crmPack (version 1.0.6)

DualEndpointBeta-class: Dual endpoint model with beta function for dose-biomarker relationship

Description

This class extends the DualEndpoint class. Here the dose-biomarker relationship \(f(x)\) is modelled by a parametric, rescaled beta density function:

Slots

E0

either a fixed number or the two uniform distribution parameters

Emax

either a fixed number or the two uniform distribution parameters

delta1

either a fixed number or the two uniform distribution parameters

mode

either a fixed number or the two uniform distribution parameters

refDoseBeta

the reference dose \(x^{*}\) (note that this is different from the refDose in the inherited DualEndpoint model)

Details

$$f(x) = E_{0} + (E_{max} - E_{0}) * Beta(\delta_{1}, \delta_{2}) * (x/x^{*})^{\delta_{1}} * (1 - x/x^{*})^{\delta_{2}}$$

where \(x^{*}\) is the maximum dose (end of the dose range to be considered), \(\delta_{1}\) and \(\delta_{2}\) are the two beta parameters, and \(E_{0}\) and \(E_{max}\) are the minimum and maximum levels, respectively. For ease of interpretation, we parametrize with \(\delta_{1}\) and the mode of the curve instead, where $$mode = \delta_{1} / (\delta_{1} + \delta_{2}),$$ and multiplying this with \(x^{*}\) gives the mode on the dose grid.

All parameters can currently be assigned uniform distributions or be fixed in advance. Note that E0 and Emax can have negative values or uniform distributions reaching into negative range, while delta1 and mode must be positive or have uniform distributions in the positive range.

Examples

model <- DualEndpointBeta(E0 = c(0, 100),
                          Emax = c(0, 500),
                          delta1 = c(0, 5),
                          mode = c(1, 15),
                          refDose=10,
                          useLogDose=TRUE,
                          refDoseBeta = 1000,
                          mu = c(0, 1),
                          Sigma = matrix(c(1, 0, 0, 1), nrow=2),
                          sigma2W = c(a=0.1, b=0.1),
                          rho = c(a=1, b=1))