Power for Paired Binary Data — PairedPower • bbssr

Calculates the exact power of a test comparing two treatments on a binary endpoint in a matched-pairs design, for given probabilities of the two kinds of discordant pairs.

Usage

PairedPower(
  p10,
  p01,
  N,
  alpha,
  Test,
  alternative = c("greater", "less", "two.sided", "equivalence"),
  n.grid = 100,
  bb.gamma = 0,
  margin = 0,
  ref.pvalue = FALSE
)

Arguments

p10: Probability that only treatment 1 responds in a pair. A vector is allowed
p01: Probability that only treatment 2 responds in a pair, of the same length as p10. A single value of either is used with every value of the other
N: Number of pairs
alpha: Level of significance for the alternative specified by alternative
Test: Type of statistical test. Options: 'McNemar', 'McNemar-cc', 'McNemar-exact', 'McNemar-midP', 'McNemar-uncond' or 'Paired-Score'
alternative: Direction of the alternative hypothesis. Options: 'greater' (default) for p10 - p01 > -margin, 'less' for p10 - p01 < margin, 'two.sided' for p10 != p01, or 'equivalence' for -lower < p10 - p01 < upper
n.grid: Number of grid points used to search over the probability of a discordant pair in the test 'McNemar-uncond'. Default is 100
bb.gamma: Confidence level parameter of the Berger-Boos procedure for the test 'McNemar-uncond'. The default of 0 disables the procedure
margin: Margin on the scale of the difference p10 - p01. The default of 0 gives a test of superiority, and a value other than 0 tests the null hypothesis p10 - p01 <= -margin against p10 - p01 > -margin when alternative is 'greater', and p10 - p01 >= margin against p10 - p01 < margin when it is 'less'. A negative value tests for superiority by more than its absolute value. A margin other than 0 requires Test = 'Paired-Score' and a one-sided alternative. For alternative = 'equivalence' the margin is the pair c(lower, upper), both in (0, 1), or a single value used for both, and the null hypothesis p10 - p01 <= -lower or p10 - p01 >= upper is tested
ref.pvalue: Logical. If TRUE, the maximization over the probability of a discordant pair in the test 'McNemar-uncond' is refined between the grid points, see Details. Default is FALSE

Value

An object of class bbssr_ppower, a data frame with one row for each element of p10, containing:

p10, p01: Probabilities of the two kinds of discordant pairs
N: Number of pairs
alpha: Level of significance
Test: Name of the statistical test
alternative: Direction of the alternative hypothesis
Power: Exact power

The attribute margin holds the margin.

Details

The numbers of the two kinds of discordant pairs and of concordant pairs follow the multinomial distribution with N trials and probabilities p10, p01 and 1 - p10 - p01, and the power is the probability of the rejection region of PairedRR under this distribution, computed by complete enumeration. The probabilities of the concordant pairs with both and with neither treatment responding do not enter, since no test depends on how the concordant pairs split.

Examples

# Average exact power of the asymptotic McNemar test with 25 pairs over the alternatives
# of Berger and Sidik (2003, Section 5.1)
alt <- do.call(rbind, lapply(seq(0.025, 0.475, by = 0.05), function(q) {
  data.frame(p01 = q, p10 = seq(q + 0.05, 1 - q, by = 0.05))
}))
pw <- PairedPower(alt$p10, alt$p01, N = 25, alpha = 0.05, Test = 'McNemar')
mean(pw$Power)
#> [1] 0.6181377