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twoCoprimary

Overview

twoCoprimary provides comprehensive tools for sample size and power calculation in clinical trials with two co-primary endpoints. In co-primary endpoint trials, treatment success requires demonstrating statistically significant effects on all primary endpoints simultaneously. This package implements state-of-the-art methodologies that properly account for correlation between endpoints, leading to more efficient trial designs.

📖 Documentation Website

Key Features

The package supports five combinations of co-primary endpoints:

Two continuous endpoints - Normal distribution with correlation (Sozu et al., 2011)
Two binary endpoints (asymptotic) - Large sample approximation methods (Sozu et al., 2010)
Two binary endpoints (exact) - Exact inference for small to medium samples (Homma & Yoshida, 2025)
Mixed continuous and binary - Biserial correlation structure (Sozu et al., 2012)
Mixed count and continuous - Negative binomial for overdispersed counts (Homma & Yoshida, 2024)

All methods provide: - ✅ Sample size calculation given target power - ✅ Power calculation given sample size - ✅ Proper Type I error control without multiplicity adjustment - ✅ Accounting for correlation between endpoints - ✅ Support for unbalanced allocation ratios

Installation

Install from CRAN:

install.packages("twoCoprimary")

Or install the development version from GitHub:

# install.packages("pak")
pak::pak("gosukehommaEX/twoCoprimary")

Quick Start

Example 1: Two Continuous Endpoints

Calculate sample size for a trial with two continuous co-primary endpoints:

library(twoCoprimary)

# Sample size calculation
result <- ss2Continuous(
  delta1 = 0.5,      # Standardized effect size for endpoint 1
  delta2 = 0.4,      # Standardized effect size for endpoint 2
  rho = 0.3,         # Correlation between endpoints
  alpha = 0.025,     # One-sided significance level
  power = 0.80,      # Target power
  r = 1              # Allocation ratio (1:1)
)

print(result)
#> 
#> Sample size calculation for two continuous co-primary endpoints
#> 
#> Parameters:
#>   Effect sizes: delta1 = 0.5, delta2 = 0.4
#>   Correlation: rho = 0.3
#>   Significance level: alpha = 0.025 (one-sided)
#>   Target power: 1 - beta = 0.8
#>   Allocation ratio: r = 1
#> 
#> Results:
#>   Sample size per group: n1 = n2 = 130
#>   Total sample size: N = 260

Example 2: Two Binary Endpoints (Exact Method)

For small to medium sample sizes, use exact methods:

# Sample size with exact inference
result_exact <- ss2BinaryExact(
  p11 = 0.30, p12 = 0.15,    # Response rates for endpoint 1
  p21 = 0.50, p22 = 0.30,    # Response rates for endpoint 2
  rho1 = 0.3, rho2 = 0.3,    # Within-group correlations
  alpha = 0.025,             # One-sided significance level
  power = 0.80,              # Target power
  r = 1,                     # Allocation ratio
  test_method = "Fisher"     # Exact test method
)

print(result_exact)

Example 3: Mixed Count and Continuous Endpoints

For COPD/asthma trials with exacerbation count and lung function:

# Exacerbation rates (events per year)
r1 <- 0.80  # Treatment group
r2 <- 1.25  # Control group

# Sample size calculation
result_mixed <- ss2MixedCountContinuous(
  r1 = r1, r2 = r2,          # Event rates
  nu = 1.0,                  # Dispersion parameter
  t = 1,                     # Follow-up period (years)
  mu1 = 250, mu2 = 200,      # Mean FEV1 (mL)
  sd = 300,                  # Common SD
  rho1 = 0.5, rho2 = 0.5,    # Correlations
  alpha = 0.025,
  power = 0.80,
  r = 1
)

print(result_mixed)

Documentation

Comprehensive vignettes are available:

References

Homma, G., & Yoshida, T. (2025). Exact power and sample size in clinical trials with two co-primary binary endpoints. Statistical Methods in Medical Research, 34(1). https://doi.org/10.1177/09622802251368697
Homma, G., & Yoshida, T. (2024). Sample size calculation for clinical trials with co‐primary outcomes: Negative binomial and continuous outcomes. Pharmaceutical Statistics, 23(3), 368-392. https://doi.org/10.1002/pst.2337
Sozu, T., Kanou, T., Hamada, C., & Yoshimura, I. (2011). Power and sample size calculations in clinical trials with multiple primary variables. Japanese Journal of Biometrics, 32(2), 83-96. https://doi.org/10.5691/jjb.32.83
Sozu, T., Sugimoto, T., Hamasaki, T., & Evans, S. R. (2012). Sample size determination in clinical trials with multiple co-primary binary endpoints including mixed binary and continuous endpoints. Biometrical Journal, 54(5), 716-729. https://doi.org/10.1002/bimj.201100221
Sozu, T., Sugimoto, T., Hamasaki, T., & Evans, S. R. (2010). Sample size determination in superiority clinical trials with multiple co-primary correlated endpoints. Statistics in Medicine, 29(21), 2219-2227. https://doi.org/10.1002/sim.3972

Citation

citation("twoCoprimary")

Getting Help

For bug reports and feature requests, please use the GitHub issue tracker
For questions about usage, see the documentation website

License

These binaries (installable software) and packages are in development.
They may not be fully stable and should be used with caution. We make no claims about them.
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