BOP2-ENR: a Bayesian optimal phase II design for adaptive enrichment with family-wise error rate control and a bound on joint-claim power
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.
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BibTeX
@misc{takeda2026bop2enr,
title = {{BOP2-ENR: a Bayesian optimal phase II design for adaptive enrichment with family-wise error rate control and a bound on joint-claim power}},
author = {Kentaro Takeda and Belay B. Yimer and Masahiro Kojima},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.38759},
eprint = {2609.38759},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.38759},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - BOP2-ENR: a Bayesian optimal phase II design for adaptive enrichment with family-wise error rate control and a bound on joint-claim power
AU - Kentaro Takeda
AU - Belay B. Yimer
AU - Masahiro Kojima
PY - 2026
DA - 2026/09/30
PB - arXiv
DO - 10.48550/arxiv.2609.38759
UR - https://arxiv.org/abs/2609.38759
AB - 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.
ER -