twoCoprimary (version 1.0.0)

power2BinaryExact: Exact Power Calculation for Two Co-Primary Binary Endpoints

Description

Calculates the exact power for a two-arm superiority trial with two co-primary binary endpoints using the bivariate binomial distribution, as described in Homma and Yoshida (2025).

Usage

power2BinaryExact(n1, n2, p11, p12, p21, p22, rho1, rho2, alpha, Test)

Value

A data frame with the following columns:

n1

Sample size for group 1

n2

Sample size for group 2

p11, p12, p21, p22

Response probabilities

rho1, rho2

Correlations

alpha

One-sided significance level

Test

Testing method used

power1

Power for the first endpoint alone

power2

Power for the second endpoint alone

powerCoprimary

Exact power for both co-primary endpoints

Arguments

n1

Sample size for group 1 (test group)

n2

Sample size for group 2 (control group)

p11

True probability of responders in group 1 for the first outcome (0 < p11 < 1)

p12

True probability of responders in group 1 for the second outcome (0 < p12 < 1)

p21

True probability of responders in group 2 for the first outcome (0 < p21 < 1)

p22

True probability of responders in group 2 for the second outcome (0 < p22 < 1)

rho1

Correlation between the two outcomes for group 1

rho2

Correlation between the two outcomes for group 2

alpha

One-sided significance level (typically 0.025 or 0.05)

Test

Statistical testing method. One of:

• "Chisq": One-sided Pearson chi-squared test

• "Fisher": Fisher exact test

• "Fisher-midP": Fisher mid-p test

• "Z-pool": Z-pooled exact unconditional test

• "Boschloo": Boschloo exact unconditional test

Details

This function calculates exact power using equation (9) in Homma and Yoshida (2025): $$power_A(\theta) = \sum_{(a_{1,1},a_{2,1})\in\mathcal{A}_1} \sum_{(a_{1,2},a_{2,2})\in\mathcal{A}_2} f(a_{1,1}|N_1,p_{1,1}) \times f(a_{2,1}|N_2,p_{2,1}) \times g(a_{1,2}|a_{1,1},N_1,p_{1,1},p_{1,2},\gamma_1) \times g(a_{2,2}|a_{2,1},N_2,p_{2,1},p_{2,2},\gamma_2)$$

where \(\mathcal{A}_k\) is the rejection region for endpoint k, and \((Y_{j,1}, Y_{j,2}) \sim BiBin(N_j, p_{j,1}, p_{j,2}, \gamma_j)\) follows the bivariate binomial distribution.

The correlation bounds are automatically checked using corrbound2Binary.

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), 1-19.

Examples

# Exact power calculation using Boschloo test
power2BinaryExact(
  n1 = 100,
  n2 = 50,
  p11 = 0.5,
  p12 = 0.4,
  p21 = 0.3,
  p22 = 0.2,
  rho1 = 0.7,
  rho2 = 0.7,
  alpha = 0.025,
  Test = 'Boschloo'
)

# Exact power with Fisher exact test
power2BinaryExact(
  n1 = 80,
  n2 = 80,
  p11 = 0.6,
  p12 = 0.5,
  p21 = 0.4,
  p22 = 0.3,
  rho1 = 0.5,
  rho2 = 0.5,
  alpha = 0.025,
  Test = 'Fisher'
)

# \donttest{
# Larger sample sizes (computationally intensive)
power2BinaryExact(
  n1 = 200,
  n2 = 100,
  p11 = 0.5,
  p12 = 0.4,
  p21 = 0.3,
  p22 = 0.2,
  rho1 = 0.6,
  rho2 = 0.6,
  alpha = 0.025,
  Test = 'Chisq'
)
# }