PPpSceptical | R Documentation |
The project power of the sceptical p-value is computed for a specified level, the relative variance, significance level and power for a standard significance test of the original study, and the alternative hypothesis.
PPpSceptical(
level,
c,
alpha,
power,
alternative = c("one.sided", "two.sided"),
type = c("golden", "nominal", "controlled")
)
level |
Threshold for the calibrated sceptical p-value. Default is 0.025. |
c |
Numeric vector of variance ratios of the original and replication effect estimates. This is usually the ratio of the sample size of the replication study to the sample size of the original study. |
alpha |
Significance level for a standard significance test in the original study. Default is 0.025. |
power |
Power to detect the assumed effect with a standard significance test in the original study. |
alternative |
Specifies if |
type |
Type of recalibration. Can be either "golden" (default), "nominal" (no recalibration), or "controlled". |
PPpSceptical
is the vectorized version of
the internal function .PPpSceptical_
.
Vectorize
is used to vectorize the function.
The project power of the sceptical p-value
Leonhard Held, Samuel Pawel
Held, L. (2020). The harmonic mean chi-squared test to substantiate scientific findings. Journal of the Royal Statistical Society: Series C (Applied Statistics), 69, 697-708. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1111/rssc.12410")}
Held, L., Micheloud, C., Pawel, S. (2022). The assessment of replication success based on relative effect size. The Annals of Applied Statistics. 16:706-720.\Sexpr[results=rd]{tools:::Rd_expr_doi("10.1214/21-AOAS1502")}
Maca, J., Gallo, P., Branson, M., and Maurer, W. (2002). Reconsidering some aspects of the two-trials paradigm. Journal of Biopharmaceutical Statistics, 12, 107-119. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1081/bip-120006450")}
pSceptical
, levelSceptical
, T1EpSceptical
## compare project power for different recalibration types
types <- c("nominal", "golden", "controlled")
c <- seq(0.4, 5, by = 0.01)
alpha <- 0.025
power <- 0.9
pp <- sapply(X = types, FUN = function(t) {
PPpSceptical(type = t, c = c, alpha, power, alternative = "one.sided",
level = 0.025)
})
## compute project power of 2 trials rule
za <- qnorm(p = 1 - alpha)
mu <- za + qnorm(p = power)
pp2TR <- power * pnorm(q = za, mean = sqrt(c) * mu, lower.tail = FALSE)
matplot(x = c, y = pp * 100, type = "l", lty = 1, lwd = 2, las = 1, log = "x",
xlab = bquote(italic(c)), ylab = "Project power (%)", xlim = c(0.4, 5),
ylim = c(0, 100))
lines(x = c, y = pp2TR * 100, col = length(types) + 1, lwd = 2)
abline(v = 1, lty = 2)
abline(h = 90, lty = 2, col = "lightgrey")
legend("bottomright", legend = c(types, "2TR"), lty = 1, lwd = 2,
col = seq(1, length(types) + 1))
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