model_negbin_logquad {beaver}

Negative Binomial Log-Quadratic Dose Response

Description

Model settings fora negative binomial distribution assuming a log-quadratic model on the mean. This function is to be used within a call to beaver_mcmc().

Usage

model_negbin_logquad(
  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 Quadratic

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 * log(1 + d_i) + b3 * log(1 + d_i) ^ 2

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

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

b3 ~ N(`mu_b3`, `sigma_b3`^2)

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 a quadratic 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_emax(), model_negbin_exp(), model_negbin_indep(), model_negbin_linear(), model_negbin_loglinear(), model_negbin_quad(), model_negbin_sigmoid_emax()