Assign hyperparameters and other values for longitudinal
modeling. The output of this function is intended to be used as
the input to the longitudinal
argument of the dose response model
functions, e.g., model_linear
.
model_longitudinal_linear(mu_a, sigma_a, t_max)
model_longitudinal_itp(mu_a, sigma_a, a_c1 = 0, b_c1 = 1, t_max)
model_longitudinal_idp(
mu_a,
sigma_a,
a_c1 = 0,
b_c1 = 1,
a_c2 = -1,
b_c2 = 0,
t_max
)
hyperparameters of the specified longitudinal model. See below for parameterization.
a scalar, typically indicating the latest observed time for subjects. This will influence the interpretation of the parameters of each model.
A named list of the arguments in the function call. The list has
S3 classes assigned which are used internally within dreamer_mcmc()
.
Let \(f(d)\) be a dose response model. The expected value of the response, y, is: $$E(y) = g(d, t)$$ $$g(d, t) = a + (t / t_max) * f(d)$$ $$a \sim N(mu_a, sigma_a)$$
Let \(f(d)\) be a dose response model. The expected value of the response, y, is: $$E(y) = g(d, t)$$ $$g(d, t) = a + f(d) * ((1 - exp(- c1 * t))/(1 - exp(- c1 * t_max)))$$ $$a \sim N(mu_a, sigma_a)$$ $$c1 \sim Uniform(a_c1, b_c1)$$
Increasing-Decreasing-Plateau (IDP).
Let \(f(d)\) be a dose response model. The expected value of the response, y, is: $$E(y) = g(d, t)$$ $$g(d, t) = a + f(d) * (((1 - exp(- c1 * t))/(1 - exp(- c1 * d1))) * I(t < d1) + (1 - gam * ((1 - exp(- c2 * (t - d1))) / (1 - exp(- c2 * (d2 - d1))))) * I(d1 <= t <= d2) + (1 - gam) * I(t > d2))$$ $$a \sim N(mu_a, sigma_a)$$ $$c1 \sim Uniform(a_c1, b_c1)$$ $$c2 \sim Uniform(a_c2, b_c2)$$ $$d1 \sim Uniform(0, t_max)$$ $$d2 \sim Uniform(d1, t_max)$$ $$gam \sim Uniform(0, 1)$$