Posterior.exact.sim {bcrm}

Returns posterior mean parameter value and summaries of distributions for probability of DLT at each dose level

Description

Returns posterior mean parameter value and summaries of distributions for probability of DLT at each dose level

Usage

Posterior.exact.sim(tox, notox, sdose, ff, prior.alpha, pointest)

Arguments

tox

A vector of length k showing the number of patient who had toxicities at each dose level

notox

A vector of length k showing the number of patients who did not have toxicities at each dose level

sdose

A vector of length k listing the standardised doses to be used in the CRM model.

ff

A string indicating the functional form of the dose-response curve. Options are

ht

1-parameter hyperbolic tangent

logit1

1-parameter logistic

power

1-parameter power

logit2

2-parameter logistic

prior.alpha

A list of length 3 containing the distributional information for the prior. The first element is a number from 1-4 specifying the type of distribution. Options are

1. Gamma(a, b), where a=shape, b=scale: mean=a*b, variance=a*b*b

2. Uniform(a, b), where a=min, b=max

3. Lognormal(a, b), where a=mean on the log scale, b=variance on the log scale

4. Bivariate Lognormal(a, b), where a=mean vector on the log scale, b=Variance-covariance matrix on the log scale. This prior should be used only in conjunction with a two-parameter logistic model.

The second and third elements of the list are the parameters a and b, respectively.

pointest

Which summary estimate of the posterior distribution should be used to choose the next dose. Options are "plugin" (default) where the posterior mean of the model parameter(s) is plugged into the function form to obtain estimates of toxicity, or "mean" where the posterior mean probabilities of toxicity are directly used. Alternatively, a number between 0 and 1 can be specified representing the quantile of the maximum tolerated dose (MTD) posterior distribution (e.g. 0.5 specifies the posterior median). This produces an Escalation With Overdose Control (EWOC) design if the quantile is less than 0.5 (see details). Currently, EWOC designs must be fit using MCMC methods.

Author(s)

Michael Sweeting [e-mail] (University of Cambridge, UK), drawing on code originally developed by J. Jack Lee and Nan Chen, Department of Biostatistics, the University of Texas M. D. Anderson Cancer Center

References

Sweeting M., Mander A., Sabin T. bcrm: Bayesian Continual Reassessment Method Designs for Phase I Dose-Finding Trials. Journal of Statistical Software (2013) 54: 1–26. http://www.jstatsoft.org/article/view/v054i13

See Also

bcrm, find.x

Examples

## Dose-escalation cancer trial example as described in Neuenschwander et al 2008.
## Pre-defined doses
dose <- c(1, 2.5, 5, 10, 15, 20, 25, 30, 40, 50, 75, 100, 150, 200, 250)
## Pre-specified probabilities of toxicity
## [dose levels 11-15 not specified in the paper,  and are for illustration only]
p.tox0 <- c(0.010, 0.015, 0.020, 0.025, 0.030, 0.040, 0.050,
  0.100, 0.170, 0.300, 0.400, 0.500, 0.650, 0.800, 0.900)
## Data from the first 5 cohorts of 18 patients
tox <- c(0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0)
notox <- c(3, 4, 5, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0)
## Target toxicity level
target.tox <- 0.30

## Prior distribution for the MTD given a lognormal(0, 1.34^2) distribution for alpha
## and a power model functional form
prior.alpha <- list(3, 0, 1.34^2)
ff <- "power"
samples.alpha <- getprior(prior.alpha, 2000)
mtd <- find.x(ff, target.tox, alpha=samples.alpha)
hist(mtd)

## Standardised doses
sdose <- find.x(ff, p.tox0, alpha=1)
point.est <- "plugin"
## Posterior distribution of the MTD (on standardised dose scale) using data 
## from the cancer trial described in Neuenschwander et al 2008.
posterior.samples <- Posterior.exact.sim(tox, notox, sdose, ff, prior.alpha, point.est)