sim_multi_stage {polle}

Simulate Multi-Stage Data

Description

Simulate Multi-Stage Data

Usage

sim_multi_stage(
  n,
  par = list(tau = 10, gamma = c(0, -0.2, 0.3), alpha = c(0, 0.5, 0.2, -0.5, 0.4), beta =
    c(3, -0.5, -0.5), psi = 1, xi = 0.3),
  a = function(t, x, beta, ...) {
     prob <- lava::expit(beta[1] + (beta[2] * t^2) +
    (beta[3] * x))
     stats::rbinom(n = 1, size = 1, prob = prob)
 },
  seed = NULL
)

Arguments

n

Number of observations.

par

Named list with distributional parameters.

• tau: \tau

• gamma: \gamma

• alpha: \alpha

• beta: \beta

• psi: \psi

• xi: \xi

a

Function used to specify the action/treatment at every stage.

seed

Integer.

Details

sim_multi_stage samples n iid observation O with the following distribution:

W \sim \mathcal{N}(0, 1)\\ B \sim Ber(\xi)

For k\geq 1 let

(T_k - T_{k-1})| X_{k-1}, A_{k-1}, W \sim \begin{cases} Exp\Big\{\exp\left(\gamma^T [1, X_{k-1}, W] \right) \Big\} + \psi \quad A_{k-1} = 1\\ \infty \quad A_{k-1} = 0 \end{cases}\\ X_{k}\mid T_k, X_{k-1}, B \sim \begin{cases} \mathcal{N}\left\{ \alpha^T [1, T_k, T^2_k, X_{k-1}, B], 1\right\} \quad T_k < \infty \\ 0 \quad T_k = \infty \end{cases}\\ A_k \mid X_k, T_k \sim \begin{cases} Ber\left\{ expit\left(\beta^T[1, T_{k}^2, X_k] \right)\right\} \quad T_k < \infty\\ 0 \quad T_k = \infty, \end{cases}

Note that \psi is the minimum increment.

Value

list with elements stage_data (data.table) and baseline_data (data.table).