Introduction | Regulatory context: FDA guidance on OS monitoring in oncology | Design framework overview | Design with non-binding bounds (test.type = 8) | Spending function specification | Summary | Detailed boundary table | Interpreting the boundaries | Boundary crossing probabilities | Visualization | Z-value boundaries | Approximate treatment effect at boundaries | Conditional power at boundaries | Spending function plot | B-values at boundaries | Design with binding bounds (test.type = 7) | Comparing binding and non-binding | Efficacy bounds at alternate $\alpha$ levels | Practical considerations | Choice of spending functions | Interpreting the harm bound | Harm bound capping | When to use test.type = 7 vs. test.type = 8 | Binding and non-binding harm monitoring | Adjusting the boundaries | References

Motivation | Quick start | How gsSurvPower uses your inputs | Hazard ratio roles | Analysis timing: calendar time vs. event-driven | Quick decision guide | Spending and method | Stratified targetEvents | Power under alternative assumptions | Power under a different hazard ratio | Power over a range of hazard ratios | Multiple timing criteria | Setup | Baseline: design assumptions | Scenario 1: slower enrollment | Scenario 2: higher control failure rate | Controlling spending with informationRates | Comparison with gsDesign power plots | Bounds stability | Changing alpha | Binding type planning sensitivity example (test.type = 3) | Example: event-based timing | Example: slower enrollment at fixed analysis times | Example: calendar-based spending | Example: stratified event targets | Example: biomarker subgroup to stratified design | Step 1: Design for the biomarker-positive subgroup | Step 2: Power for the overall (stratified) population

Introduction | Parameters | Example 1: Futility testing only at the first interim | Plotting | Example 2: No efficacy testing at the first interim | Example 3: Survival design with selective bounds via gsSurv | Example 4: Selective harm monitoring (test.type 7/8) | Example 5: Combining selective efficacy and futility | Validation rules | Accessing stored flags | Type I Error Preservation | How it works | Non-binding futility (test.type 4 or 6) | Binding futility (test.type 3 or 5)

Introduction | Parameterization | Exact binomial approach | The time-to-event approach | Generating a design | The time-to-event design | Converting to an exact binomial design | Combined summary table | Checking design properties | $\alpha$-spending | $\beta$-spending | Bound update at time of analysis for example 2 | Summary | References

Introduction | Trial setup and initial design | Initial sample size calculation | End-to-end helper workflow | Simulation | Interim analysis | Information computation | Sample size re-estimation | Final analysis | Updating bounds | References

Purpose | Example task | Time-scale setup | Wald versus score sizing | Calendar-time group sequential design | Simulate, cut, and test a small data set | Production workflow reminder | What this skill is and is not

Purpose | What is a skill file? | Using the skill with an AI assistant | Overview of examples | FLAME trial | The user's input | Skill Step 1: Extract what is stated | Skill Step 2: Prompt for essentials | Skill Step 3: Apply defaults for non-essentials | Skill Step 4: Handle dropout correctly | Skill Step 5: Confirm time units | Skill Step 6: Compute the sample size | Skill-compatible replication | Extensions beyond the core skill | Score sizing (comparison) | Compare the two sizing rules | What if the protocol required an event gap? | Verify by simulation (fixed design) | IMPACT trial | Extraction and computation | Sensitivity to dispersion | Impact of the 28-day event gap | OPERA I/II trials | Friede & Schmidli - formula validation | Published $n_0$ values | Replication | Non-inferiority extension | Mutze et al. - group sequential parameterization examples | Fixed-design information | Real-data reverse engineering: CHARM-Preserved | Small-sample regime: BOLD trial | PARADIGM-HF: recurrent-event re-analysis | Summary | Successes | Challenges | Lessons for skill development | Practical notes for literature replication | References

Introduction | Load pre-computed results | Scenario grid | Type I error comparison | Power comparison | Z-score density comparison (null simulations) | Fallback method frequency | Summary

Introduction | Planned trial design | Fixed design | Group sequential design | Group sequential sample size under each nuisance scenario | Expected information fraction at planned time of each interim | Scenario grid | Simulation engine | Running simulations | Results | Starting sample-size sensitivity | Power by rate ratio and SSR strategy | Power by nuisance scenario | Adapted sample size distribution | Expected sample size at study stop | Calendar and information at each analysis | Discussion | Key findings | Information-based interim timing | Futility at low information | Blinded information fallback | Computational considerations | References

Introduction | Fixed design derivation | Outcome and dropout distributions | Enrollment and trial duration | Deriving design with no interim analyses | Varying enrollment duration to power trial | Group sequential design | Additional parameters | Generating the design | Textual summary | Tabular summaries | Summary plots | Update bounds at time of analysis | Evaluating interim results | References

Introduction | Schoenfeld approximation support | Power and sample size with nEvents() | Group sequential design | Information based design | Approximating boundary characteristics | Examples | Lachin and Foulkes design | Model assumptions | Fixed design | Plotting | Event accrual | References

Overview | Starting point: SAS PROC SEQDESIGN survival example | Key differences: SAS SEQDESIGN vs. R gsDesign | 1. Event formula | 2. Alpha handling in gsDesign() and gsSurv() | 3. Accrual duration and follow-up time | Reproducing the fractional-time design with gsSurv() | gsSurv() with aligned parameters | References

