Purpose | The design | Simulate the trial under the null | Simulate under the alternative | Comparing the boundary-crossing probabilities | Beyond proportional hazards | 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 | ahr_fast vs AHR::ahrKM | Representative results | Why it is faster | References

Purpose | Kaplan-Meier survival | Log-rank test | Weighted log-rank test | Cox hazard ratio | Restricted mean survival time | Milestone survival | Average hazard with survival weight | Average hazard ratio | Max-combo test | Robust modestly-weighted log-rank test | Summary | References

Overview | Function families | A minimal example | Where to go next | References

Overview | 1. Numerical agreement with the survival package | 1.1 survfit_fast() versus survfit() + summary() | 1.2 survdiff_fast() versus survdiff() | 1.3 coxph_fast() versus coxph() | 2. Speed comparison | 3. Simulation example | 3.1 Generate simulated data | 3.2 Apply the three analysis functions to each simulated trial | 3.3 Summarize the results across 100 simulations | References

Motivating Scenario | 1. Bayesian Model: Normal-Inverse-Wishart Conjugate | 1.1 Prior Distribution | 1.2 Posterior Distribution | 1.3 Posterior of the Bivariate Treatment Effect | 1.4 Nine-Region Grid (Posterior Probability) | 1.5 Four-Region Grid (Predictive Probability) | 2. Posterior Predictive Distribution | 3. Two Computation Methods | 3.1 Monte Carlo Simulation (CalcMethod = 'MC') | 3.2 Moment-Matching Approximation (CalcMethod = 'MM') | 4. Study Designs | 4.1 Controlled Design | 4.2 Uncontrolled Design | 4.3 External Design (Power Prior) | Vague prior (prior = 'vague') | N-Inv-Wishart prior (prior = 'N-Inv-Wishart') | 5. Operating Characteristics | 5.1 Definition | 5.2 Example: Controlled Design, Posterior Probability | 6. Optimal Threshold Search | 6.1 Objective and Algorithm | 6.2 Example: Controlled Design, Posterior Probability | 7. Summary

Introduction | Covered Scenarios | Endpoint Type | Probability Metric | Study Design | Prior Distribution | Package Structure and Function Overview | Quick-Start Examples | Posterior Probability: Single Binary Endpoint | Posterior Probability: Single Continuous Endpoint | Go/NoGo Decision: Operating Characteristics | Optimal Threshold Search | Further Reading

Motivating Scenario | 1. Bayesian Model: Normal-Inverse-Chi-Squared Conjugate | 1.1 Prior Distribution | 1.2 Posterior Distribution | 1.3 Posterior of the Treatment Effect | 2. Posterior Predictive Probability | 2.1 Predictive Distribution | 2.2 Posterior Predictive Probability | 3. Three Computation Methods | 3.1 Numerical Integration (NI) | 3.2 Monte Carlo Simulation (MC) | 3.3 Moment-Matching Approximation (MM) | 3.4 Comparison of the Three Methods | 4. Study Designs | 4.1 Controlled Design | 4.2 Uncontrolled Design (Single-Arm) | 4.3 External Design (Power Prior) | Vague prior (prior = 'vague') | N-Inv-$\chi^2$ prior (prior = 'N-Inv-Chisq') | Example: external control design, vague prior | 5. Operating Characteristics | 5.1 Definition | 5.2 Example: Controlled Design, Posterior Probability | 6. Optimal Threshold Search | 6.1 Objective | 6.2 Example: Controlled Design, Posterior Probability | 7. Summary

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

Motivating Scenario | 1. Bayesian Model: Beta-Binomial Conjugate | 1.1 Prior Distribution | 1.2 Posterior Distribution | 1.3 Posterior of the Treatment Effect | 2. Posterior Predictive Probability | 2.1 Beta-Binomial Predictive Distribution | 2.2 Posterior Predictive Probability of Future Success | 3. Study Designs | 3.1 Controlled Design | 3.2 Uncontrolled Design (Single-Arm) | 3.3 External Design (Power Prior) | 4. Operating Characteristics | 4.1 Definition | 4.2 Example: Controlled Design, Posterior Probability | 5. Optimal Threshold Search | 5.1 Objective and Algorithm | 5.2 Example: Controlled Design, Posterior Probability | 6. Summary

