Package: twoCoprimary 1.1.1

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