crmPack (version 1.0.6)

LogisticNormalMixture-class: Standard logistic model with flexible mixture of two bivariate normal priors

Description

This is standard logistic regression model with a mixture of two bivariate normal priors on the intercept and slope parameters. The weight of the two normal priors is a model parameter, hence it is a flexible mixture. This type of prior is often used with a mixture of a minimal informative and an informative component, in order to make the CRM more robust to data deviations from the informative component.

Slots

comp1

the specifications of the first component: a list with mean, cov and prec for the first bivariate normal prior

comp2

the specifications of the second component

weightpar

the beta parameters for the weight of the first component

refDose

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

Details

The covariate is the natural logarithm of the dose \(x\) divided by the reference dose \(x^{*}\):

$$logit[p(x)] = \alpha + \beta \cdot \log(x/x^{*})$$ where \(p(x)\) is the probability of observing a DLT for a given dose \(x\).

The prior is $$(\alpha, \beta) \sim w * Normal(\mu_{1}, \Sigma_{1}) + (1 - w) * Normal(\mu_{2}, \Sigma_{2})$$

The weight w for the first component is assigned a beta prior B(a, b).

The slots of this class comprise two lists, containing the mean vector, the covariance and precision matrices of the two bivariate normal distributions each, the parameters of the beta prior for the first component weight, as well as the reference dose.

Examples

model <- LogisticNormalMixture(comp1 = list(mean = c(-0.85, 1),
                                            cov = matrix(c(1, -0.5, -0.5, 1), 
                                                         nrow = 2)),
                               comp2 = list(mean = c(1, 1.5),
                                            cov = matrix(c(1.2, -0.45, -0.45, 0.6), 
                                                         nrow = 2)),
                               weightpar = c(a=1, b=1),
                               refDose = 50)