Wpgsd

Internal utilities

• find_astar() - Find adjusted alpha for spending function
• find_xi() - Find xi parameter for bounds

Workflow patterns

For detailed code templates, read references/code_patterns.md.

Topics covered:

• Event count tables and correlation matrix generation
• Generating event tables from ADSL/ADTTE datasets
• Bonferroni bounds (type = 0, baseline comparison)
• WPGSD bounds with overall alpha spending (type = 2, Method 3b)
• WPGSD bounds with separate alpha spending (type = 3, Method 3c)
• WPGSD bounds with fixed alpha spending (type = 1, Method 3a)
• Closed testing with observed p-values
• Sequential p-values with calc_seq_p() (WPGSD and Bonferroni)
• Overlapping populations example (biomarker subgroups + overall)
• Common control example (multiple experimental arms vs control)
• Manual correlation construction for k > 2 analyses

Important design considerations

• generate_bounds() type parameter: 0 = Bonferroni (baseline), 1 = fixed spending, 2 = overall spending (single SF), 3 = separate spending (per-hypothesis SFs with inflation factor xi)
• Spending functions: For type 0 and 3, sf/sfparm/t are lists (one per hypothesis); for type 2, they are scalars (single overall SF)
• Correlation sources: Overlapping populations (shared patients), nested populations (subgroup ⊂ overall), or common control arm (shared control events)
• Event table (H1, H2) pairs: (i, i) = events for hypothesis i alone; (i, j) = events in the intersection of populations i and j
• Nested populations: If H1 ⊂ H3 (e.g., subgroup within overall), then n_{1∧3} = n_1 (all H1 events are also H3 events)
• Common control: If H1, H2 share a control arm, then n_{1∧2} = control arm events only
• Closed testing is required: WPGSD does not guarantee consonance, so full closed testing via closed_test() is needed (not just shortcut testing)
• Power at design stage: Either (a) design with Bonferroni and use WPGSD only at analysis, or (b) use the minimum p-value bound across intersection hypotheses to power each elementary hypothesis

Known limitations

• generate_corr() bug for k > 2: Incorrectly computes within-hypothesis cross-analysis entries for non-adjacent analyses. For k > 2, build the event-count matrix D manually and compute corr = diag(1/sqrt(diag(D))) %*% D %*% diag(1/sqrt(diag(D))). See code_patterns.md section on manual correlation.