multi-endpoint-sim

name: multi-endpoint-sim description: > Guide users through multi-endpoint group sequential trial simulation with multiplicity-controlled testing. Use this skill when the user asks about: simulating trials with OS, PFS, and ORR endpoints, illness-death model simulation with gsDesign bounds, sequential p-values in simulation loops, combining graphicalMCP with gsDesign for simulation-based operating characteristics, cumulative rejection probabilities, or building a full pipeline from design through simulation to multiplicity-adjusted testing.

Multi-Endpoint Group Sequential Trial Simulation

This cross-package skill covers the full pipeline for simulating multi-endpoint trials with group sequential bounds and graphical multiplicity control.

Required packages

library(gsDesign)       # Group sequential design and sequential p-values
library(gMCPLite)       # Illness-death model (sim_illness_death, cut_illness_death)
library(graphicalMCP)   # Multiplicity graph and graph_test_shortcut
library(simtrial)       # wlr() for logrank Z-statistics
library(parallel)       # mclapply for simulation

When to use this skill

• Designing a trial with multiple endpoints (OS, PFS, ORR) tested at different analyses
• Simulating correlated endpoints via the illness-death model
• Computing simulation-based operating characteristics (power, rejection probabilities)
• Applying graphical multiplicity testing per simulated trial
• Using sequential p-values from gsDesign::sequentialPValue() in simulation loops

Pipeline overview

1. Design: Use gsDesign::gsSurvCalendar() for the sample-size-driving endpoint (OS), gsDesign::gsSurvPower() for secondary time-to-event (PFS), and gsDesign::nBinomial() for binary endpoints (ORR).
2. Multiplicity graph: Build with graphicalMCP::graph_create() allocating alpha across hypotheses.
3. Transition rates: Calibrate with build_transition_rates(), modify for piecewise hazards.
4. Simulation: Use sim_illness_death() + cut_illness_death() to generate ADTTE data at each analysis time.
5. Test statistics: simtrial::wlr() for TTE endpoints, gsDesign::testBinomial() for binary.
6. Sequential testing: Compute sequential p-values with gsDesign::sequentialPValue(), then test with graphicalMCP::graph_test_shortcut() at each analysis.
7. Operating characteristics: Track first rejection analysis per hypothesis, compute cumulative rejection probabilities.

Key code patterns

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

Topics covered:

• Test statistic functions (logrank via wlr, binomial via testBinomial)
• Sign conventions for Z-statistics across packages
• Simulation loop structure (parallel processing)
• Spending time computation from actual vs planned events
• Sequential p-value computation at each analysis
• Per-trial graphical testing loop
• Cumulative rejection probability table
• Correlation matrix of test statistics

Related skills

• gsDesign: Design and spending functions (gsSurvCalendar, sfExtremeValue2, testLower, sequentialPValue). Sequential p-value theory: Liu & Anderson (2008).
• illness-death: Illness-death model calibration and piecewise rate modification
• simtrial: wlr() for logrank Z-statistics
• graphicalMCP: graph_create() and graph_test_shortcut() for multiplicity testing
• graphicalMCP-gsDesign2: Similar workflow using gsDesign2 instead of gsDesign (observed data, not simulation). Includes theoretical basis for the Maurer-Bretz (2013) framework.

Important design considerations

• Theoretical basis: The per-trial sequential testing loop implements Algorithm 1 of Maurer & Bretz (2013). Sequential p-values from sequentialPValue() (Liu & Anderson, 2008) are passed to graph_test_shortcut() at each analysis to control FWER.

• Sign conventions: wlr() returns positive Z when experimental is better. testBinomial(x1=exp, x2=ctrl) returns positive Z when experimental is better. Both conventions must match for sequentialPValue() (which expects positive Z = favorable).

• Spending time in simulation: Use pmin(planned_events, actual_events) / planned_final_events at interim analyses and spending time = 1 at final analyses. This prevents over-spending when simulated events exceed planned.

• ORR is not group sequential: ORR is tested at a single analysis (e.g., IA2). Use the nominal p-value pnorm(-z_orr) directly rather than a sequential p-value.

• Separate design vs simulation effects: Use the design HR for sample size and bounds (e.g., 0.75), but weaker simulation HR (e.g., 0.80) for realistic operating characteristics.

• Graph carries forward: Use the same graph_test_shortcut() call at each analysis with updated sequential p-values. The graph handles alpha reallocation from rejected hypotheses.

• Track first rejection: Record the first analysis at which each hypothesis is rejected. Use this to compute cumulative rejection probabilities by analysis.