calcWINS.data.frame: Win statistics calculation using a data frame

In hce: Design and Analysis of Hierarchical Composite Endpoints

Win statistics calculation using a data frame

Description

Win statistics calculation using a data frame

Usage

## S3 method for class 'data.frame'
calcWINS(
  x,
  AVAL,
  TRTP,
  ref,
  alpha = 0.05,
  WOnull = 1,
  SE_WP_Type = c("biased", "unbiased"),
  ...
)

Arguments

x	a data frame containing subject-level data.
AVAL	variable in the data with ordinal analysis values.
TRTP	the treatment variable in the data.
ref	the reference treatment group.
alpha	2-sided significance level. The default is 0.05.
WOnull	the null hypothesis. The default is 1.
SE_WP_Type	biased or unbiased standard error for win probability. The default is biased.
...	additional parameters.

Details

When SE_WP_Type = "unbiased", the calculations for win proportion, net benefit, and win odds utilize the unbiased standard error from Brunner-Konietschke (2025) paper which is a reformulation of the original formula proposed by Bamber (1975).

Value

a list containing win statistics and their confidence intervals. It contains the following named data frames:

• summary a data frame containing number of wins, losses, and ties of the active treatment group and the overall number of comparisons.

• WP a data frame containing the win probability and its confidence interval.

• NetBenefit a data frame containing the net benefit and its confidence interval. This is just a ⁠2x-1⁠ transformation of WP and its CI.

• WO a data frame containing the win odds and its confidence interval.

• WR1 a data frame containing the win ratio and its confidence interval, using the transformed standard error of the gamma statistic.

• WR2 a data frame containing the win ratio and its confidence interval, using the standard error calculated using Pties.

• gamma a data frame containing Goodman Kruskal's gamma and its confidence interval.

• SE a data frame containing standard errors used to calculated the Confidence intervals for win statistics.

References

The theory of win statistics is covered in the following papers:

• Win proportion and win odds confidence interval calculation:
  
  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.
  
  DeLong ER et al. (1988) "Comparing the Areas Under Two or More Correlated Receiver Operating Characteristic Curves: A Nonparametric Approach." Biometrics 44.3: 837-845. doi:10.2307/2531595.
  
  Brunner E et al. (2021) "Win odds: an adaptation of the win ratio to include ties." Statistics in Medicine 40.14: 3367-3384. doi:10.1002/sim.8967.
  
  Gasparyan SB et al. (2021) "Adjusted win ratio with stratification: calculation methods and interpretation." Statistical Methods in Medical Research 30.2: 580-611. doi:10.1177/0962280220942558.
  
  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.
  
  Brunner E, Konietschke F. (2025) "An unbiased rank-based estimator of the Mann–Whitney variance including the case of ties." Statistical Papers 66.20. doi:10.1007/s00362-024-01635-0.

• Win ratio: the first CI utilizes the standard error derived from the gamma statistic standard error as outlined by:
  
  Gasparyan SB, Kowalewski EK, Buenconsejo J, Koch GG. (2023) "Hierarchical Composite Endpoints in COVID-19: The DARE-19 Trial." In Case Studies in Innovative Clinical Trials, Chapter 7, 95–148. Chapman; Hall/CRC. doi:10.1201/9781003288640-7.

• Win ratio: the second CI utilizes the standard error presented by:
  
  Yu RX, Ganju J. (2022) "Sample size formula for a win ratio endpoint." Statistics in Medicine 41.6: 950-63. doi:10.1002/sim.9297.

• Goodman Kruskal's gamma and CI: matches implementation in DescTools::GoodmanKruskalGamma() and based on:
  
  Agresti A. (2002) Categorical Data Analysis. John Wiley & Sons, pp. 57-59. doi:10.1002/0471249688.
  
  Brown MB, Benedetti JK. (1977) "Sampling Behavior of Tests for Correlation in Two-Way Contingency Tables." Journal of the American Statistical Association 72, 309-315. doi:10.1080/01621459.1977.10480995.
  
  Goodman LA, Kruskal WH. (1954) "Measures of association for cross classifications." Journal of the American Statistical Association 49, 732-764. doi:10.1080/01621459.1954.10501231.
  
  Goodman LA, Kruskal WH. (1963) "Measures of association for cross classifications III: Approximate sampling theory." Journal of the American Statistical Association 58, 310-364. doi:10.1080/01621459.1963.10500850.

See Also

calcWINS(), calcWINS.hce(), calcWINS.formula().

Examples

calcWINS(x = COVID19b, AVAL = "GROUP", TRTP = "TRTP", ref = "Placebo")
## Biased vs unbiased
n0 <- 10; n1 <- 20; p0 <- 0.2; p1 <- 0.5; x <- 1:20; delta <- 0.5
WP0 <- (p1 - p0)/2 + 0.5
DAT <- NULL
for(i in x){
  dat <- data.frame(AVAL = c(rbinom(n1, size = 1, p1), rbinom(n0, size = 1, p0)), 
  TRTP = c(rep("A", n1), rep("P", n0)))
  CL1 <- calcWINS(x = dat, AVAL = "AVAL", TRTP = "TRTP", ref = "P")$WP
  CL1$Type <- "biased"
  CL2 <- calcWINS(x = dat, AVAL = "AVAL", TRTP = "TRTP", 
                  ref = "P", SE_WP_Type = "unbiased")$WP
  CL2$Type <- "unbiased"
  DAT <- rbind(DAT, CL1, CL2)
}
WP <- DAT$WP[DAT$Type == "unbiased"]
plot(x, WP, pch = 19, xlab = "Simulations", ylab = "Win Probability", ylim = c(0., 1.))
points(x + delta, WP, pch = 19)
arrows(x, DAT$LCL[DAT$Type == "unbiased"], 
       x, DAT$UCL[DAT$Type == "unbiased"], angle = 90, code = 3, length = 0.05, "green")
arrows(x + delta, DAT$LCL[DAT$Type == "biased"], 
       x + delta, DAT$UCL[DAT$Type == "biased"], angle = 90, code = 3, length = 0.05, col = "red")
abline(h = WP0, col = "blue", lty = 3)
legend("bottomleft", legend = c("True WP", "Biased", "Unbiased"), 
                    col = c(4, 2, 3), lty = c(3, 1, 1 ), cex = 0.5)

hce documentation built on April 3, 2025, 11:17 p.m.