Power Analysis for McNemar's Exact Test (Paired Proportions)
proportions.mcnemar.RdCalculates 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.
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
TRUErounds 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
FALSEno output is printed on the console.- pretty
logical; whether the output should show Unicode characters (if encoding allows for it).
FALSEby 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. 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. 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. 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. 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. 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
#> control_1 control_0
#> case_1 30 20
#> case_0 10 40
# convert to a 2 x 2 proportion table
props <- freqs / sum(freqs)
props
#> control_1 control_0
#> case_1 0.3 0.2
#> case_0 0.1 0.4
# 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")
#> +--------------------------------------------------+
#> | POWER CALCULATION |
#> +--------------------------------------------------+
#>
#> Paired Proportions
#>
#> Method : McNemar's Exact
#>
#> ---------------------------------------------------
#> Hypotheses
#> ---------------------------------------------------
#> H0 (Null Claim) : prob10 - prob01 = 0
#> H1 (Alt. Claim) : prob10 - prob01 != 0
#>
#> ---------------------------------------------------
#> Results
#> ---------------------------------------------------
#> Paired Sample Size = 100
#> Type 1 Error (alpha) = 0.043
#> Type 2 Error (beta) = 0.627
#> Statistical Power = 0.373 <<
#>
# 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")
#> +--------------------------------------------------+
#> | SAMPLE SIZE CALCULATION |
#> +--------------------------------------------------+
#>
#> Paired Proportions
#>
#> Method : McNemar's Exact
#>
#> ---------------------------------------------------
#> Hypotheses
#> ---------------------------------------------------
#> H0 (Null Claim) : prob10 - prob01 = 0
#> H1 (Alt. Claim) : prob10 - prob01 != 0
#>
#> ---------------------------------------------------
#> Results
#> ---------------------------------------------------
#> Paired Sample Size = 249 <<
#> Type 1 Error (alpha) = 0.037
#> Type 2 Error (beta) = 0.199
#> Statistical Power = 0.801
#>
# 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
)
#> prob11 prob10 prob01 prob00
#> 0.35 0.20 0.10 0.35