What the package does | The seven tests | Rejection regions | Power and sample size | Blinded sample size re-estimation | Restricted and unrestricted rules | Re-estimating from observed interim data | Two-sided tests | Type I error rate of a re-estimation design | Where to go next | References

Design and notation | Tests | Power and number of pairs | Blinded sample size re-estimation | Type I error rate | Non-inferiority and equivalence | References

Design and notation | Tests | Power and sample size | Blinded sample size re-estimation | Type I error rate | Analyses that ignore the strata | Random stratum and group sizes | Several designs | Three or more strata | References

Purpose | Friede and Kieser (2004) | Figure 1 (p. 272) | Figure 2 (p. 273) | Figure 3 (p. 274) | Figure 4 (p. 277) | Kieser (2020), Chapter 21 | Figure 21.1 (p. 229) | Figure 21.2 (p. 231) | Figure 21.3 (p. 233) | Figure 21.4 (p. 234) | Kieser (2020), Chapter 23 | Figure 23.1 (p. 251) | Figure 23.2 (p. 252) | Figure 23.3 (p. 252) | Friede, Mitchell and Mueller-Velten (2007) | Figure 1 (p. 908) | Figure 2 (p. 909) | Figure 3 (p. 911) | Boschloo (1970) | Figure 2 (p. 3) | Berger and Sidik (2003) | Figure 2 (p. 105) | Fagerland, Lydersen and Laake (2013) | Figure 1 (p. 4) | Figure 2 (p. 6) | Schepers et al. (2026) | Figure 1 (p. 5) | Agreement of the stored values with the package | References

Conditional tests against stats | Unconditional tests against a direct evaluation | Why the tie handling matters | Comparison with the Exact package | Comparison with exact2x2 | Type I error rate of every test | Speed | Sample size search | Re-estimation designs | Reproduction of published results | Summary | References

Two questions, two functions | Planning | Evaluating the re-estimation rule | The interim analysis | What the decision looks like across interim outcomes | Truncation at the boundary | Unequal allocation | Practical notes

Notation | Conditional tests | Two-sided conventions | Unconditional tests | Refining the maximum between the grid points | Ties in the ordering statistic | The Berger-Boos procedure | Relationships between the tests | Blinded sample size re-estimation | The largest type I error rate | Choosing a test | References

The type I error rate of a re-estimation design | The rate over the nuisance parameter | Exact tests in the final analysis | The adjusted significance level | Control within a confidence interval | Conditional rejection probabilities | Non-inferiority | References

Hypotheses and margin | The two tests | Sample size | Blinded sample size re-estimation | Type I error rate on the boundary | Margin on the scale of the risk ratio | Tests of equivalence | References

Correspondence of the functions | Correspondence of the arguments | Posterior probability for observed data | Operating characteristics | Calibration of the thresholds | External data and hypothetical controls | Changes in the results

Decisions in a proof-of-concept study | Specifying a study | A first example | Plots | Endpoints and computation | Random numbers | Validation | Further reading | References

Model | Decision for observed data | Forms of the control group | External control data | Hypothetical control | Fixed control | Predictive criterion | Operating characteristics | Decision boundary | Smaller effects as favorable | Calibration of the thresholds | Reference

Model | Decision for observed data | Prior distributions and external data | Hypothetical control | Fixed control | Predictive criterion | Operating characteristics | Decision boundary | Calibration of the thresholds | References

Model | Decision for observed data | Conduct of the study | Predictive criterion | Operating characteristics | Calibration of the thresholds | Decision boundary | Hazard ratio | Reference

Model | Regions and criteria | Decision for observed data | External data and hypothetical controls | Efficacy and safety endpoints | Operating characteristics | Calibration of the thresholds | Reference

Model | Decision for observed data | Hypothetical control | Fixed control | Operating characteristics | Decision boundary | Calibration of the thresholds | References

The design | An example | Comparing scenarios | Design options | The decision table for the protocol | Running the trial | Working with the trial data | Agreement with the BOIN package | References

What the package does | Decision boundaries | Operating characteristics for one scenario | Comparing scenarios | Design options | Working with the trial data | Comparing with the 3+3 design | Agreement with the BOIN package | References

Purpose | The innovaTV 301 trial | Simulating the trial | Interim and final analyses | Spending boundaries | Operating characteristics | Comparison with the closed-form design | Beyond proportional hazards | References

