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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

The exact methods for binary endpoints use a compiled kernel for the bivariate binomial distribution and evaluate the co-primary power as a matrix product, so a complete sample size search at a total sample size of several hundred takes about a second. The rejection regions of the Z-pooled and Boschloo exact unconditional tests agree with those of the Exact package.

See NEWS for what changed in version 1.1.0.

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,      # Effect size for endpoint 1
  delta2 = 0.5,      # Effect size for endpoint 2
  sd1 = 1,           # Standard deviation for endpoint 1
  sd2 = 1,           # Standard deviation for endpoint 2
  rho = 0.5,         # Correlation between endpoints
  r = 1,             # Balanced allocation
  alpha = 0.025,     # One-sided significance level
  beta = 0.2,        # Type II error (80% power)
  known_var = TRUE
)

print(result)
# Sample size calculation for two continuous co-primary endpoints
# 
#              n1 = 79
#              n2 = 79
#               N = 158
#           delta = 0.5, 0.5
#              sd = 1, 1
#             rho = 0.5
#      allocation = 1
#           alpha = 0.025
#            beta = 0.2
#       known_var = TRUE

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 = 0.50, p12 = 0.30,    # Response rates for group 1
  p21 = 0.30, p22 = 0.10,    # Response rates for group 2
  rho1 = 0.3, rho2 = 0.3,    # Within-group correlations
  alpha = 0.025,             # One-sided significance level
  beta = 0.2,                # Type II error (80% power)
  r = 1,                     # Allocation ratio
  Test = "Fisher"            # Exact test method
)

print(result_exact)
# Sample size calculation for two binary co-primary endpoints
# 
#              n1 = 111
#              n2 = 111
#               N = 222
#     p (group 1) = 0.5, 0.3
#     p (group 2) = 0.3, 0.1
#             rho = 0.3, 0.3
#      allocation = 1
#           alpha = 0.025
#            beta = 0.2
#            Test = Fisher

Example 3: Mixed Count and Continuous Endpoints

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

# Sample size calculation
result <- ss2MixedCountContinuous(
    r1 = 1.0,              # Count rate in treatment group
    r2 = 1.25,             # Count rate in control group
    nu = 0.8,              # Dispersion parameter
    t = 1,                 # Follow-up time
    mu1 = -50,             # Mean for treatment (negative = benefit)
    mu2 = 0,               # Mean for control
    sd = 250,              # Standard deviation
    r = 1,                 # Balanced allocation
    rho1 = 0.5,            # Correlation in treatment group
    rho2 = 0.5,            # Correlation in control group
    alpha = 0.025,         # One-sided significance level
    beta = 0.2             # Type II error (80% power)
)

print(result)
# Sample size calculation for mixed count and continuous co-primary endpoints
# 
#              n1 = 705
#              n2 = 705
#               N = 1410
#              sd = 250
#            rate = 1, 1.25
#              nu = 0.8
#               t = 1
#              mu = -50, 0
#             rho = 0.5, 0.5
#      allocation = 1
#           alpha = 0.025
#            beta = 0.2

Documentation

Comprehensive vignettes are available:

References

Homma, G., & Yoshida, T. (2024). Sample size calculation in clinical trials with two co-primary endpoints including overdispersed count and continuous outcomes. Pharmaceutical Statistics, 23(1), 46-59. https://doi.org/10.1002/pst.2337
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(11), 2183-2201. https://doi.org/10.1177/09622802251368697
Sozu, T., Sugimoto, T., & Hamasaki, T. (2010). Sample size determination in clinical trials with multiple co-primary binary endpoints. Statistics in Medicine, 29(21), 2169-2179. https://doi.org/10.1002/sim.3972
Sozu, T., Sugimoto, T., & Hamasaki, T. (2011). Sample size determination in superiority clinical trials with multiple co-primary correlated endpoints. Journal of Biopharmaceutical Statistics, 21(4), 650-668. https://doi.org/10.1080/10543406.2011.551329
Sozu, T., Sugimoto, T., & Hamasaki, T. (2012). Sample size determination in clinical trials with multiple co-primary endpoints including mixed continuous and binary variables. Biometrical Journal, 54(5), 716-729. https://doi.org/10.1002/bimj.201100221

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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