Obtain samples from the maximum tolerated dose (MTD) distribution.

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Description

Given a posterior (or prior) sample of the parameters, this function inverts the given functional form to obtain samples from the MTD distribution.

Usage

1
find.x(ff, ptox, alpha)

Arguments

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

ptox

The required probability of DLT. For example, if the MTD distribution is sought then set ptox to the target toxicity level.

alpha

A sample from the posterior (or prior) distribution of the parameter(s).

Details

Given a posterior (or prior) sample of the parameters, this function inverts the given functional form to obtain samples from the MTD distribution or any other targeted quantile.

Author(s)

Michael Sweeting mjs212@medschl.cam.ac.uk (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, getprior, Posterior.exact, Posterior.BRugs, Posterior.R2WinBUGS

Examples

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## 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)

## Posterior distribution of the MTD (on standardised dose scale) using data 
## from the cancer trial described in Neuenschwander et al 2008.
## Using rjags
posterior.samples<-Posterior.rjags(tox,notox,sdose,ff,prior.alpha
  ,burnin.itr=2000,production.itr=2000)
posterior.mtd<-find.x(ff,target.tox,alpha=posterior.samples)
hist(posterior.mtd)