nbinbf01: Sample size determination for binomial Bayes factor

Description

This function computes the required sample size to obtain a binomial Bayes factor (binbf01) more extreme than a threshold k with a specified target power.

Usage

nbinbf01(
  k,
  power,
  p0 = 0.5,
  type = c("point", "direction"),
  a = 1,
  b = 1,
  dp = NA,
  da = a,
  db = b,
  dl = 0,
  du = 1,
  lower.tail = TRUE,
  nrange = c(1, 10^4),
  ...
)

Value

The required sample size to achieve the specified power

Arguments

k: Bayes factor threshold
power: Target power
p0: Tested binomial proportion. Defaults to 0.5
type: Type of test. Can be "point" or "directional". Defaults to "point"
a: Number of successes parameter of the beta analysis prior distribution. Defaults to 1
b: Number of failures parameter of the beta analysis prior distribution. Defaults to 1
dp: Fixed binomial proportion assumed for the power calculation. Set to NA to use a truncated beta design prior instead (specified via the da, db, dl, and du arguments). Defaults to NA
da: Number of successes parameter of the truncated beta design prior distribution. Is only taken into account if dp = NA. Defaults to the same value a as specified for the analysis prior
db: Number of failures parameter of the truncated beta design prior distribution. Is only taken into account if dp = NA. Defaults to the same value b as specified for the analysis prior
dl: Lower truncation limit of of the truncated beta design prior distribution. Is only taken into account if dp = NA. Defaults to 0
du: Upper truncation limit of of the truncated beta design prior distribution. Is only taken into account if dp = NA. Defaults to 1
lower.tail: Logical indicating whether Pr(\(\mathrm{BF}_{01}\) \(\leq\) k) (TRUE) or Pr(\(\mathrm{BF}_{01}\) \(>\) k) (FALSE) should be computed. Defaults to TRUE
nrange: Sample size search range over which numerical search is performed. Defaults to c(1, 10^4)
...: Other arguments passed to stats::uniroot

Author

Samuel Pawel

Examples

Run this code

## sample size parameters
pow <- 0.9
p0 <- 3/4
a <- 1
b <- 1
k <- 1/10

if (FALSE) {
## sample sizes for directional testing
(nH1 <- nbinbf01(k = k, power = pow, p0 = p0, type = "direction", a = a,
                 b = b, da = a, db = b, dl = p0, du = 1))
(nH0 <- nbinbf01(k = 1/k, power = pow, p0 = p0, type = "direction", a = a,
                 b = b, da = a, db = b, dl = 0, du = p0, lower.tail = FALSE))
nseq <- seq(1, 1.1*max(c(nH1, nH0)), length.out = 100)
powH1 <- pbinbf01(k = k, n = nseq, p0 = p0, type = "direction", a = a,
                  b = b, da = a, db = b, dl = p0, du = 1)
powH0 <- pbinbf01(k = 1/k, n = nseq, p0 = p0, type = "direction", a = a,
                  b = b, da = a, db = b, dl = 0, du = p0, lower.tail = FALSE)
matplot(nseq, cbind(powH1, powH0), type = "s", xlab = "n", ylab = "Power", lty = 1,
        ylim = c(0, 1), col = c(2, 4), las = 1)
abline(h = pow, lty = 2)
abline(v = c(nH1, nH0), col = c(2, 4), lty = 2)
legend("topleft", legend = c("H1", "H0"), lty = 1, col = c(2, 4))

## sample sizes for point null testing
(nH1 <- nbinbf01(k = k, power = pow, p0 = p0, type = "point", a = a,
                 b = b, da = a, db = b))
(nH0 <- nbinbf01(k = 1/k, power = pow, p0 = p0, type = "point", a = a,
                 b = b, dp = p0, lower.tail = FALSE, nrange = c(1, 10^5)))
nseq <- seq(1, max(c(nH1, nH0)), length.out = 100)
powH1 <- pbinbf01(k = k, n = nseq, p0 = p0, type = "point", a = a,
                  b = b, da = a, db = b, dl = 0, du = 1)
powH0 <- pbinbf01(k = 1/k, n = nseq, p0 = p0, type = "point", a = a,
                  b = b, dp = p0, lower.tail = FALSE)
matplot(nseq, cbind(powH1, powH0), type = "s", xlab = "n", ylab = "Power", lty = 1,
        ylim = c(0, 1), col = c(2, 4), las = 1)
abline(h = pow, lty = 2)
abline(v = c(nH1, nH0), col = c(2, 4), lty = 2)
legend("topleft", legend = c("H1", "H0"), lty = 1, col = c(2, 4))
}