Overview | Function families | A minimal example | Formulas, data frames, and plots | Where to go next | References

Overview | The two scenarios | Methods compared | Results | Interpretation | Notes | References

Design and sample size | Scenarios | A single simulated trial | Power comparison | References

Overview | The Fleischer model | The design | Design parameters | Data generation | Primary endpoint analysis (PFS) | Key secondary endpoint analysis (OS) | Efficacy and futility boundaries | Operating characteristics | Sequential testing of PFS then OS | Correlation of the log-rank statistics | Remarks | References

Purpose | Setup | survfit_fast vs survfit + summary | survdiff_fast vs survdiff | coxph_fast vs coxph | rmst_fast vs survRM2::rmst2 | survdiff_fast(weight = "fh") vs nph::logrank.test | wmst_fast vs survWMST::wmst | milestone_fast vs survfit + summary | medsurv_fast vs nph::nphparams | maxcombo_fast vs nph::logrank.maxtest | rmw_fast vs nphRCT::wlrt | wkm_fast vs nphsim::wkm.Stat | ahsw_fast vs survAH::ah2 | ahr_fast vs AHR::ahrKM | Representative results | Why it is faster | Whole simulation studies | References

Overview | Design | PFS analysis and the crossover decision | Switching scenarios | Overall survival at the final analysis | Computing time | A check with the rank-preserving structural failure time model | Remarks | References

Purpose | Reference data | Kaplan-Meier survival | Log-rank test | Weighted log-rank test | Cox hazard ratio | Restricted mean survival time | Window mean survival time | Weighted Kaplan-Meier test | Milestone survival | Median survival time | Average hazard with survival weight | Average hazard ratio | Max-combo test | Robust modestly-weighted log-rank test | Analysis cutoffs | Treatment switching | Summary | References

What this vignette shows | The two criteria | The scenario | Step 1: simulate the trial with a region-specific accrual delay | Step 2: one event-driven, by-subgroup analysis pass | Step 3: assemble the per-look effect estimates and the two indicators | Step 4: apply the group-sequential boundaries | Step 5: conditional regional consistency probabilities | Tying back to the trio: standard operating characteristics | Notes and extensions | References

Overview | A Weibull model with a cure fraction | Analysis times | Log-rank and max-combo tests | Crossover after the interim analysis | Remarks

Overview | Design parameters | Data generation | Pairwise analysis against the shared control | The pairwise_fast() convenience wrapper | Operating characteristics under the alternative | Correlation between the contrasts | Family-wise error rate under the global null | Remarks | References

A reference design | Exact power or the normal approximation | Another test or level for the re-estimation | Whole numbers | Bounds on the final sample size | Interim sample sizes | Risk ratio and odds ratio | Distribution of the final sample size | References

One data frame for many designs | Summaries and plots | Initial sample sizes from a planning proportion | Designs specified in different ways | A true effect other than the assumed one

Why backfill | The rules of BF-BOIN | Operating characteristics of BF-BOIN | Points the articles leave open | BE-BOIN | Agreement with the BOIN and TITE-BOIN designs | How the implementation is checked | References

Why a time-to-event design | The decision table | Operating characteristics | Agreement with the BOIN design | References

Overview | Background | Clinical Context | Why Mixed Endpoints? | Statistical Framework | Model and Assumptions | Correlation Structure: Biserial Correlation | Hypothesis Testing | Test Statistics | Joint Distribution and Power Calculation | Sample Size Determination | Replicating Sozu et al. (2012) Table 2 | Replicating Sozu et al. (2012) Supporting Information Table 5 | Part C: Fisher's exact test | Basic Usage Examples | Example 1: Balanced Design | Example 2: Effect of Correlation | Example 3: Comparison of Test Methods | Example 4: Unbalanced Allocation | Power Verification | Practical Recommendations | Design Considerations | When to Use This Method | Challenges and Considerations | References

Overview | Background | Clinical Context | Why Negative Binomial Distribution? | Statistical Framework | Model and Assumptions | Correlation Structure | Hypothesis Testing | Test Statistics | Joint Distribution and Correlation | Power Calculation | Sample Size Determination | Correlation Bounds | Example: Calculate Correlation Bounds | Replicating Homma and Yoshida (2024) Table 1 (Case B) | Basic Usage Examples | Example 1: Balanced Design | Example 2: Effect of Correlation | Example 3: Effect of Dispersion Parameter | Example 4: Unbalanced Allocation | Power Verification | Practical Recommendations | Design Considerations | When to Use This Method | Challenges and Considerations | References

