sizeWO: Sample size calculation for the win odds test (no ties)

In hce: Design and Analysis of Hierarchical Composite Endpoints

Sample size calculation for the win odds test (no ties)

Description

Sample size calculation for the win odds test (no ties)

Usage

sizeWO(
  WO,
  power,
  SD = NULL,
  k = 0.5,
  alpha = 0.05,
  WOnull = 1,
  alternative = c("shift", "max", "ordered")
)

Arguments

WO	a numeric vector of win odds values.
power	the given power. A numeric vector of length 1.
SD	assumed standard deviation of the win proportion. By default uses the conservative SD. A numeric vector of length 1.
k	proportion of active group in the overall sample size. Default is 0.5 (balanced randomization). A numeric vector of length 1.
alpha	the significance level for the 2-sided test. Default is 0.05. A numeric vector of length 1.
WOnull	the win odds value of the null hypothesis (default is 1). A numeric vector of length 1.
alternative	a character string specifying the class of the alternative hypothesis, must be one of "shift" (default), "max" or "ordered". You can specify just the initial letter.

Details

alternative = "max" refers to the maximum variance of the win proportion across all possible alternatives. The maximum variance equals WP*(1 - WP)/k where the win probability is calculated as ⁠WP = WO/(WO + 1).⁠ alternative = "shift" specifies the variance across alternatives from a shifted family of distributions (Wilcoxon test). The variance formula, as suggested by Noether, is calculated based on the null hypothesis as follows ⁠1/(12*k*(1 - k)).⁠ alternative = "ordered" specifies the variance across alternatives from stochastically ordered distributions which include shifted distributions.

Value

a data frame containing the sample size with input values.

References

• All formulas were presented in
  
  Bamber D (1975) "The area above the ordinal dominance graph and the area below the receiver operating characteristic graph." Journal of Mathematical Psychology 12.4: 387-415. doi:10.1016/0022-2496(75)90001-2.

• Noether's formula for shifted alternatives
  
  Noether GE (1987) "Sample size determination for some common nonparametric tests." Journal of the American Statistical Association 82.398: 645-7. doi:10.1080/01621459.1987.10478478.

• For shift alternatives see also
  
  Gasparyan SB et al. (2021) "Power and sample size calculation for the win odds test: application to an ordinal endpoint in COVID-19 trials." Journal of Biopharmaceutical Statistics 31.6: 765-787. doi:10.1080/10543406.2021.1968893.

See Also

powerWO(), minWO() for WO power or minimum detectable WO calculation.

Examples

sizeWO(WO = 1.25, power = 0.9)
sizeWO(WO = 1.25, power = 0.9, k = 0.75)
sizeWO(WO = seq(1.05, 1.5, 0.05), power = 0.9)
# Comparison of different alternatives
x <- seq(1.05, 5, 0.05)
N1 <- sizeWO(WO = x, power = 0.9, alternative = "m")$SampleSize
N2 <- sizeWO(WO = x, power = 0.9, alternative = "o")$SampleSize
N3 <- sizeWO(WO = x, power = 0.9, alternative = "s")$SampleSize
d <- data.frame(WO = x, N_m = N1, N_o = N2, N_s = N3)
## Check the power for the ordered alternative
check <- c()
for(i in seq_along(x)){
check[i] <- powerWO(N = d[i, "N_o"], WO = d[i, "WO"], alternative = "o")$power
}
d$power_check_o <- check
print(d)

hce documentation built on Oct. 16, 2024, 9:06 a.m.