BOOST: Power-Optimal Strong-FWER Testing for Block-Structured Multiplicity
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866911723071471616 |
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| author | Dubey, Prasanjit Huo, Xiaoming |
| author_facet | Dubey, Prasanjit Huo, Xiaoming |
| contents | Structured multiple-testing problems (gatekeeping trials, dose-finding, multi-tissue eQTL mapping, bundled-challenger A/B experiments) organize hypotheses into design-imposed blocks and demand strong family-wise error rate (FWER) control for confirmatory claims. Practitioners currently use objective-agnostic stepwise rules (Bonferroni, Holm, Hochberg, Hommel), closed-testing and graphical extensions, or hierarchical and resampling methods; none is power-optimal within the block-separable class these designs induce. We introduce BOOST (Block-Optimal Objective-driven Strong-FWER Testing), the power-optimal strong-FWER procedure for block size three, with three guarantees: (i) finite-sample strong-FWER validity at $O(K)$ cost (versus $O(K^2)$ for general closed testing) without independence assumptions, with a strict Sidak improvement under cross-block independence; (ii) power-optimal allocation across heterogeneous blocks via an equalized-marginal KKT condition, solvable by bisection in $O(B\log(1/\varepsilon))$; and (iii) a sample-split plug-in variant for unknown alternative density $g$, attaining $α$-control up to $O(B_T \mathbb E\|g-\widehat g\|_\infty)$ inflation with per-hypothesis power deficit independent of $B_T$. Simulations across independent, equicorrelated, sparse, and mis-specified regimes show 1.4-1.7$\times$ power gains over the strongest existing baseline at calibrated FWER. On two published datasets (BLUEPRINT cross-lineage cis-eQTL and Upworthy bundled-challenger A/B experiments), BOOST certifies an order of magnitude more full-block discoveries than existing baselines at controlled FWER. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_27664 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | BOOST: Power-Optimal Strong-FWER Testing for Block-Structured Multiplicity Dubey, Prasanjit Huo, Xiaoming Methodology Structured multiple-testing problems (gatekeeping trials, dose-finding, multi-tissue eQTL mapping, bundled-challenger A/B experiments) organize hypotheses into design-imposed blocks and demand strong family-wise error rate (FWER) control for confirmatory claims. Practitioners currently use objective-agnostic stepwise rules (Bonferroni, Holm, Hochberg, Hommel), closed-testing and graphical extensions, or hierarchical and resampling methods; none is power-optimal within the block-separable class these designs induce. We introduce BOOST (Block-Optimal Objective-driven Strong-FWER Testing), the power-optimal strong-FWER procedure for block size three, with three guarantees: (i) finite-sample strong-FWER validity at $O(K)$ cost (versus $O(K^2)$ for general closed testing) without independence assumptions, with a strict Sidak improvement under cross-block independence; (ii) power-optimal allocation across heterogeneous blocks via an equalized-marginal KKT condition, solvable by bisection in $O(B\log(1/\varepsilon))$; and (iii) a sample-split plug-in variant for unknown alternative density $g$, attaining $α$-control up to $O(B_T \mathbb E\|g-\widehat g\|_\infty)$ inflation with per-hypothesis power deficit independent of $B_T$. Simulations across independent, equicorrelated, sparse, and mis-specified regimes show 1.4-1.7$\times$ power gains over the strongest existing baseline at calibrated FWER. On two published datasets (BLUEPRINT cross-lineage cis-eQTL and Upworthy bundled-challenger A/B experiments), BOOST certifies an order of magnitude more full-block discoveries than existing baselines at controlled FWER. |
| title | BOOST: Power-Optimal Strong-FWER Testing for Block-Structured Multiplicity |
| topic | Methodology |
| url | https://arxiv.org/abs/2605.27664 |