model_negbin_loglinear {beaver}

Negative Binomial Log-Linear Dose Response

Description

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

Usage

model_negbin_loglinear(mu_b1, sigma_b1, mu_b2, sigma_b2, w_prior = 1)

Arguments

mu_b1, sigma_b1, mu_b2, sigma_b2

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 Log-Linear

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)

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

b2 ~ N(`mu_b2`, `sigma_b2`^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 log-linear 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_logquad(), model_negbin_quad(), model_negbin_sigmoid_emax()