Power Calculation for Two-Arm Trials with Binary Endpoints

Description

Calculates power for two-arm trials with binary endpoints using exact statistical tests. The function supports five different one-sided tests and can handle vectors of probabilities.

Usage

BinaryPower(p1, p2, N1, N2, alpha, Test)

Arguments

Details

The function supports the following five one-sided tests:

• The one-sided Pearson chi-squared test (Chisq)

• The Fisher exact test (Fisher)

• The Fisher mid-p test (Fisher-midP)

• The Z-pooled exact unconditional test (Z-pool)

• The Boschloo exact unconditional test (Boschloo)

The power calculation is based on the exact distribution of the test statistic under the specified alternative hypothesis.

Value

A numeric value or vector of power values. If vectors are provided for p1 and p2, a vector of powers corresponding to each combination will be returned.

Author(s)

Gosuke Homma (my.name.is.gosuke@gmail.com)

Examples

# Simple power calculation with fast Chi-squared test
power1 <- BinaryPower(p1 = 0.5, p2 = 0.2, N1 = 5, N2 = 5,
                     alpha = 0.025, Test = 'Chisq')
print(power1)


# More computationally intensive examples
# Single power calculation with larger sample size
power2 <- BinaryPower(p1 = 0.5, p2 = 0.2, N1 = 10, N2 = 40,
                     alpha = 0.025, Test = 'Boschloo')
print(power2)

# Multiple power calculations
p1_vec <- c(0.5, 0.6, 0.7, 0.8)
p2_vec <- c(0.2, 0.2, 0.2, 0.2)
powers <- BinaryPower(p1 = p1_vec, p2 = p2_vec, N1 = 10, N2 = 40,
                     alpha = 0.025, Test = 'Fisher')
print(powers)

Power Calculation for Two-Arm Trials with Binary Endpoints Using Blinded Sample Size Re-estimation (BSSR)

Description

Calculates the power for two-arm trials with binary endpoints when blinded sample size re-estimation (BSSR) is implemented. The function supports five different statistical tests and allows for both restricted and unrestricted designs with optional weighted approaches.

Usage

BinaryPowerBSSR(
  asmd.p1,
  asmd.p2,
  p,
  Delta.A,
  Delta.T,
  N1,
  N2,
  omega,
  r,
  alpha,
  tar.power,
  Test,
  restricted,
  weighted
)

Arguments

Details

The function supports the following five one-sided tests:

• The one-sided Pearson chi-squared test (Chisq)

• The Fisher exact test (Fisher)

• The Fisher mid-p test (Fisher-midP)

• The Z-pooled exact unconditional test (Z-pool)

• The Boschloo exact unconditional test (Boschloo)

Value

A data frame containing:

p1

True probability of responders for group 1

p2

True probability of responders for group 2

p

True probability of pooled responders from both groups

power.BSSR

Power for BSSR design

power.TRAD

Power for traditional design

Author(s)

Gosuke Homma (my.name.is.gosuke@gmail.com)

Examples

# Simple BSSR calculation with fast Chi-squared test
result1 <- BinaryPowerBSSR(
  asmd.p1 = 0.6, asmd.p2 = 0.3,
  p = 0.45,
  Delta.A = 0.3, Delta.T = 0.3,
  N1 = 5, N2 = 5, omega = 0.5, r = 1,
  alpha = 0.025, tar.power = 0.8,
  Test = 'Chisq',
  restricted = FALSE, weighted = FALSE
)
print(result1)


# More computationally intensive BSSR examples
result2 <- BinaryPowerBSSR(
  asmd.p1 = 0.45,
  asmd.p2 = 0.09,
  p = seq(0.14, 0.23, by = 0.01),
  Delta.A = 0.36,
  Delta.T = 0.36,
  N1 = 24,
  N2 = 24,
  omega = 0.5,
  r = 1,
  alpha = 0.025,
  tar.power = 0.8,
  Test = 'Z-pool',
  restricted = FALSE,
  weighted = TRUE
)
print(result2)

Rejection Region for Two-Arm Trials with Binary Endpoints

Description

Provides a rejection region (RR) for two-arm trials with binary endpoints using various exact statistical tests. The function supports five different one-sided tests.

Usage

BinaryRR(N1, N2, alpha, Test)

Arguments

Details

The function supports the following five one-sided tests:

• The one-sided Pearson chi-squared test (Chisq)

• The Fisher exact test (Fisher)

• The Fisher mid-p test (Fisher-midP)

• The Z-pooled exact unconditional test (Z-pool)

• The Boschloo exact unconditional test (Boschloo)

Value

A logical matrix representing the rejection region (RR). Matrix dimensions are (N1+1) x (N2+1), where TRUE indicates rejection of the null hypothesis.

Author(s)

Gosuke Homma (my.name.is.gosuke@gmail.com)

Examples

# Simple example with small sample sizes (runs quickly)
N1 <- 5
N2 <- 5
alpha <- 0.025
Test <- 'Chisq'
RR <- BinaryRR(N1, N2, alpha, Test)
print(dim(RR))  # Should be (6, 6)


# More computationally intensive example
N1 <- 20
N2 <- 10
alpha <- 0.025
Test <- 'Boschloo'
RR <- BinaryRR(N1, N2, alpha, Test)
print(RR)

Sample Size Calculation for Two-Arm Trials with Binary Endpoints

Description

Calculates the required sample size for two-arm trials with binary endpoints using various exact statistical tests. The function supports five different one-sided tests.

Usage

BinarySampleSize(p1, p2, r, alpha, tar.power, Test)

Arguments

Details

The function supports the following five one-sided tests:

• The one-sided Pearson chi-squared test (Chisq)

• The Fisher exact test (Fisher)

• The Fisher mid-p test (Fisher-midP)

• The Z-pooled exact unconditional test (Z-pool)

• The Boschloo exact unconditional test (Boschloo)

The calculation uses a three-step approach:

1. Calculate initial sample size using normal approximation for chi-squared test

2. Perform power calculation with the initial sample size

3. Use grid search algorithm to find the optimal sample size

Value

A data frame containing:

p1

True probability of responders for group 1

p2

True probability of responders for group 2

r

Allocation ratio to group 1

alpha

One-sided level of significance

tar.power

Target power

Test

Name of the statistical test

Power

Calculated power

N1

Required sample size of group 1

N2

Required sample size of group 2

N

Total required sample size

Author(s)

Gosuke Homma (my.name.is.gosuke@gmail.com)

Examples

# Simple sample size calculation with fast Chi-squared test
result1 <- BinarySampleSize(p1 = 0.4, p2 = 0.2, r = 1, alpha = 0.025,
                           tar.power = 0.8, Test = 'Chisq')
print(result1)


# More computationally intensive examples
# Sample size for Fisher exact test
result2 <- BinarySampleSize(p1 = 0.5, p2 = 0.2, r = 2, alpha = 0.025,
                           tar.power = 0.9, Test = 'Fisher')
print(result2)

# Sample size for Boschloo test
result3 <- BinarySampleSize(p1 = 0.6, p2 = 0.3, r = 1, alpha = 0.025,
                           tar.power = 0.8, Test = 'Boschloo')
print(result3)