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