Create design with risk of attrition or post treatment conditioning

Creates a two-arm design with application for when estimand of interest is conditional on a post-treatment outcome (the effect on Y given R) or data is conditionally observed (Y given R). See `Details` for more information on the data generating process.

Usage

two_arm_attrition_designer(
  N = 100,
  a_R = 0,
  b_R = 1,
  a_Y = 0,
  b_Y = 1,
  rho = 0,
  args_to_fix = NULL
)

Arguments

N

An integer. Size of sample.

a_R

A number. Constant in equation relating treatment to responses.

b_R

A number. Slope coefficient in equation relating treatment to responses.

a_Y

A number. Constant in equation relating treatment to outcome.

b_Y

A number. Slope coefficient in equation relating treatment to outcome.

rho

A number in [0,1]. Correlation between shocks in equations for R and Y.

args_to_fix

A character vector. Names of arguments to be args_to_fix in design.

Value

A post-treatment design.

Details

The data generating process is of the form:

R ~ (a_R + b_R*Z > u_R)

Y ~ (a_Y + b_Y*Z > u_Y)

where u_R and u_Y are joint normally distributed with correlation rho.

Author

DeclareDesign Team

Examples

# To make a design using default argument (missing completely at random):
two_arm_attrition_design <- two_arm_attrition_designer()
if (FALSE) {
diagnose_design(two_arm_attrition_design)
}
# Attrition can produce bias even for unconditional ATE even when not
# associated with treatment
if (FALSE) {
diagnose_design(two_arm_attrition_designer(b_R = 0, rho = .3))
}
# Here the linear estimate using R=1 data is unbiased for
# "ATE on Y (Given R)" with b_R = 0 but not when  b_R = 1   
if (FALSE) {
diagnose_design(redesign(two_arm_attrition_design, b_R = 0:1, rho = .2))
}