DualEndpoint-class: General class for the dual endpoint model

In crmPack: Object-Oriented Implementation of CRM Designs

General class for the dual endpoint model

Description

The idea of the dual-endpoint models is to model not only the dose-toxicity relationship, but also to model at the same time the relationship of a PD biomarker with the dose. The subclasses of this class detail how the dose-biomarker relationship is parametrized and are those to be used. This class here shall contain all the common features to reduce duplicate code. (However, this class must not be virtual, because we need to create objects of it during the construction of subclass objects.)

Details

Currently a probit regression model

probit[p(x)] = \beta_{Z1} + \beta_{Z2} \cdot x/x^{*}

or

probit[p(x)] = \beta_{Z1} + \beta_{Z2} \cdot \log(x/x^{*})

in case that the option useLogDose is TRUE. Here p(x) is the probability of observing a DLT for a given dose x, \Phi is the standard normal cdf, and x^{*} is the reference dose.

The prior is

\left( \beta_{Z1} , log(\beta_{Z2}) \right) \sim Normal(\mu, \Sigma)

.

For the biomarker response w at a dose x, we assume

w(x) \sim Normal(f(x), \sigma^{2}_{W})

and f(x) is a function of the dose x, which is further specified in the subclasses. The biomarker variance \sigma^{2}_{W} can be fixed or assigned an inverse gamma prior distribution; see the details below under slot sigma2W.

Finally, the two endpoints y (the binary DLT variable) and w (the biomarker) can be correlated, by assuming a correlation \rho between the underlying continuous latent toxicity variable z and the biomarker w. Again, this correlation can be fixed or assigned a prior distribution from the scaled beta family; see the details below under slot rho.

Please see the Hive page for more details on the model and the example vignette by typing crmPackExample() for a full example.

Slots

mu

For the probit toxicity model, mu contains the prior mean vector

Sigma

For the probit toxicity model, contains the prior covariance matrix

refDose

For the probit toxicity model, the reference dose

useLogDose

For the probit toxicity model, whether a log transformation of the (standardized) dose should be used?

sigma2W

Either a fixed value for the biomarker variance, or a vector with elements a and b for the inverse-gamma prior parameters.

rho

Either a fixed value for the correlation (between -1 and 1), or a vector with elements a and b for the Beta prior on the transformation kappa = (rho + 1) / 2, which is in (0, 1). For example, a=1,b=1 leads to a uniform prior on rho.

useFixed

a list with logical value for each of the parameters indicating whether a fixed value is used or not; this slot is needed for internal purposes and not to be touched by the user.

See Also

Current subclasses: DualEndpointRW, DualEndpointBeta

crmPack documentation built on June 26, 2024, 5:07 p.m.