Motivating Scenario | 1. Bayesian Model: Dirichlet-Multinomial Conjugate | 1.1 Response Pattern Parameterisation | 1.2 Prior: Dirichlet Distribution | 1.3 Posterior Distribution | 1.4 Within-Group Correlation | 1.5 Nine-Region Grid (Posterior Probability) | 1.6 Four-Region Grid (Predictive Probability) | 2. Posterior Predictive Distribution | 2.1 Dirichlet-Multinomial Predictive Distribution | 2.2 Monte Carlo Evaluation | 3. Study Designs | 3.1 Controlled Design | 3.2 Uncontrolled Design | 3.3 External Control Design (Power Prior) | 4. Operating Characteristics | 4.1 Definition | 4.2 Example: Controlled Design, Posterior Probability | 5. Optimal Threshold Search | 5.1 Objective and Algorithm | 5.2 Example: Controlled Design, Posterior Probability | 6. Summary

Overview | Key Features | Installation | Basic Usage | Running a Basic BOIN Simulation | Understanding the Output | BOIN Standard Implementation | Key Parameters | Safety Features | Extra Safety Stopping | Maximum Conservatism | Multi-Scenario Simulations | Output Formatting Options | Percentage Format | Markdown Table Format | HTML Format | Accessing Detailed Results | Design Comparison | Performance Benchmarking | Advanced Features | Custom Cohort Sizes | Titration Phase | Stopping Reasons | References | See Also

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 | 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 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

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 | 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 | 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) | 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

Introduction | Validation of BinaryPower Function | Test Parameters | Quick Verification Example | 1. Pearson Chi-squared Test | 2. Fisher Exact Test | 3. Fisher Mid-p Test | 4. Z-pooled Exact Unconditional Test | 5. Boschloo Exact Unconditional Test | Performance Comparison | Enhanced Computational Speed Benchmarks | BinaryPower Performance Comparison | Performance Visualization | Speed Improvement Summary | Summary of Validation Results | Accuracy Validation | Performance Improvements | Key Advantages of bbssr | Conclusion | Session Information

Introduction | What is Blinded Sample Size Re-estimation? | Key Advantages of BSSR | Getting Started | Basic Usage | Power Calculation for Traditional Design | Sample Size Calculation | Blinded Sample Size Re-estimation (BSSR) | Basic BSSR Example | Comparing BSSR Design Rules | Understanding the Results | Design Rule Comparison | Key Observations | Statistical Tests Available | Test Comparison Example | Practical Considerations | When to Use BSSR | Design Choice Guidelines | Next Steps

Introduction | Theoretical Foundation of BSSR | The Problem with Fixed Sample Sizes | The BSSR Solution | Mathematical Framework | Exact Statistical Tests | 1. Pearson Chi-squared Test ('Chisq') | 2. Fisher Exact Test ('Fisher') | 3. Fisher Mid-p Test ('Fisher-midP') | 4. Z-pooled Exact Unconditional Test ('Z-pool') | 5. Boschloo Exact Unconditional Test ('Boschloo') | Mathematical Relationships | Test Comparison | BSSR Methodology | Design Approaches | 1. Restricted Design (restricted = TRUE) | 2. Unrestricted Design (restricted = FALSE) | 3. Weighted Design (weighted = TRUE) | BSSR Implementation Example | Power Calculations | Traditional vs BSSR Power | Practical Implementation Guidelines | Choosing the Right Test | Choosing the BSSR Approach | Sample Size Planning | Regulatory Considerations | Type I Error Control | Documentation Requirements | Advanced Topics | Multiple Allocation Ratios | Sensitivity Analysis | Conclusion