proportions.mcnemar: Power Analysis for McNemar's Exact Test (Paired Proportions)

In pwrss: Statistical Power and Sample Size Calculation Tools

Power Analysis for McNemar's Exact Test (Paired Proportions)

Description

Calculates power or sample size for McNemar's test on paired binary outcomes. Approximate and exact methods are available (check references for details).

Validated via PASS and G*Power.

Usage

  power.exact.mcnemar(prob10, prob01, n.paired = NULL,
                    power = NULL,  alpha = 0.05,
                    alternative = c("two.sided", "one.sided"),
                    method = c("exact", "approximate"),
                    ceiling = TRUE, verbose = TRUE, pretty = FALSE)

Arguments

prob10	(joint) probability of success in case (or after) but failure in matched control (or before). 'prob10' and 'prob01' are known as discordant probs.
prob01	(joint) probability of failure in case (or after) but success in matched control (or before). prob10' and 'prob01' are known as discordant probs.
n.paired	number of pairs, which is sum of cell frequencies in 2 x 2 table (f11 + f10 + f01 + f00), or number of rows in a data frame with matched variables 'case' and 'control' or 'after' and 'before'.
power	statistical power, defined as the probability of correctly rejecting a false null hypothesis, denoted as 1 - \beta.
alpha	type 1 error rate, defined as the probability of incorrectly rejecting a true null hypothesis, denoted as \alpha.
method	character; the method used for power calculation. "exact" specifies Fisher's exact test, while "approximate" refers to the z-test based on the normal approximation.
alternative	character; the direction or type of the hypothesis test: "not equal", "greater", "less". Optionally, users can specify 'two.sided' as an alternative to 'not equal' for consistency with other R statistical functions.
ceiling	logical; if TRUE rounds up sample size in each cell. This procedure assumes symmetry for concordant probs, which are 'p11' and 'p00'). Thus results may differ from other software by a few units. To match results set 'ceiling = FALSE'.
verbose	logical; if FALSE no output is printed on the console.
pretty	logical; whether the output should show Unicode characters (if encoding allows for it). FALSE by default.

Value

parms	list of parameters used in calculation.
test	type of the test, which is "exact" or "z".
odds.ratio	odds ratio.
mean	mean of the alternative distribution.
sd	standard deviation of the alternative distribution.
null.mean	mean of the null distribution.
null.sd	standard deviation of the null distribution.
z.alpha	critical value(s).
power	statistical power (1-\beta).
n.paired	paired sample size, which is sum of cell frequencies in 2 x 2 table (f11 + f10 + f01 + f00), or number of rows in a data frame with variables 'case' and 'control' or 'after' and 'before'.

References

Bennett, B. M., & Underwood, R. E. (1970). 283. Note: On McNemar's Test for the 2 * 2 Table and Its Power Function. Biometrics, 26(2), 339-343. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.2307/2529083")}

Connor, R. J. (1987). Sample size for testing differences in proportions for the paired-sample design. Biometrics, 43(1), 207-211. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.2307/2531961")}

Duffy, S. W. (1984). Asymptotic and exact power for the McNemar test and its analogue with R controls per case. Biometrics, 40(4) 1005-1015. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.2307/2531151")}

McNemar, Q. (1947). Note on the sampling error of the difference between correlated proportions or percentages. Psychometrika, 12(2), 153-157. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1007/BF02295996")}

Miettinen, O. S. (1968). The matched pairs design in the case of all-or-none responses. Biometrics, 24(2), 339-352. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.2307/2528039")}

Examples

# example data for a matched case-control design
# subject  case     control
# <int>    <dbl>    <dbl>
#   1        1        1
#   2        0        1
#   3        1        0
#   4        0        1
#   5        1        1
#   ...     ...      ...
#   100      0        0

# example data for a before-after design
# subject  before   after
# <int>    <dbl>    <dbl>
#   1        1        1
#   2        0        1
#   3        1        0
#   4        0        1
#   5        1        1
#   ...     ...      ...
#   100      0        0

# convert to a 2 x 2 frequency table
freqs <- matrix(c(30, 10, 20, 40), nrow = 2, ncol = 2)
colnames(freqs) <- c("control_1", "control_0")
rownames(freqs) <- c("case_1", "case_0")
freqs

# convert to a 2 x 2 proportion table
props <- freqs / sum(freqs)
props

# discordant pairs (0 and 1, or 1 and 0) in 'props' matrix
# are the sample estimates of prob01 and prob10

# post-hoc exact power
power.exact.mcnemar(prob10 = 0.20, prob01 = 0.10,
                    n.paired = 100, alpha = 0.05,
                    method = "exact", alt = "two.sided")

# required sample size for exact test
# assuming prob01 and prob10 are population parameters
power.exact.mcnemar(prob10 = 0.20, prob01 = 0.10,
                    power = 0.80, alpha = 0.05,
                    method = "exact", alt = "two.sided")

# we may not have 2 x 2 joint probs
# convert marginal probs to joint probs
joint.probs.2x2(prob1 = 0.55, # mean of case group (or after)
                    prob2 = 0.45, # mean of matched control group (or before)
                    # correlation between matched case-control or before-after
                    rho = 0.4141414
)

pwrss documentation built on Sept. 16, 2025, 9:11 a.m.