power analysis for an experiment with one-sided noncompliance

noncompliance_diagnosis.R

library(DeclareDesign)
library(tidyverse)

# Declare the design ----------------------------------------

compliance_rate <- 0.5

design <-
  declare_model(
    N = 1000,
    type = sample(x = c("Never-Taker", "Complier"), 
                  size = N,
                  prob = c(1 - compliance_rate, compliance_rate),
                  replace = TRUE),
    U = rnorm(N),
    # potential outcomes of Y with respect to D
    # compliers experience a 0.2 sd effect
    potential_outcomes(
      Y ~ case_when(
        type == "Never-Taker" ~ 0.75 - 0.20 * D + U,
        type == "Complier" ~ 0.25 + 0.20 * D + U
      ),
      conditions = list(D = c(0, 1))
    ),
    # potential outcomes of D with respect to Z
    potential_outcomes(
      D ~ if_else(Z == 1 & type == "Complier", 1, 0),
      conditions = list(Z = c(0, 1))
    )
  ) +
  declare_inquiry(
    CACE = mean(Y_D_1[type == "Complier"] - 
                  Y_D_0[type == "Complier"])
  ) +
  declare_assignment(Z = complete_ra(N)) +
  declare_measurement(D = reveal_outcomes(D ~ Z),
                      Y = reveal_outcomes(Y ~ D)) +
  declare_estimator(
    Y ~ D | Z,
    .method = iv_robust,
    inquiry = "CACE"
  )


# simulate at compliance rate = 0.5 -------------------------

simulations <- simulate_design(design)

simulations |> 
  summarize(power = mean(p.value <= 0.05))

# redesign over compliance rates ----------------------------

simulations <-
  design |>
  redesign(compliance_rate = c(0.2, 0.5, 0.8)) |>
  simulate_designs()

simulations |> 
  group_by(compliance_rate) |> 
  summarize(power = mean(p.value <= 0.05))