model_negbin_emax {beaver}

Negative Binomial EMAX Dose Response

Description

Model settings for a negative binomial distribution assuming an EMAX Model on the mean. This function is to be used within a call to beaver_mcmc().

Usage

model_negbin_emax(
  mu_b1,
  sigma_b1,
  mu_b2,
  sigma_b2,
  mu_b3,
  sigma_b3,
  w_prior = 1
)

Arguments

mu_b1, sigma_b1, mu_b2, sigma_b2, mu_b3, sigma_b3

hyperparameters. See the model description below for context.

w_prior

the prior weight for the model.

Value

A list with the model's prior weight and hyperparameter values.

Negative Binomial EMAX

Let y_{ij} be the jth subject on dose d_i. The model is

y_{ij} ~ NB(p_i, r_i)

p_i ~ Uniform(0, 1)

r_{ij} = (\mu_{ij} * p_i) / (1 - p_i)

log(\mu_{ij}) = x_{ij} * b1 + b2 * d_i / (b3 + d_i)

b1 ~ N(`mu_b1`, `sigma_b1`^2)

b2 ~ N(`mu_b2`, `sigma_b2`^2)

b3 ~ N(`mu_b3`, `sigma_b3`^2) (Truncated to be positive)

The model is parameterized in terms of the mean of the negative binomial distribution and the usual probability parameter p. The prior on the mean is an EMAX model, and the prior on p at each dose is Uniform(0, 1). The model can adjust for baseline covariates, (

x_{ij}

).

See Also

Other models: beaver_mcmc(), model_negbin_exp(), model_negbin_indep(), model_negbin_linear(), model_negbin_loglinear(), model_negbin_logquad(), model_negbin_quad(), model_negbin_sigmoid_emax()