DualEndpointBeta — DualEndpointBeta-class • crmPack

DualEndpointBeta is the class for the dual endpoint model with beta function for dose-biomarker relationship.

Usage

DualEndpointBeta(E0, Emax, delta1, mode, ref_dose_beta = 1, ...)

.DefaultDualEndpointBeta()

Arguments

E0: (numeric)
either a fixed number or the two uniform distribution parameters.
Emax: (numeric)
either a fixed number or the two uniform distribution parameters.
delta1: (numeric)
either a fixed positive number or the two parameters of the uniform distribution, that can take only positive values.
mode: (numeric)
either a fixed positive number or the two parameters of the uniform distribution, that can take only positive values.
ref_dose_beta: (number)
the reference dose $x*$ (strictly positive number). Note that this is different from the ref_dose in the inherited DualEndpoint model).
...: parameters passed to DualEndpoint().

Details

This class extends the DualEndpoint class so that the dose-biomarker relationship $f(x)$ is modelled by a parametric, rescaled beta density function: $$f(x) = E0 + (Emax - E0) * Beta(delta1, delta2) * (x/x*)^{delta1} * (1 - x/x*)^{delta2},$$ where $x*$ is the maximum dose (end of the dose range to be considered), $delta1$ and $delta2$ are the two beta function parameters, and $E0$, $Emax$ are the minimum and maximum levels, respectively. For ease of interpretation, we use the parametrization based on $delta1$ and the mode, where $$mode = delta1 / (delta1 + delta2),$$ so that multiplying this by $x*$ 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.

Slots

E0: (numeric)
either a fixed number or the two uniform distribution parameters.
Emax: (numeric)
either a fixed number or the two uniform distribution parameters.
delta1: (numeric)
either a fixed positive number or the two parameters of the uniform distribution, that can take only positive values.
mode: (numeric)
either a fixed positive number or the two parameters of the uniform distribution, that can take only positive values.
ref_dose_beta: (positive_number)
the reference dose $x*$ (note that this is different from the ref_dose in the inherited DualEndpoint model).

Note

Typically, end users will not use the .DefaultDualEndpointBeta() function.

Examples

my_model <- DualEndpointBeta(
  mean = c(0, 1),
  cov = matrix(c(1, 0, 0, 1), nrow = 2),
  ref_dose = 10,
  use_log_dose = TRUE,
  sigma2W = c(a = 0.1, b = 0.1),
  rho = c(a = 1, b = 1),
  E0 = c(0, 100),
  Emax = c(0, 500),
  delta1 = c(0, 5),
  mode = c(1, 15),
  ref_dose_beta = 1000
)

`DualEndpointBeta`