LogisticNormalMixture — LogisticNormalMixture-class • crmPack

LogisticNormalMixture is the class for standard logistic regression model with a mixture of two bivariate normal priors on the intercept and slope parameters.

Usage

LogisticNormalMixture(comp1, comp2, weightpar, ref_dose)

.DefaultLogisticNormalMixture()

Arguments

comp1: (ModelParamsNormal)
bivariate normal prior specification of the first component. See ModelParamsNormal for more details.
comp2: (ModelParamsNormal)
bivariate normal prior specification of the second component. See ModelParamsNormal for more details.
weightpar: (numeric)
the beta parameters for the weight of the first component. It must a be a named vector of length 2 with names a and b and with strictly positive values.
ref_dose: (number)
the reference dose $x*$ (strictly positive number).

Details

The covariate is the natural logarithm of the dose $x$ divided by the reference dose $x*$, i.e.: $$logit[p(x)] = alpha0 + alpha1 * log(x/x*),$$ where $p(x)$ is the probability of observing a DLT for a given dose $x$. The prior $$(alpha0, alpha1) ~ w * Normal(mean1, cov1) + (1 - w) * Normal(mean2, cov2).$$ The weight w for the first component is assigned a beta prior B(a, b).

Slots

comp1: (ModelParamsNormal)
bivariate normal prior specification of the first component.
comp2: (ModelParamsNormal)
bivariate normal prior specification of the second component.
weightpar: (numeric)
the beta parameters for the weight of the first component. It must a be a named vector of length 2 with names a and b and with strictly positive values.
ref_dose: (positive_number)
the reference dose.

Note

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.

Typically, end-users will not use the .DefaultLogisticNormalMixture() function.

Examples

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

`LogisticNormalMixture`