crmPack (version 2.0.0)

DualEndpointRW-class: DualEndpointRW

Description

DualEndpointRW is the class for the dual endpoint model with random walk prior for biomarker.

Usage

DualEndpointRW(sigma2betaW, rw1 = TRUE, ...)
.DefaultDualEndpointRW()

Arguments

sigma2betaW

(numeric)
the prior variance factor of the random walk prior for the biomarker model. Either a fixed value or Inverse-Gamma distribution parameters, i.e. vector with two elements named a and b.

rw1

(flag)
for specifying the random walk prior on the biomarker level. When TRUE, random walk of first order is used. Otherwise, the random walk of second order is used.

...

parameters passed to DualEndpoint().

Slots

sigma2betaW

(numeric)
the prior variance factor of the random walk prior for the biomarker model. Either a fixed value or Inverse-Gamma distribution parameters, i.e. vector with two elements named a and b.

rw1

(flag)
for specifying the random walk prior on the biomarker level. When TRUE, random walk of first order is used. Otherwise, the random walk of second order is used.

Details

This class extends the DualEndpoint class so that the dose-biomarker relationship \(f(x)\) is modelled by a non-parametric random walk of first or second order. That means, for the first order random walk we assume $$betaW_i - betaW_i-1 ~ Normal(0, (x_i - x_i-1) * sigma2betaW),$$ where \(betaW_i = f(x_i)\) is the biomarker mean at the \(i\)-th dose gridpoint \(x_i\). For the second order random walk, the second-order differences instead of the first-order differences of the biomarker means follow the normal distribution with \(0\) mean and \(2 * (x_i - x_i-2) * sigma2betaW\) variance.

The variance parameter \(sigma2betaW\) is important because it steers the smoothness of the function \(f(x)\), i.e.: if it is large, then \(f(x)\) will be very wiggly; if it is small, then \(f(x)\) will be smooth. This parameter can either be a fixed value or assigned an inverse gamma prior distribution.

See Also

DualEndpoint, DualEndpointBeta, DualEndpointEmax.

Examples

my_model <- DualEndpointRW(
  mean = c(0, 1),
  cov = matrix(c(1, 0, 0, 1), nrow = 2),
  sigma2W = c(a = 0.1, b = 0.1),
  rho = c(a = 1, b = 1),
  sigma2betaW = 0.01,
  rw1 = TRUE
)