Introduction | What are Co-Primary Endpoints? | Statistical Properties | Hypotheses Structure | Statistical Framework | Intersection-Union Test (IUT) | Type I Error Control | Overall Power | Two Correlations | Impact of Correlation | Supported Endpoint Types | 1. Two Continuous Endpoints | 2. Two Binary Endpoints (Asymptotic Approximation) | 3. Two Binary Endpoints (Exact Methods) | 4. Mixed Continuous and Binary Endpoints | 5. Mixed Count and Continuous Endpoints | Why Does Correlation Matter? | Choosing the Right Method | Decision Guidelines | Sample Size Calculation Approach | Detailed Vignettes | References

Overview | Background | Clinical Context | When to Use Asymptotic Methods | Statistical Framework | Model and Assumptions | Correlation Structure | Hypothesis Testing | Test Statistics | Method 1: Standard Normal Approximation (AN) | Method 2: Normal Approximation with Continuity Correction (ANc) | Method 3: Arcsine Transformation (AS) | Method 4: Arcsine Transformation with Continuity Correction (ASc) | Joint Distribution and Correlation | Power Calculation | Sample Size Calculation | Replicating Sozu et al. (2010) Table III | Key Findings | Basic Usage Examples | Example 1: Equal Effect Sizes | Example 2: Unequal Effect Sizes | Example 3: Effect of Correlation | Example 4: Unbalanced Allocation | Power Verification | Comparison of Test Methods | Practical Recommendations | Design Considerations | When to Use Exact Methods Instead | Asymptotic Validity | References

Overview | Background | When to Use Exact Methods | Advantages of Exact Methods | Disadvantages | Statistical Framework | Model and Assumptions | Joint Distribution of Binary Outcomes | Number of Responders | Bivariate Binomial Distribution | Correlation Structure | Hypothesis Testing | Superiority Hypotheses | Co-Primary Endpoints (Intersection-Union Test) | Statistical Tests | Method 1: One-sided Pearson Chi-squared Test (Chisq) | Method 2: Fisher's Exact Test (Fisher) | Method 3: Fisher's Mid-P Test (Fisher-midP) | Method 4: Z-pooled Exact Unconditional Test (Z-pool) | Method 5: Boschloo's Exact Unconditional Test (Boschloo) | Tied outcomes | The nuisance parameter grid | Exact Power Calculation | Power Formula | Sample Size Calculation | Replicating Homma and Yoshida (2025) Table 4 | Practical Examples | Example 1: Basic Exact Power Calculation | Example 2: Sample Size Calculation | Example 3: Comparison of Test Methods | Impact of Correlation | Example 4: Correlation Effect | Comparison: Exact vs Asymptotic | Example 5: Exact vs AN Method | Practical Recommendations | Test Method Selection | When to Use Each Method | Correlation Estimation | Allocation Ratio | Computational Considerations | Software Implementation | References

Overview | Background and Motivation | What are Co-Primary Endpoints? | Clinical Examples | Statistical Framework | Model and Assumptions | Effect Size Parameterization | Hypothesis Testing | Test Statistics | Joint Distribution | Power Formula | Sample Size Calculation | Basic Example | Impact of Correlation | Visualization with plot() | Replicating Sozu et al. (2011) Table 1 | Power Calculation | Power for a Given Sample Size | Power Verification | Unified Interface | Unknown Variance Case | Practical Considerations | Correlation Estimation | Sensitivity Analysis | References

Background | Regional Consistency Probability | Method 1: Effect Retention Approach | Method 2: Simultaneous Positivity Approach | Package Structure | Common Parameters | Quick Start Example | Closed-form solution | Monte Carlo simulation | Visualisation | Further Reading | References

1. Continuous Endpoint | Statistical model | Consistency criteria | Example | Visualisation | 2. Binary Endpoint | 3. Count Endpoint (Negative Binomial) | Summary | References

Common trial design framework | 1. Hazard Ratio Endpoint | Statistical model | Consistency criteria | Example | Effect of dropout | Visualisation | 2. Milestone Survival Endpoint | 3. RMST Endpoint | Summary | References