# gbayesSeqSim Simulate Bayesian Sequential Treatment Comparisons Using a Gaussian Model ```r gbayesSeqSim(est, asserts) ``` ## Arguments - `est`: data frame created by `estSeqSim()` - `asserts`: list of lists. The first element of each list is the user-specified name for each assertion/prior combination, e.g., `"efficacy"`. The other elements are, in order, a character string equal to "<", ">", or "in", a parameter value `cutoff` (for "<" and ">") or a 2-vector specifying an interval for "in", and either a prior distribution mean and standard deviation named `mu` and `sigma` respectively, or a parameter value (`"cutprior"`) and tail area `"tailprob"`. If the latter is used, `mu` is assumed to be zero and `sigma` is solved for such that P(parameter > 'cutprior') = P(parameter < - 'cutprior') = `tailprob`. ## Returns a data frame with number of rows equal to that of `est` with a number of new columns equal to the number of assertions added. The new columns are named `p1`, `p2`, `p3`, ... (posterior probabilities), `mean1`, `mean2`, ... (posterior means), and `sd1`, `sd2`, ... (posterior standard deviations). The returned data frame also has an attribute `asserts` added which is the original `asserts` augmented with any derived `mu` and `sigma` and converted to a data frame, and another attribute `alabels` which is a named vector used to map `p1`, `p2`, ... to the user-provided labels in `asserts`. ## Details Simulate a sequential trial under a Gaussian model for parameter estimates, and Gaussian priors using simulated estimates and variances returned by `estSeqSim`. For each row of the data frame `est` and for each prior/assertion combination, computes the posterior probability of the assertion. ## Examples ```r ## Not run: # Simulate Bayesian operating characteristics for an unadjusted # proportional odds comparison (Wilcoxon test) # For 100 simulations, 5 looks, 2 true parameter values, and # 2 assertion/prior combinations, compute the posterior probability # Use a low-level logistic regression call to speed up simuluations # Use data.table to compute various summary measures # Total simulation time: 2s lfit <- function(x, y) { f <- rms::lrm.fit(x, y) k <- length(coef(f)) c(coef(f)[k], vcov(f)[k, k]) } gdat <- function(beta, n1, n2) { # Cell probabilities for a 7-category ordinal outcome for the control group p <- c(2, 1, 2, 7, 8, 38, 42) / 100 # Compute cell probabilities for the treated group p2 <- pomodm(p=p, odds.ratio=exp(beta)) y1 <- sample(1 : 7, n1, p, replace=TRUE) y2 <- sample(1 : 7, n2, p2, replace=TRUE) list(y1=y1, y2=y2) } # Assertion 1: log(OR) < 0 under prior with prior mean 0.1 and sigma 1 on log OR scale # Assertion 2: OR between 0.9 and 1/0.9 with prior mean 0 and sigma computed so that # P(OR > 2) = 0.05 asserts <- list(list('Efficacy', '<', 0, mu=0.1, sigma=1), list('Similarity', 'in', log(c(0.9, 1/0.9)), cutprior=log(2), tailprob=0.05)) set.seed(1) est <- estSeqSim(c(0, log(0.7)), looks=c(50, 75, 95, 100, 200), gendat=gdat, fitter=lfit, nsim=100) z <- gbayesSeqSim(est, asserts) head(z) attr(z, 'asserts') # Compute the proportion of simulations that hit targets (different target posterior # probabilities for efficacy vs. similarity) # For the efficacy assessment compute the first look at which the target # was hit (set to infinity if never hit) require(data.table) z <- data.table(z) u <- z[, .(first=min(p1 > 0.95)), by=.(parameter, sim)] # Compute the proportion of simulations that ever hit the target and # that hit it by the 100th subject u[, .(ever=mean(first < Inf)), by=.(parameter)] u[, .(by75=mean(first <= 100)), by=.(parameter)] ## End(Not run) ``` ## See Also `gbayes()`, `estSeqSim()`, `simMarkovOrd()`, `estSeqMarkovOrd()` ## Author(s) Frank Harrell

gbayesSeqSim function