conversion.mcnemar.probs: Conversion Between Joint and Marginal Probabilities for the...

In pwrss: Statistical Power and Sample Size Calculation Tools

Conversion Between Joint and Marginal Probabilities for the McNemar Test

Description

Helper function to converts joint probabilities to marginal probabilities (and vice versa) for the McNemar test applied to paired binary data.

Usage

joint.probs.2x2(prob1, prob2, rho = 0.50, verbose = TRUE)

marginal.probs.2x2(prob11, prob10, prob01, prob00, verbose = TRUE)

Arguments

prob1	(marginal) probability of success in case group (or after).
prob2	(marginal) probability of success in matched-control group (or before).
rho	the correlation between case and matched-control, or after and before (phi coefficient).
prob11	(joint) probability of success in both groups. 'prob11' and 'prob00' are known as concordant probs.
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.
prob00	(joint) probability of failure in both groups. 'prob11' and 'prob00' are known as concordant probs.
verbose	if FALSE no output is printed on the console.

Value

parms	list of parameters used in calculation.
prob1	(marginal) probability of success in case group (or after).
prob2	(marginal) probability of success in matched-control group (or before).
rho	the correlation between case and matched-control, or after and before (phi coefficient).
prob11	(joint) probability of success in both groups. 'prob11' and 'prob00' are known as concordant probs.
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.
prob00	(joint) probability of failure in both groups. 'prob11' and 'prob00' are known as concordant probs.

References

Zhang, S., Cao, J., and Ahn, C. (2017). Inference and sample size calculation for clinical trials with incomplete observations of paired binary outcomes. Statistics in Medicine, 36(4), 581-591. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1002/sim.7168")}

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 summary stats
# prob1 = mean(case) which is 0.55
# prob2 = mean(control) which is 0.45
# rho = cor(case, control) which is 0.4141414


# 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

# example summary stats
# prob1 = mean(after) which is 0.55
# prob2 = mean(before) which is 0.45
# rho = cor(after, before) which is 0.4141414

# 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


# we may not have 2 x 2 joint probs
# convert marginal probs to joint probs using summary stats
jp <- joint.probs.2x2(prob1 = 0.55, # mean of case (or after)
                          prob2 = 0.45, # mean of matched control (or before)
                          # correlation b/w matched case-control / before-after
                          rho = 0.4141414)

# required sample size for exact test
# assuming prob01 and prob10 are population parameters
power.exact.mcnemar(prob01 = jp$prob01,
                    prob10 = jp$prob10,
                    power = 0.80, alpha = 0.05,
                    method = "exact")

# convert joint probs to marginal probs and calc phi coefficient (rho)
# these values can be used in other procedures
marginal.probs.2x2(prob11 = 0.35, # mean of case (or after)
                    prob10 = 0.20, # mean of matched control (or before)
                    prob01 = 0.10,
                    prob00 = 0.35)

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