binomialPowerTable: Power Table for Binomial Tests

Description

Creates a power table for binomial tests with various control group response rates and treatment effects. The function can compute power and Type I error either analytically or through simulation. With large simulations, the function is still fast and can produce exact power values to within simulation error.

Usage

binomialPowerTable(
  pC = c(0.8, 0.9, 0.95),
  delta = seq(-0.05, 0.05, 0.025),
  n = 70,
  ratio = 1,
  alpha = 0.025,
  delta0 = 0,
  scale = "Difference",
  failureEndpoint = TRUE,
  simulation = FALSE,
  nsim = 1e+06,
  adj = 0,
  chisq = 0
)

Value

A data frame containing:

pC: Control group response or failure rate.
delta: Treatment effect.
pE: Experimental group response or failure rate.
Power: Power for the test (asymptotic or simulated).

Arguments

pC: Vector of control group response rates.
delta: Vector of treatment effects (differences in response rates).
n: Total sample size.
ratio: Ratio of experimental to control sample size.
alpha: Type I error rate.
delta0: Non-inferiority margin.
scale: Scale for the test ("Difference", "RR", or "OR").
failureEndpoint: Logical indicating if the endpoint is a failure (TRUE) or success (FALSE).
simulation: Logical indicating whether to use simulation (TRUE) or analytical (FALSE) power calculation.
nsim: Number of simulations to run when simulation = TRUE.
adj: Use continuity correction for the testing (default is 0; only used if simulation = TRUE).
chisq: Chi-squared value for the test (default is 0; only used if simulation = TRUE).

Details

The function binomialPowerTable() creates a grid of all combinations of control group response rates and treatment effects. All out of range values (i.e., where the experimental group response rate is not between 0 and 1) are filtered out. For each combination, it computes the power either analytically using nBinomial() or through simulation using simBinomial(). When using simulation, the simPowerBinomial() function (not exported) is called internally to perform the simulations. Assuming $p$ is the true probability of a positive test, the simulation standard error is $$\text{SE} = \sqrt{p(1 - p) / \text{nsim}}.$$ For example, when approximating an underlying Type I error rate of 0.025, the simulation standard error is 0.000156 with 1000000 simulations and the approximated power 95 is 0.025 +/- 1.96 * SE = 0.025 +/- 0.000306.

Examples

Run this code

# Create a power table with analytical power calculation
power_table <- binomialPowerTable(
  pC = c(0.8, 0.9),
  delta = seq(-0.05, 0.05, 0.025),
  n = 70
)

# Create a power table with simulation
power_table_sim <- binomialPowerTable(
  pC = c(0.8, 0.9),
  delta = seq(-0.05, 0.05, 0.025),
  n = 70,
  simulation = TRUE,
  nsim = 10000
)