pwrss (version 1.3.1)

marginal.probs.2x2: Conversion from marginal probabilities to joint probabilities for the McNemar test applied to paired binary data.

Description

Conversion from marginal probabilities to joint probabilities for the McNemar test applied to paired binary data.

Usage

marginal.probs.2x2(prob11, prob10, prob01, prob00, verbose = 1)

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).

Arguments

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

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.

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. https://doi.org/10.1002/sim.7168

Examples

# 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 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
#         
#   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)