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.)
muFor the probit toxicity model, mu contains the prior mean
vector
SigmaFor the probit toxicity model, contains the prior covariance matrix
refDoseFor the probit toxicity model, the reference dose
useLogDoseFor the probit toxicity model, whether a log transformation of the (standardized) dose should be used?
sigma2WEither a fixed value for the biomarker variance, or a vector
with elements a and b for the inverse-gamma prior parameters.
rhoEither 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.
useFixeda 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.
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.
Current subclasses: DualEndpointRW,
DualEndpointBeta