On a Holm-related MTP for rejecting at least k hypotheses: general validity, optimality property, confidence regions,...

Area of Science:

• Biostatistics
• Clinical Trial Methodology
• Statistical Inference

Background:

• Confirmatory clinical studies often require rejecting a minimum number of hypotheses (k out of m) for success.
• Existing Holm-type multiple testing procedures (MTPs) offer a solution but have limitations in power and flexibility.
• There is a need for MTPs that provide sharper control and potentially higher power under minimal assumptions.

Purpose of the Study:

• To develop and validate a novel, generally valid stepwise MTP for confirmatory studies.
• To demonstrate strong family-wise error rate (FWER) control for the proposed MTP.
• To enhance statistical power for rejecting at least k hypotheses compared to existing methods.

Main Methods:

• A stepwise MTP with a gatekeeping step followed by m hypothesis testing steps.
• Comparison of ordered p-values to optimized critical constants for rejection decisions.
• Proof of strong FWER control without assumptions on logical or stochastic relationships between hypotheses.

Main Results:

• The proposed MTP provides strong FWER control and is generally valid under minimal assumptions.
• The procedure offers a sharper rejection capability, potentially rejecting fewer than k hypotheses but always rejecting at least as much as existing methods.
• Optimality properties of the critical constants are established under a natural monotonicity restriction.

Conclusions:

• The developed stepwise MTP offers an improvement over existing Holm-type procedures for confirmatory clinical studies.
• This method provides enhanced statistical power and robust FWER control, applicable in various clinical trial designs.
• The MTP is suitable for complex scenarios including superiority-noninferiority, fallback testing, and multistage gatekeeping strategies.