crmPack (version 1.0.6)

DualEndpointRW-class: Dual endpoint model with RW prior for biomarker

Description

This class extends the DualEndpoint class. Here the dose-biomarker relationship \(f(x)\) is modelled by a non-parametric random-walk of first (RW1) or second order (RW2).

Slots

sigma2betaW

Contains the prior variance factor of the random walk prior for the biomarker model. If it is not a single number, it can also contain a vector with elements a and b for the inverse-gamma prior on sigma2betaW.

useRW1

for specifying the random walk prior on the biomarker level: if TRUE, RW1 is used, otherwise RW2.

Details

That means, for the RW1 we assume $$\beta_{W,i} - \beta_{W,i-1} \sim Normal(0, (x_{i} - x_{i-1}) \sigma^{2}_{\beta_{W}}),$$ where \(\beta_{W,i} = f(x_{i})\) is the biomarker mean at the i-th dose gridpoint \(x_{i}\). For the RW2, the second-order differences instead of the first-order differences of the biomarker means follow the normal distribution.

The variance parameter \(\sigma^{2}_{\beta_{W}}\) is important because it steers the smoothness of the function f(x): 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 fixed or assigned an inverse gamma prior distribution.

Non-equidistant dose grids can be used now, because the difference \(x_{i} - x_{i-1}\) is included in the modelling assumption above.

Please note that due to impropriety of the RW prior distributions, it is not possible to produce MCMC samples with empty data objects (i.e., sample from the prior). This is not a bug, but a theoretical feature of this model.

Examples

model <- DualEndpointRW(mu = c(0, 1),
                        Sigma = matrix(c(1, 0, 0, 1), nrow=2),
                        sigma2betaW = 0.01,
                        sigma2W = c(a=0.1, b=0.1),
                        rho = c(a=1, b=1),
                        smooth="RW1")