simORD: Simulate ordinal variables for two treatment groups using...

In hce: Design and Analysis of Hierarchical Composite Endpoints

Simulate ordinal variables for two treatment groups using categorization of beta distributions

Description

Simulate ordinal variables for two treatment groups using categorization of beta distributions

Usage

simORD(n, n0 = n, M, alpha1 = 8, beta1 = 7, alpha0 = 5, beta0 = 5)

Arguments

n	sample size in the active treatment group.
n0	sample size in the placebo group.
M	number of ordinal values to be simulated.
alpha1	shape1 parameter for the beta distribution in the active group.
beta1	shape2 parameter for the beta distribution in the active group.
alpha0	shape1 parameter for the beta distribution in the placebo group.
beta0	shape2 parameter for the beta distribution in the placebo group.

Value

a data frame containing the following columns:

• ID subject identifier.

• TRTP planned treatment group - "A" for active, "P" for Placebo.

• GROUPN ordinal values. The number of unique values is specified by the variable M0.

• tau the theoretical win odds.

• theta the theoretical win probability.

See Also

simHCE() for simulating hce objects.

Examples

# Example 1
set.seed(2024)
alpha1 <- 8
beta1 <- 8
alpha0 <- 4
beta0 <- 5
d <- simORD(n = 1500, n0 = 1500, M = 5, alpha1 = alpha1, beta1 = beta1, 
alpha0 = alpha0, beta0 = beta0)
x <- seq(0, 1, 0.01)
plot(x, dbeta(x, shape1 = alpha1, shape2 = beta1), 
type = "l", ylab = "Density of beta distribution", col = 2)
lines(x, dbeta(x, shape1 = alpha0, shape2 = beta0), col = 3, lty = 2)
legend("topleft", lty = c(1, 2), col = c(2, 3), legend = c("Control", "Active"))
D <- hce(GROUP = d$GROUPN, TRTP = d$TRTP)
table(D$TRTP, D$GROUP)
calcWO(D)
# Example 2
set.seed(2024)
d <- simORD(n = 100, n0 = 50, M = 2)
d_hce <- hce(GROUP = d$GROUPN, TRTP = d$TRTP)
calcWO(d_hce)
### compare with the theoretical values of the continuous distributions 
c(tau = unique(d$tau), theta = unique(d$theta))
# Example 2 - Convergence of the win odds to its theoretical value
set.seed(2024)
N <- NULL
size <- c(seq(10, 500, 1))
for(i in size){
  d <- simORD(n = i, M = 2)
  d_hce <- hce(GROUP = d$GROUPN, TRTP = d$TRTP)
  TAU <- calcWO(d_hce)
  D <- data.frame(WO = TAU$WO, n = i, tau = unique(d$tau))
  N <- rbind(N, D)
}
plot(N$n, N$WO, log = "y", ylim = c(0.5, 2), ylab = "Win Odds", xlab = "Sample size", type = "l")
lines(N$n, N$tau, col = "darkgreen", lty = 2, lwd = 2)
abline(h = 1, lty = 4, col = "red")
legend("bottomright", legend = c("Theoretical Win Odds", "Null", "Win Odds Estimate"), 
lty = c(4, 2, 1), col = c("darkgreen", "red", "black"))
title("Convergence of the win odds to its theoretical value")

hce documentation built on Aug. 23, 2025, 1:11 a.m.