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().
model_negbin_logquad(
mu_b1,
sigma_b1,
mu_b2,
sigma_b2,
mu_b3,
sigma_b3,
w_prior = 1
)A list with the model's prior weight and hyperparameter values.
hyperparameters. See the model description below for context.
the prior weight for the model.
Let \(y_{ij}\) be the \(j\)th 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, ($$x_{ij}$$).
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()