hce (version 0.7.0)

powerWO: Power calculation for the win odds test (no ties)

Description

Power calculation for the win odds test (no ties)

Usage

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

Value

a data frame containing the calculated power with input values.

Arguments

N

a numeric vector of sample size values.

WO

the given win odds for the alternative hypothesis. 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.

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

sizeWO(), minWO() for WO sample size or minimum detectable WO calculation.

Examples

# Example 1- Use the default standard deviation
powerWO(N = 1000, WO = 1.2)
powerWO(N = seq(500, 1500, 100), WO = 1.2)
# Example 2 - Use data-driven win odds and standard deviation from the COVID19 dataset
res <- calcWO(x = COVID19, AVAL = "GROUP", TRTP = "TRTP", ref = "Placebo")
print(res)
powerWO(N = 500, WO = res$WO, SD = res$SD_WP)
powerWO(N = 500, WO = res$WO) # power with the default standard deviation for the win proportion.
# Example 3 - Non-balanced 3:1 randomization
powerWO(N = 1000, WO = 1.2, k = 0.75)
# Example 4 - Comparison of different alternatives
powerWO(N = 1000, WO = 1.2, alternative = "m")
powerWO(N = 1000, WO = 1.2, alternative = "s")
powerWO(N = 1000, WO = 1.2, alternative = "o")