calcWINS.formula {hce}

Win statistics calculation using formula syntax

Description

Win statistics calculation using formula syntax

Usage

## S3 method for class 'formula'
calcWINS(x, data, ...)

Arguments

x

an object of class formula.

data

a data frame.

...

additional parameters.

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.

• For the win proportion CI calculation see
  
  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.

• The win odds CI is calculated using the formula in
  
  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.

• The win ratio the first CI uses the standard error derived from the standard error of the gamma statistic presented in
  
  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.

• The win ratio the second CI uses the standard error presented in
  
  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.

• The Goodman Kruskal's gamma and its CI match those in DescTools::GoodmanKruskalGamma() and are 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.data.frame().

Examples

# Example 1
calcWINS(x = GROUP ~ TRTP, data = COVID19b)
# Example 2
calcWINS(x = GROUP ~ TRTP, data = COVID19, ref = "Placebo", alpha = 0.01, WOnull = 1.2)