Introduction | Summary of method | Binomial endpoint designs | Fixed sample size | 1-sided design | Non-binding design | Time-to-event endpoint designs | Seasonal design with a final zero event-rate period | References

Introduction | Assumptions and parameterization | Initial group sequential setup | Example repeated and sequential p-values | Update exact bounds at analysis time | Lightweight runnable simulation | Example with lower-than-planned event rates | Larger offline runs (template) | Notes and extensions | References

Overview | Dataset 1: Near-Zero Blinded Information | Event Counts Summary | Event Distribution | Event Rates by Patient | Violin Plot of Event Rates | What Happened with the Information Calculations | Root Cause Analysis | Method of Moments Comparison | Dataset 2: Extreme High Blinded Information | Why the Mutze Test Falls Back to Poisson | Summary of Issues | Recommendations

Trial design parameters | Sample size calculation | Group sequential design | Simulation study | Load simulation results | Simulation results summary | Summary of verification results | Overall operating characteristics | Power comparison by analysis | Visualization of Z-statistics | Notes

Notation | Methodology | Negative binomial distribution | Gamma-Poisson mixture motivation | Graphical illustration | Sample size formula | Relationship between Zhu-Lakkis, Friede-Schmidli, and Mutze et al. | Non-inferiority and super-superiority | Average exposure | Setup | Calendar exposure without dropout | Calendar exposure with dropout | Maximum follow-up | Weighted average across segments | Group-specific parameters | Variance inflation for variable follow-up ($Q$ factor) | Event gaps | Simulation verification of average exposure | Statistical information | Per-subject Fisher information | Total information | Information in practice: blinded and unblinded estimation | Connection to sample size | Examples | Basic calculation [@zhu2014sample] | Piecewise constant accrual | Accrual with dropout and max follow-up | Group-specific dropout rates | Calculating power for fixed design | Unequal allocation | Example with event gap | References

Simulation setup | Defining input parameters | Running the simulation | Analyzing the data | Inspect first ten records | Plotting events | Cutting data by analysis date | Missing data assumptions and imputation | Wald test [@mutze2019group] | Finding analysis date for target events | Generating and verifying negative binomial data | Simulation with dispersion | Verifying the dispersion parameter | Visualizing the distribution | References

Introduction | Simulation design | Parameters | Theoretical calculation | Simulation results | Power comparison | Summary of verification results (corrected design) | Distribution of the test statistic | Wald vs score Z-score comparison | Distribution statistics for log(RR) | Type I error: Wald vs score test | Scenario sweep: impact of the Jensen correction | Discussion: why we apply the correction

Introduction | Statistical background | Negative binomial count model | Imputation draw | Bootstrap–MI combination | Worked example | Simulating longitudinal count data | Introducing missing data by mechanism | Running impute_nb() | Inspecting imputed values | Comparing imputed means by strategy | Pooled analysis with Rubin's rules (standard MI) | Bootstrap–MI for variance estimation | Using the building-block functions directly | Step 1 — Fit the GLMM | Step 2 — MAR imputation | Step 3 — MNAR reference-based imputation | Step 4 — Composite strategy (no model required) | Key considerations | Session info

Introduction | The Poisson mixture model | Supporting functions | Scenario assumptions | Examples | Event accumulation | Study design | Design assumptions | Study design and event accumulation | Considerations | References

Overview | Response rate example | Summarizing design properties | Safety monitoring example | Summary | References

Overview and notation | Sample size | Testing and confidence intervals | Non-inferiority and super-superiority | Simulation | Power table | Summary | References

Introduction | Implementation in gsDesign | Method 1 | Method 2 | Method 3 | Replicating published examples | Summary | References

Introduction | Design | Update design at time of interim analysis | Testing and conditional power | Predictive power | References

Introduction | The problem considered | Sample size | Examples | Power | Verification with simulation | Group sequential design | References

Non-inferiority design | Super-superiority design

Simulation setup | Simulation loop | Results summary | Visualization | Group sequential design evaluation

Simulation setup | Define parameters | Run simulation | Analysis at a cut date | Seasonal and treatment effect estimation | Variance and information

Introduction | Group sequential design framework | Bounds for testing | One-sided testing | Asymmetric two-sided testing | Spending function design | References

Introduction | Example | References

Introduction | Examples | References

Overview | Design | Multiplicity diagram for hypothesis testing | Group sequential designs for each hypothesis | H1: OS, Subgroup | H2: OS, All | H3: PFS, Subgroup | H4: PFS, All | H5 and H6: ORR | Design list | Spending plan and spending time | Results entry at time of analysis | Timing of analyses and resulting event counts and spending times | Nominal p-values for each analysis | Testing hypotheses | Compute sequential p-values for each hypothesis | Evaluate hypothesis rejection using gMCPLite | Verification of hypotheses rejected | Multiplicity graph sequence from gMCPLite | Comparison of sequential p-values to multiplicity graphs | Bounds at final $\alpha$ allocated for group sequential tests | Session information | References

Introduction | The basic graph layout | Specifying hypothesis names and $\alpha$-allocation | Text formatting and location, ellipse size | Using colors and legends | Specifying the transition matrix between hypotheses | References