power.exact.mcnemar: 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 using the PASS documentation and G*Power.

Usage

power.exact.mcnemar(
  prob10 = NULL,
  prob01 = NULL,
  req.sign = "+",
  n.paired = NULL,
  power = NULL,
  alpha = 0.05,
  alternative = c("two.sided", "one.sided"),
  method = c("exact", "approximate"),
  ceil.n = TRUE,
  verbose = 1,
  utf = FALSE
)
power.exact.twoprops.mcnemar(
  prob10 = NULL,
  prob01 = NULL,
  req.sign = "+",
  n.paired = NULL,
  power = NULL,
  alpha = 0.05,
  alternative = c("two.sided", "one.sided"),
  method = c("exact", "approximate"),
  ceil.n = TRUE,
  verbose = 1,
  utf = FALSE
)

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 the 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'.

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.
req.sign: whether estimated prob is smaller or larger than the other (when minimum detectable prob is of interest).
n.paired: number of pairs, which is sum of cell frequencies in the 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 \(\alpha\).
alternative: character; the direction or type of the hypothesis test: "two.sided" or "one.sided".
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.
ceil.n: 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 ceil.n to FALSE.
verbose: 1 by default (returns test, hypotheses, and results), if 2 a more detailed output is given (plus key parameters and definitions), if 0 no output is printed on the console.
utf: logical; whether the output should show Unicode characters (if encoding allows for it). FALSE by default.

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. https://doi.org/10.2307/2529083

Connor, R. J. (1987). Sample size for testing differences in proportions for the paired-sample design. Biometrics, 43(1), 207-211. https://doi.org/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. https://doi.org/10.2307/2531151

McNemar, Q. (1947). Note on the sampling error of the difference between correlated proportions or percentages. Psychometrika, 12(2), 153-157. https://doi.org/10.1007/BF02295996

Miettinen, O. S. (1968). The matched pairs design in the case of all-or-none responses. Biometrics, 24(2), 339-352. https://doi.org/10.2307/2528039

Examples

Run this code

# example data for a matched case-control design
# subject  case     control
#         
#   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
#         
#   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,
                    alternative = "two.sided", method = "exact")

# 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,
                    alternative = "two.sided", method = "exact")

# 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
)

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