Model settings for a negative binomial distribution assuming
a Sigmoidal EMAX Model on the mean. This function is to be used within a
call to beaver_mcmc().
model_negbin_sigmoid_emax(
mu_b1,
sigma_b1,
mu_b2,
sigma_b2,
mu_b3,
sigma_b3,
mu_b4,
sigma_b4,
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 $$y_{ij} ~ NB(p_i, r_i)$$ $$p_i ~ Uniform(0, 1)$$ $$r_{ij} = (\mu_{ij} * p_i) / (1 - p_i)$$ $$log(\mu_{ij}) = x_{ij} * b1 + b2 * d_i ^ b4 / (b3 + d_i ^ b4)$$ $$b1 ~ N(`mu_b1`, `sigma_b1`^2)$$ $$b2 ~ N(`mu_b2`, `sigma_b2`^2)$$ $$b3 ~ N(`mu_b3`, `sigma_b3`^2) (Truncated to be positive)$$ $$b3 ~ N(`mu_b4`, `sigma_b4`^2) (Truncated to be positive)$$ 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, ($$x_{ij}$$).
Other models:
beaver_mcmc(),
model_negbin_emax(),
model_negbin_exp(),
model_negbin_indep(),
model_negbin_linear(),
model_negbin_loglinear(),
model_negbin_logquad(),
model_negbin_quad()