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Power Table for Binomial Tests

Source: R/binomialPowerTable.R
binomialPowerTable.Rd

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
)

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).

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).

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.

See also

nBinomial, simBinomial

Examples

# 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
)