# Simulate ordinal variables for two treatment groups using categorization of beta distributions ```r 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. ## Returns 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. ## Examples ```r # 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") ``` ## See Also `simHCE()` for simulating `hce` objects.

simORD function