gbayesSeqSim {Hmisc}

gbayesSeqSim

Description

Simulate Bayesian Sequential Treatment Comparisons Using a Gaussian Model

Usage

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.

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.

Value

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.

Author(s)

Frank Harrell

See Also

gbayes(), estSeqSim(), simMarkovOrd(), estSeqMarkovOrd()

Examples

## 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)