rejection rate summarizes the proportion of baskets across the 1000 simulated trials where efficacy was concluded, the expected sample size presents the average number enrolled in a given null or alternative basket, and the stop rate describes the proportion of baskets that terminated early at any point for futility.
Fig 3.
Comparisons of trial operating characteristics for mixed scenario (8 null, 2 alternative baskets).
Black coloring is for null baskets and gray coloring for alternative baskets. The dotted lines represent Simon’s two-stage minimax design, dashed lines represent a design with interim monitoring after each participant based on Bayesian predictive probability futility monitoring, dashed-dotted lines represent Simon’s (2016) design with information sharing with posterior probability futility monitoring, and the solid lines represent a Bayesian design that also facilitates information sharing across baskets based on exchangeability of the response rate with predictive probability futility monitoring. The rejection rate summarizes the proportion of baskets across the 1000 simulated trials where efficacy was concluded, the expected sample size presents the average number enrolled in a given null or alternative basket, and the stop rate describes the proportion of baskets that terminated early at any point for futility.
Fig 4.
Comparisons of trial operating characteristics for equally mixed scenario (5 null, 5 alternative baskets).
Black coloring is for null baskets and gray coloring for alternative baskets. The dotted lines represent Simon’s two-stage minimax design, dashed lines represent a design with interim monitoring after each participant based on Bayesian predictive probability futility monitoring, dashed-dotted lines represent Simon’s (2016) design with information sharing with posterior probability futility monitoring, and the solid lines represent a Bayesian design that also facilitates information sharing across baskets based on exchangeability of the response rate with predictive probability futility monitoring. The rejection rate summarizes the proportion of baskets across the 1000 simulated trials where efficacy was concluded, the expected sample size presents the average number enrolled in a given null or alternative basket, and the stop rate describes the proportion of baskets that terminated early at any point for futility.