twoCoprimary (version 1.0.0)

ss2BinaryExact: Exact Sample Size Calculation for Two Co-Primary Binary Endpoints

Description

Calculates the required sample size for a two-arm superiority trial with two co-primary binary endpoints using exact methods, as described in Homma and Yoshida (2025).

Usage

ss2BinaryExact(p11, p12, p21, p22, rho1, rho2, r, alpha, beta, Test)

Value

A data frame with the following columns:

p11, p12, p21, p22

Response probabilities

rho1, rho2

Correlations

r

Allocation ratio

alpha

One-sided significance level

beta

Type II error rate

Test

Testing method used

n1

Required sample size for group 1

n2

Required sample size for group 2

N

Total sample size (n1 + n2)

Arguments

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

r

Allocation ratio of group 1 to group 2 (group 1:group 2 = r:1, where r > 0)

alpha

One-sided significance level (typically 0.025 or 0.05)

beta

Target type II error rate (typically 0.1 or 0.2)

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 uses a sequential search algorithm to find the minimum sample size that achieves the target power:

Step 1: Initialize with sample size from approximate method (AN). This provides a good starting point for the exact calculation.

Step 2: Use sequential search algorithm (Homma and Yoshida 2025, Algorithm 1):

• Calculate power at initial sample size

• If power >= target: decrease n2 until power < target, then add 1 back

• If power < target: increase n2 until power >= target

Step 3: Return final sample sizes.

Note: Due to the saw-tooth nature of exact power (power does not increase monotonically with sample size), this sequential search ensures the minimum sample size that achieves the target power.

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

# Quick example with Chi-squared test (faster)
ss2BinaryExact(
  p11 = 0.6,
  p12 = 0.5,
  p21 = 0.4,
  p22 = 0.3,
  rho1 = 0.3,
  rho2 = 0.3,
  r = 1,
  alpha = 0.025,
  beta = 0.2,
  Test = "Chisq"
)

# \donttest{
# More computationally intensive example with Fisher test
ss2BinaryExact(
  p11 = 0.5,
  p12 = 0.4,
  p21 = 0.3,
  p22 = 0.2,
  rho1 = 0.5,
  rho2 = 0.5,
  r = 1,
  alpha = 0.025,
  beta = 0.2,
  Test = "Fisher"
)
# }