MinimalInformative: Construct a minimally informative prior
In 0liver0815/onc-crmpack-test: Object-Oriented Implementation of CRM Designs

Description Usage Arguments Details Value Examples

This function constructs a minimally informative prior, which is captured in a LogisticNormal (or LogisticLogNormal) object.

MinimalInformative(
  dosegrid,
  refDose,
  threshmin = 0.2,
  threshmax = 0.3,
  probmin = 0.05,
  probmax = 0.05,
  ...
)

`dosegrid`	the dose grid
`refDose`	the reference dose
`threshmin`	Any toxicity probability above this threshold would be very unlikely (see `probmin`) at the minimum dose (default: 0.2)
`threshmax`	Any toxicity probability below this threshold would be very unlikely (see `probmax`) at the maximum dose (default: 0.3)
`probmin`	the prior probability of exceeding `threshmin` at the minimum dose (default: 0.05)
`probmax`	the prior probability of being below `threshmax` at the maximum dose (default: 0.05)
`...`	additional arguments for computations, see `Quantiles2LogisticNormal`, e.g. `refDose` and `logNormal=TRUE` to obtain a minimal informative log normal prior.

Based on the proposal by Neuenschwander et al (2008, Statistics in Medicine), a minimally informative prior distribution is constructed. The required key input is the minimum (d_{1} in the notation of the Appendix A.1 of that paper) and the maximum value (d_{J}) of the dose grid supplied to this function. Then threshmin is the probability threshold q_{1}, such that any probability of DLT larger than q_{1} has only 5% probability. Therefore q_{1} is the 95% quantile of the beta distribution and hence p_{1} = 0.95. Likewise, threshmax is the probability threshold q_{J}, such that any probability of DLT smaller than q_{J} has only 5% probability (p_{J} = 0.05). The probabilities 1 - p_{1} and p_{J} can be controlled with the arguments probmin and probmax, respectively. Subsequently, for all doses supplied in the dosegrid argument, beta distributions are set up from the assumption that the prior medians are linear in log-dose on the logit scale, and Quantiles2LogisticNormal is used to transform the resulting quantiles into an approximating LogisticNormal (or LogisticLogNormal) model. Note that the reference dose is not required for these computations.

see Quantiles2LogisticNormal

# Setting up a minimal informative prior 
# max.time is quite small only for the purpose of showing the example. They 
# should be increased for a real case.
set.seed(132)
coarseGrid <- c(0.1, 10, 30, 60, 100)
minInfModel <- MinimalInformative(dosegrid = coarseGrid,
                                  refDose=50,
                                  threshmin=0.2,
                                  threshmax=0.3,
                                  control=## for real case: leave out control 
                                    list(max.time=0.1)) 

# Plotting the result
matplot(x=coarseGrid,
        y=minInfModel$required,
        type="b", pch=19, col="blue", lty=1,
        xlab="dose",
        ylab="prior probability of DLT")
matlines(x=coarseGrid,
         y=minInfModel$quantiles,
         type="b", pch=19, col="red", lty=1)
legend("right",
       legend=c("quantiles", "approximation"),
       col=c("blue", "red"),
       lty=1,
       bty="n")