2022
DOI: 10.1111/biom.13726
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Optimal Multiple Testing and Design in Clinical Trials

Abstract: A central goal in designing clinical trials is to find the test that maximizes power (or equivalently minimizes required sample size) for finding a false null hypothesis subject to the constraint of type I error. When there is more than one test, such as in clinical trials with multiple endpoints, the issues of optimal design and optimal procedures become more complex. In this paper, we address the question of how such optimal tests should be defined and how they can be found. We review different notions of po… Show more

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Cited by 5 publications
(13 citation statements)
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References 30 publications
(83 reference statements)
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“…The first direction is to focus on applications to clinical trials, where a small number of tests K is typically performed and where optimizing power (equivalently, decreasing sample size to achieve equal power) can be especially critical for reducing costs. In follow‐up work (Heller et al, 2021), we have focused on the application to clinical trials, examining how multiple testing in clinical trials can be framed within our framework and demonstrating the potential benefits from following this route. In this framework, it is also possible to efficiently deal with general dependence structure and non‐exchangeability, as we discuss.…”
Section: Applications and Extensionsmentioning
confidence: 99%
“…The first direction is to focus on applications to clinical trials, where a small number of tests K is typically performed and where optimizing power (equivalently, decreasing sample size to achieve equal power) can be especially critical for reducing costs. In follow‐up work (Heller et al, 2021), we have focused on the application to clinical trials, examining how multiple testing in clinical trials can be framed within our framework and demonstrating the potential benefits from following this route. In this framework, it is also possible to efficiently deal with general dependence structure and non‐exchangeability, as we discuss.…”
Section: Applications and Extensionsmentioning
confidence: 99%
“…However, the optimal decision rule among all weakly monotone rules that provide strong FWEL control is not typically a rectangular decision rule. For the binary loss function, we show in Heller et al (2022) that the optimal solution can be found using a simple and efficient algorithm. This solution is not necessarily within the class of rectangular decision rules.…”
Section: Related Optimality Resultsmentioning
confidence: 99%
“…Indeed, unless weights for losses are all equal, some hypotheses will be tested at a level higher than the FWEL level they should pass if tested individually. Obviously if we add a requirement that the individual level be constrained, so a hypothesis can be rejected only if its 𝑝-values are at most 𝛼 (the marginally nominal 𝛼 constraint suggested in Heller et al 2022), then for the separable rule the optimal rule is that rejection occurs for each hypothesis if and only if its 𝑝-value is ≤ 𝛼.…”
Section: The Criteria Offeredmentioning
confidence: 99%
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“…In the specific example of Figure 2, the prevalence is different between the two subgroups, leading to larger thresholds for testing an effect in the smaller subgroup (and making it easier to reject the associated null hypothesis) because the costs of incorrect decisions are smaller. Of course, if one feels uncomfortable with rejection thresholds being larger than 𝛼, then one can include additional constraints, as suggested by Benjamini et al (2023) in reference to Heller et al (2022).…”
mentioning
confidence: 99%