Model Creation: Longitudinal Models — model

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
)

Arguments

mu_a, sigma_a, a_c1, b_c1, a_c2, b_c2: hyperparameters of the specified longitudinal model. See below for parameterization.
t_max: a scalar, typically indicating the latest observed time for subjects. This will influence the interpretation of the parameters of each model.

Value

A named list of the arguments in the function call. The list has S3 classes assigned which are used internally within dreamer_mcmc().

Longitudinal Linear

Let $f(d)$ be a dose response model. The expected value of the response, y, is: $$E(y) = g(d, t)$$ $$g(d, t) = a + (t / t_max) * f(d)$$ $$a \sim N(mu_a, sigma_a)$$

Longitudinal ITP

Let $f(d)$ be a dose response model. The expected value of the response, y, is: $$E(y) = g(d, t)$$ $$g(d, t) = a + f(d) * ((1 - exp(- c1 * t))/(1 - exp(- c1 * t_max)))$$ $$a \sim N(mu_a, sigma_a)$$ $$c1 \sim Uniform(a_c1, b_c1)$$

Longitudinal IDP

Increasing-Decreasing-Plateau (IDP).

Let $f(d)$ be a dose response model. The expected value of the response, y, is: $$E(y) = g(d, t)$$ $$g(d, t) = a + f(d) * (((1 - exp(- c1 * t))/(1 - exp(- c1 * d1))) * I(t < d1) + (1 - gam * ((1 - exp(- c2 * (t - d1))) / (1 - exp(- c2 * (d2 - d1))))) * I(d1 <= t <= d2) + (1 - gam) * I(t > d2))$$ $$a \sim N(mu_a, sigma_a)$$ $$c1 \sim Uniform(a_c1, b_c1)$$ $$c2 \sim Uniform(a_c2, b_c2)$$ $$d1 \sim Uniform(0, t_max)$$ $$d2 \sim Uniform(d1, t_max)$$ $$gam \sim Uniform(0, 1)$$