Exact (version 3.3)

power.exact.test: Power Calculations for 2x2 Tables with Independent Samples

Description

Calculates the power of the design for known sample sizes and true probabilities.

Usage

power.exact.test(p1, p2, n1, n2, alternative = c("two.sided", "less", "greater"),
    alpha = 0.05, npNumbers = 100, np.interval = FALSE, beta = 0.001,
    method = c("z-pooled", "z-unpooled", "boschloo", "santner and snell", "csm",
               "fisher", "pearson chisq", "yates chisq"),
    tsmethod = c("square", "central"), simulation = FALSE, nsim = 100,
    delta = 0, convexity = TRUE, useStoredCSM = TRUE)

Value

A list with class "power.htest" containing the following components:

n1, n2

The respective sample sizes

p1, p2

The respective success probabilities

alpha

Significance level

power

Power of the test

alternative

A character string describing the alternative hypothesis

delta

Null hypothesis of the difference in proportion

method

A character string describing the method to determine more extreme tables

Arguments

p1

The probability of success given in first group

p2

The probability of success given in second group

n1

The sample size in first group

n2

The sample size in second group

alternative

Indicates the alternative hypothesis: must be either "two.sided", "less", or "greater"

alpha

Significance level

npNumbers

Number: The number of nuisance parameters considered

np.interval

Logical: Indicates if a confidence interval on the nuisance parameter should be computed

beta

Number: Confidence level for constructing the interval of nuisance parameters considered. Only used if np.interval=TRUE

method

Indicates the method for finding more extreme tables: must be either "Z-pooled", "Z-unpooled", "Santner and Snell", "Boschloo", "CSM", "Fisher", "Pearson Chisq", or "Yates Chisq"

tsmethod

Indicates two-sided method: must be either "square" or "central"

simulation

Logical: Indicates if the power calculation is exact or estimated by simulation

nsim

Number of simulations run. Only used if simulation=TRUE

delta

Number: null hypothesis of the difference in proportion

convexity

Logical: assumes convexity for interval approach. Only used if np.interval=TRUE

useStoredCSM

Logical: uses stored CSM ordering matrix. Only used if method="csm"

Author

Peter Calhoun

Details

The power calculations are for binomial models with independent samples. The design must know the fixed sample sizes in advance. There are (n1+1) x (n2+1) possible tables that could be produced. There are two ways to calculate the power: simulate the tables under two independent binomial distributions or determine the rejection region for all possible tables and calculate the exact power. The calculations can be done using any exact.test computation, Fisher's exact test, or chi-square tests (Yates' or Pearson's; note: these are not exact tests). The power calculations utilize the convexity property, which greatly speeds up computation time (see exact.reject.region documentation).

References

Berger, R. (1994) Power comparison of exact unconditional tests for comparing two binomial proportions. Institute of Statistics Mimeo Series No. 2266

Berger, R. (1996) More powerful tests from confidence interval p values. American Statistician, 50, 314-318

Boschloo, R. D. (1970), Raised Conditional Level of Significance for the 2x2-table when Testing the Equality of Two Probabilities. Statistica Neerlandica, 24, 1-35

See Also

exact.reject.region and statmod

Examples

# Superiority power #
power.exact.test(p1=0.15, p2=0.60, n1=15, n2=30, method="Z-pooled")
power.exact.test(p1=0.15, p2=0.60, n1=15, n2=30, method="Fisher")
power.exact.test(p1=0.15, p2=0.60, n1=15, n2=30, method="Boschloo",
                 np.interval=TRUE, beta=0.001)
if (FALSE) {
# Ensure that the ExactData R package is available before running the CSM test.
if (requireNamespace("ExactData", quietly = TRUE)) {
power.exact.test(p1=0.15, p2=0.60, n1=15, n2=30, method="CSM")
}
}

# Non-inferiority power #
power.exact.test(p1=0.30, p2=0.30, n1=65, n2=65, method="Z-pooled",
                 delta=0.2, alternative="less")