BOP2-ENR: a Bayesian optimal phase II design for adaptive enrichment with family-wise error rate control and a bound on joint-claim power

2026-09-29

AI Summary

This study addresses the inability of the BOP2 design to accommodate biomarker-adaptive enrichment and multiplicity control by proposing the BOP2-ENR design. This approach enables interim enrichment through independent monitoring of biomarker-negative and biomarker-positive cohorts, introduces the strong family-wise error rate, derives exact bounds for false joint claims under mixed configurations, and clarifies the role of futility gating in error control and joint power. Monte Carlo simulations demonstrate that the proposed design satisfies prespecified stringent boundaries across diverse endpoint scenarios, confirming the critical role of the enrichment mechanism in controlling error rates under mixed configurations.

Abstract

The Bayesian optimal phase II (BOP2) design accommodates simple and complex endpoints but does not address biomarker-guided enrichment or multiplicity control across pooled and subgroup claims. We propose BOP2-ENR, which monitors biomarker-negative (NG) and biomarker-positive (PG) cohorts separately, permits interim enrichment to PG, and calibrates pooled and PG-restricted claims. Strong family-wise error rate (FWER) control is defined over a prespecified monotone-activity parameter space. Under the mixed configuration in which NG is inactive and PG is active, the probability of a false joint claim is bounded by the probability that NG survives futility monitoring. This exact single-cohort bound does not involve the final efficacy cutoff and also yields a ceiling on joint-claim power. For efficacy-toxicity monitoring, subgroup inactivity is defined by a union null and safety is established separately within each subgroup. Across the scenarios considered and binary, co-primary and efficacy-toxicity endpoints, all selected designs met the prespecified exact-bound and Monte Carlo verification criteria; in sensitivity analyses over odds ratios between component outcomes assumed independent in calibration, point estimates of the error-control quantities remained below the nominal level, although power was association-sensitive. The bound was nearly attained as PG efficacy approached the boundary of the nuisance space, whereas disabling enrichment produced mixed-configuration error rates near one. BOP2-ENR therefore extends the BOP2 framework to adaptive enrichment while clarifying that the NG futility gate governs the mixed-configuration component of strong error control and the attainable power of a joint claim.

Problem

• Bayesian optimal phase II design
• adaptive enrichment
• family-wise error rate control
• biomarker-guided
• joint-claim power

Innovation

• Bayesian optimal phase II design
• adaptive enrichment
• family-wise error rate control
• joint-claim power bound
• biomarker-guided design