crmPack (version 1.0.6)

LogisticLogNormalMixture-class: Standard logistic model with online mixture of two bivariate log normal priors

Description

This model can be used when data is arising online from the informative component of the prior, at the same time with the data of the trial of main interest. Formally, this is achieved by assuming that the probability of a DLT at dose \(x\) is given by

Slots

shareWeight

the prior weight for sharing the same model \(p_{1}(x)\)

Details

$$p(x) = \pi p_{1}(x) + (1 - \pi) p_{2}(x)$$

where \(\pi\) is the probability for the model \(p(x)\) being the same as the model \(p_{1}(x)\) - this is the informative component of the prior. From this model data arises in parallel: at doses xshare, DLT information yshare is observed, in total nObsshare data points, see DataMixture. On the other hand, \(1 - \pi\) is the probability of a separate model \(p_{2}(x)\). Both components have the same log normal prior distribution, which can be specified by the user, and which is inherited from the LogisticLogNormal class.

See Also

the DataMixture class for use with this model

Examples

## decide on the dose grid:
doseGrid <- 1:80

## and MCMC options:
options <- McmcOptions()

## the classic model would be:
model <- LogisticLogNormal(mean = c(-0.85, 1),
                           cov = matrix(c(1, -0.5, -0.5, 1), nrow = 2),
                           refDose = 50)

nodata <- Data(doseGrid=doseGrid)

priorSamples <- mcmc(nodata, model, options)
plot(priorSamples, model, nodata)

## set up the mixture model and data share object:
modelShare <- LogisticLogNormalMixture(shareWeight=0.1,
                                       mean = c(-0.85, 1),
                                       cov = matrix(c(1, -0.5, -0.5, 1), nrow = 2),
                                       refDose = 50)

nodataShare <- DataMixture(doseGrid=doseGrid,
                           xshare=
                             c(rep(10, 4),
                               rep(20, 4),
                               rep(40, 4)),
                           yshare=
                             c(rep(0L, 4),
                               rep(0L, 4),
                               rep(0L, 4)))

## now compare with the resulting prior model:
priorSamplesShare <- mcmc(nodataShare, modelShare, options)
plot(priorSamplesShare, modelShare, nodataShare)