LogisticKadaneBetaGamma-class | R Documentation |
LogisticKadaneBetaGamma
LogisticKadaneBetaGamma
is the class for the logistic model in the parametrization
of Kadane et al. (1980), using a beta and a gamma distribution as the model priors.
LogisticKadaneBetaGamma(theta, xmin, xmax, alpha, beta, shape, rate)
.DefaultLogisticKadaneBetaGamma()
theta |
( |
xmin |
( |
xmax |
( |
alpha |
( |
beta |
( |
shape |
( |
rate |
( |
Let rho0 = p(xmin)
be the probability of a DLT at the minimum dose
xmin
, and let gamma
be the dose with target toxicity probability theta
,
i.e. p(gamma) = theta
. Then it can easily be shown that the logistic
regression model has intercept
[gamma * logit(rho0) - xmin * logit(theta)] / [gamma - xmin]
and slope
[logit(theta) - logit(rho0)] / [gamma - xmin].
The prior for gamma
, is
gamma ~ Gamma(shape, rate).
.
The prior for rho0 = p(xmin)
, is
rho0 ~ Beta(alpha, beta).
theta
(proportion
)
the target toxicity probability.
xmin
(number
)
the minimum of the dose range.
xmax
(number
)
the maximum of the dose range.
alpha
(number
)
the first shape parameter of the Beta prior distribution
of rho0 = p(xmin)
the probability of a DLT at the minimum dose xmin
.
beta
(number
)
the second shape parameter of the Beta prior distribution
of rho0 = p(xmin)
the probability of a DLT at the minimum dose xmin
.
shape
(number
)
the shape parameter of the Gamma prior distribution
of gamma
the dose with target toxicity probability theta
.
rate
(number
)
the rate parameter of the Gamma prior distribution
of gamma
the dose with target toxicity probability theta
.
The slots of this class, required for creating the model, are the same
as in the LogisticKadane
class. In addition, the shape parameters of the
Beta prior distribution of rho0
and the shape and rate parameters of the
Gamma prior distribution of gamma
, are required for creating the prior model.
Typically, end users will not use the .Default()
function.
ModelLogNormal
, LogisticKadane
.
my_model <- LogisticKadaneBetaGamma(
theta = 0.3,
xmin = 0,
xmax = 7,
alpha = 1,
beta = 19,
shape = 0.5625,
rate = 0.125
)
Add the following code to your website.
For more information on customizing the embed code, read Embedding Snippets.