Description

This package provides functions for inference the difference in quantiles and probability indices comparing two treatment arms.

Installation

devtools::install_github(repo = 'zrmacc/Ordinal')

Examples

Simulated example data.

library(Ordinal)
arm0 <- as.numeric(rmultinom(n = 1, size = 200, prob = c(0.25, 0.25, 0.25, 0.25)))
arm1 <- as.numeric(rmultinom(n = 1, size = 200, prob = c(0.10, 0.30, 0.30, 0.30)))
names(arm0) = names(arm1) <- paste0('Category ', seq(1:4))
show(arm0)

## Category 1 Category 2 Category 3 Category 4 
##         43         45         62         50

show(arm1)

## Category 1 Category 2 Category 3 Category 4 
##         28         46         70         56

Difference in Quantiles

To find a confidence interval and p-vaue for the difference in medians $q = 0.5$:

# Confidence interval calculation.
ci <- QuantDiffCI(
  counts0 = arm0,
  counts1 = arm1,
  q = 0.5
)
round(ci, digits = 2)

## Quantile     Arm1     Arm0    Delta        L        U 
##     0.50     2.82     2.33     0.49     0.25     0.71

# P-value calculation. 
pval <- QuantDiffP(
  counts0 = arm0,
  counts1 = arm1,
  q = 0.5
)
round(pval, digits = 2)

## Quantile     Arm1     Arm0    Delta        P 
##     0.50     2.82     2.33     0.49     0.00

Note that the medians are linearly interpolated within integer bins.

Difference in Probability Indices

The difference in probability indices is defined as: $$ \Delta = P(Y_{1} > Y_{0}) - P(Y_{0} > Y_{1}). $$

To find a confidence interval and p-vaue for the difference in probability indices:

# Confidence interval calculation.
ci <- ProbIndexDiffCI(
  counts0 = arm0,
  counts1 = arm1
)
round(ci, digits = 2)

##  Arm1  Arm0 Delta     L     U 
##  0.49  0.26  0.23  0.13  0.32

# P-value calculation. 
pval <- ProbIndexDiffP(
  counts0 = arm0,
  counts1 = arm1
)
round(pval, digits = 2)

##  Arm1  Arm0 Delta     P 
##  0.49  0.26  0.23  0.00