Create a simple two arm design with a possibly prognostic covariate

Builds a design with one treatment and one control arm. Treatment effects can be specified either by providing control_mean and treatment_mean or by specifying a control_mean and ate. Non random assignment is specified by a possible correlation, rho_WZ, between W and a latent variable that determines the probability of Z. Nonignorability is specified by a possible correlation, rho_WY, between W and outcome Y.

two_arm_covariate_designer(
  N = 100,
  prob = 0.5,
  control_mean = 0,
  sd = 1,
  ate = 1,
  h = 0,
  treatment_mean = control_mean + ate,
  rho_WY = 0,
  rho_WZ = 0,
  args_to_fix = NULL
)

Arguments

N	An integer. Sample size.
prob	A number in [0,1]. Probability of assignment to treatment.
control_mean	A number. Average outcome in control.
sd	A positive number. Standard deviation of shock on Y.
ate	A number. Average treatment effect.
h	A number. Controls heterogeneous treatment effects by W. Defaults to 0.
treatment_mean	A number. Average outcome in treatment. Overrides ate if both specified.
rho_WY	A number in [-1,1]. Correlation between W and Y.
rho_WZ	A number in [-1,1]. Correlation between W and Z.
args_to_fix	A character vector. Names of arguments to be args_to_fix in design.

Value

A simple two-arm design with covariate W.

Details

Units are assigned to treatment using complete random assignment. Potential outcomes are normally distributed according to the mean and sd arguments.

See vignette online.

Author

DeclareDesign Team

Examples

#Generate a simple two-arm design using default arguments
two_arm_covariate_design <- two_arm_covariate_designer()
# Design with no confounding but a prognostic covariate 
prognostic <- two_arm_covariate_designer(N = 40, ate = .2, rho_WY = .9, h = .5)
if (FALSE) {
diagnose_design(prognostic)
}
# Design with confounding 
confounding <- two_arm_covariate_designer(N = 40, ate = 0, rho_WZ = .9, rho_WY = .9, h = .5)
if (FALSE) {
diagnose_design(confounding, sims = 2000)
}

# Curse of power: A biased design may be more likely to mislead the larger it is 
curses <- expand_design(two_arm_covariate_designer, 
                        N = c(50, 500, 5000), ate = 0, rho_WZ = .2, rho_WY = .2)
if (FALSE) {
diagnoses <- diagnose_design(curses)
subset(diagnoses$diagnosands_df, estimator_label == "No controls")[,c("N", "power")]
}