Version Compatibility

Reference examples tested with: R gMCP 0.8.16+, graphicalMCP 0.2+, gatekeeping, multcomp, multxpert; Python statsmodels 0.14+ for basic FDR/FWER methods.

Before using code patterns, verify installed versions match. If versions differ:

• R: packageVersion('<pkg>') then ?function_name
• Python: pip show <package> then help(module.function)

If code throws ImportError, AttributeError, or TypeError, introspect the installed package and adapt the example to match the actual API rather than retrying.

Multiplicity Control for Confirmatory Trials

"Design the multiplicity strategy for my trial" -> Specify a closed-testing procedure (graphical, gatekeeping, hierarchical, or step-down Bonferroni-Holm) that controls family-wise error rate at the trial-wide level across primary endpoints, key secondary endpoints, and subgroup analyses, with provable strong FWER control.

The Foundational Theorem -- Closed Testing Is Necessary

Marcus, Peritz & Gabriel 1976 Biometrika 63:655: a hypothesis H_I (I ⊆ {1,...,m}) is rejected iff every intersection hypothesis ∩_{J⊇I} H_J is rejected by a valid α-level local test. Strong FWER control holds for ANY choice of local tests.

Goeman, Hemerik & Solari 2021 Ann Stat 49:1218 tightens this: closed testing is not merely sufficient — it is necessary for admissibility under FDP/FWER/k-FWER. Every admissible multiplicity procedure is equivalent to some closed test. Graphical procedures, gatekeepers, Hommel, fixed-sequence, fallback — all are closed tests in disguise.