crmPack (version 1.0.6)

ProbitLogNormal-class: Probit model with bivariate log normal prior

Description

This is probit regression model with a bivariate normal prior on the intercept and log slope. The covariate is the dose \(x\) itself, potentially divided by a reference dose \(x^{*}\), or the logarithm of it:

Slots

mu

the prior mean vector \(\mu\)

Sigma

the prior covariance matrix \(\Sigma\)

refDose

the reference dose \(x^{*}\)

useLogDose

should the log of (standardized) dose be used?

Details

$$probit[p(x)] = \alpha + \beta \cdot x/x^{*}$$ or $$probit[p(x)] = \alpha + \beta \cdot \log(x/x^{*})$$ in case that the option useLogDose is TRUE. Here \(p(x)\) is the probability of observing a DLT for a given dose \(x\).

The prior is $$(\alpha, \log(\beta)) \sim Normal(\mu, \Sigma)$$

The slots of this class contain the mean vector and the covariance matrix of the bivariate normal distribution, as well as the reference dose. Note that the parametrization inside the class uses alpha0 and alpha1.

This model is also used in the DualEndpoint classes, so this class can be used to check the prior assumptions on the dose-toxicity model - even when sampling from the prior distribution of the dual endpoint model is not possible.

Examples

model <- ProbitLogNormal(mu = c(-0.85, 1),
                           Sigma = matrix(c(1, -0.5, -0.5, 1), nrow = 2))

## we can also specify a reference dose, and use a log transformation of
## standardized dose in the model:
model <- ProbitLogNormal(mu = c(-0.85, 1),
                         Sigma = matrix(c(1, -0.5, -0.5, 1), nrow = 2),
                         refDose = 7.2,
                         useLogDose=TRUE)