R/data_binary.R

In MRTAnalysis: Assessing Proximal, Distal, and Mediated Causal Excursion Effects for Micro-Randomized Trials

#' A synthetic data set of an MRT with binary proximal outcomes
#'
#' @description
#' Baseline model:
#' \deqn{\log E\{Y_{t+1} \mid A_t = 0, I_t = 1\} =
#'       \alpha_0 + \alpha_1 \cdot \mathrm{time} / \mathrm{total\_T}
#'       + \alpha_2 \cdot \mathbf{1}(\mathrm{time} > \mathrm{total\_T}/2).}
#'
#' Treatment effect model:
#' \deqn{\log RR_t = \beta_0 + \beta_1 \cdot \mathrm{time} / \mathrm{total\_T}.}
#'
#' Randomization probabilities \eqn{p_t} cycle over 0.3, 0.5, 0.7 (with repetition).
#' Availability is exogenous at 0.8 for all time points.
#'
#' @format A data frame with 3000 observations and 10 variables:
#' \describe{
#'   \item{userid}{Individual id number.}
#'   \item{time}{Decision point index.}
#'   \item{time_var1}{Time-varying covariate 1, the \"standardized time in study\",
#'     defined as the current decision point index divided by the total number
#'     of decision points.}
#'   \item{time_var2}{Time-varying covariate 2, indicator of \"the second half of the study\",
#'     defined as whether the current decision point index is greater than the total number
#'     of decision points divided by 2.}
#'   \item{Y}{Binary proximal outcome.}
#'   \item{A}{Treatment assignment: whether the intervention is randomized to be delivered (=1)
#'     or not (=0) at the current decision point.}
#'   \item{rand_prob}{Randomization probability \eqn{P(A=1)} for the current decision point.}
#'   \item{avail}{Availability indicator (=1 available, =0 not available) at the current decision point.}
#' }
"data_binary"