power.paired.test: Power Calculations for 2x2 Tables with Paired Samples

In Exact: Unconditional Exact Test

Power Calculations for 2x2 Tables with Paired Samples

Description

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

Usage

power.paired.test(p12, p21, N, alternative = c("two.sided", "less", "greater"),
    alpha = 0.05, npNumbers = 100, np.interval = FALSE, beta = 0.001,
    method = c("uam", "ucm", "uamcc", "csm", "cm", "am", "amcc"),
    tsmethod = c("square", "central"),
    simulation = FALSE, nsim = 100,
    delta = 0, convexity = TRUE, useStoredCSM = TRUE)

Arguments

p12	The probability of success in first group and failure in second group. This is the probability of the discordant pair x12
p21	The probability of failure in first group and success in second group. This is the probability of the discordant pair x21
N	The total sample size
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 the more extreme tables: must be either "UAM", "UCM", "UAMCC", "CSM", "CM", "AM", or "AMCC"
tsmethod	A character string describing the method to implement two-sided tests
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"

Details

The power calculations are for paired samples. All possible tables can be represented by an (N+1) x (N+1) matrix. There are two ways to calculate the power: simulate the tables under a trinomial distribution or determine the rejection region for all possible tables and calculate the exact power. The power calculations can be determined for any unconditional exact test in paired.exact.test, the Conditional McNemar's (CM) exact test, the Asymptotic McNemar's (AM) test, or Asymptotic McNemar's test with Continuity Correction (AMCC) (note: asymptotic tests are not exact tests). The power calculations utilize the convexity property, which greatly speeds up computation time (see paired.reject.region documentation).

Value

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

N	The total sample size
p12, p21	The respective discordant 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

Note

McNemar's asymptotic tests are not exact test and may have inflated type 1 error rates. These options were added to compute the power efficiently when using asymptotic tests.

Author(s)

Peter Calhoun

References

Berger, R.L. and Sidik, K. (2003) Exact unconditional tests for 2 x 2 matched-pairs design. Statistical Methods in Medical Research, 12, 91–108

See Also

paired.reject.region

Examples

# Superiority power #
power.paired.test(p12=0.15, p21=0.45, N=40, method="UAM")
## Not run: 
# Ensure that the ExactData R package is available before running the CSM test.
if (requireNamespace("ExactData", quietly = TRUE)) {
power.paired.test(p12=0.15, p21=0.45, N=40, method="CSM")
}

## End(Not run)

# Non-inferiority power #
power.paired.test(p12=0.30, p21=0.30, N=80, method="UAM",
                  alternative="less", delta=0.2)

Exact documentation built on Sept. 11, 2024, 6:17 p.m.