RIIM (version 2.0.0)

IPPW_IV: The bias-corrected Wald estimator for the complier average treatment effect

Description

This function implements the bias-corrected Wald estimator for randomization-based estimation and inference for the complier average treatment effect under inexact matching, proposed in Zhu, Zhang, Guo and Heng (2024). By default, the matching design implemented in the package is optimal full matching, and the estimated propensity scores used in our method are obtained by the XGBoost method.

Usage

IPPW_IV(Y, Z, X, D, min.controls = 0.0001, max.controls = 10000, 
        caliper = TRUE, calipersd = 0.2, classical = FALSE, gamma = 0.1, 
        lower.bound, upper.bound, by,alpha)

Value

estimate

The estimate for the complier average treatment effect using the bias-corrected Wald estimator.

CI

The confidence interval for the complier average treatment effect using the bias-corrected Wald estimator.

value

The corresponding z-scores for the hypothetical values of the complier average treatment effect.

balance

The pre- and post-matching covariate balance table.

Arguments

Y

The observed outcome vector.

Z

The binary instrument vector.

X

The covariates matrix. Each row is an individual.

D

The binary treatment indicator vector.

min.controls

The minimum ratio of the unencouraged to the encouraged permitted within a matched set. The default is 0.0001.

max.controls

The maximum ratio of the unencouraged to the encouraged permitted within a matched set. The default is 10000.

caliper

Whether adding a propensity score caliper or not. The default is TRUE.

calipersd

The standard deviation of the logit propensity score for caliper. The default is 0.2.

classical

Whether using the classical estimator (proposed by Kang et al. (2016)) to estimate the complier average treatment effect. The default is FALSE.

gamma

The regularization threshold. The default is 0.1.

lower.bound

The starting value of the search region for the point estimate.

upper.bound

The end value of the search region for the point estimate.

by

The increment of the search region for the point estimate.

alpha

The prespecified level alpha for the 1-alpha confidence interval.

Author

Jianan Zhu (maintainer), Jeffrey Zhang, Zijian Guo and Siyu Heng.

References

Fogarty, C. B. (2018). On mitigating the analytical limitations of finely stratified experiments. Journal of the Royal Statistical Society Series B: Statistical Methodology, 80(5), 1035-1056.

Hansen, B. B. (2004). Full matching in an observational study of coaching for the SAT. Journal of the American Statistical Association, 99(467), 609-618.

Hansen, B. B. and Klopfer, S. O. (2006). Optimal full matching and related designs via network flows. Journal of Computational and Graphical Statistics, 15(3), 609-627.

Kang, H., Kreuels, B., May, J., and Small, D. S. (2016). Full matching approach to instrumental variables estimation with application to the effect of malaria on stunting. The Annals of Applied Statistics, 10(1), 335-364.

Rosenbaum, P. R. (1991). A characterization of optimal designs for observational studies. Journal of the Royal Statistical Society: Series B (Methodological), 53(3), 597-610.

Zhu, J., Zhang, J., Guo, Z., and Heng, S. (2024). Randomization-Based Inference for Average Treatment Effect in Inexactly Matched Observational Studies. arXiv preprint, arXiv:2308.02005.

Examples

library(MASS)
library(xgboost)
library(optmatch)

# Generate data
set.seed(1)
d = 3
n = 30
sigma = diag(d)

# generate X
X_d = mvtnorm::rmvnorm(n, mean = rep(0,d), sigma = sigma)

# generate Z
C = -2.5 
fx = 0.1*(X_d[,1])^3 + 0.3*(X_d[,2]) + 0.2*log((X_d[,3])^2) + 
     abs(X_d[,1]*X_d[,2]) + rnorm(n,0,1) + C
p = exp(fx)/(1+exp(fx)) # the probability of receiving the treatment
Z = rep(0,length(p))
for(i in seq_along(p)){
  Z[i] = rbinom(1,1,p[i])
}

#joint distribution
matrix = matrix(c(1,0.8,0.8,1),2,2)
sigma = mvrnorm(n,c(0,0),matrix)
  
# generate the treatment effect D:
fx_D0 = 0.1*X_d[,3] + 0.4*sin(X_d[,2]) + 0.4*abs(X_d[,3])- 1 + sigma[,1]  
ibu <- rnorm(n,0,1)
D_0 = ifelse(fx_D0>ibu,1,0)
  
fx_D1 = fx_D0 + 2 + 0.8*X_d[,2]^2
D_1 = ifelse(fx_D1>ibu,1,0)
D = (1-Z)*D_0 + Z*D_1
  
# generate continuous outcome Y:
Y_0 = 0.4*(X_d[,1])^2 + 0.1*abs(X_d[,2]) + 0.2*cos(X_d[,3]) + sigma[,2]   
Y_1 = Y_0 + 1 + 0.1*X_d[,1] + 0.3*X_d[,3]^2
Y = (1-D)*Y_0 + D*Y_1

# The output
est = IPPW_IV(Y,Z,X_d,D,min.controls = 0.01, max.controls = 100,caliper=FALSE,  
      calipersd = 0.2, classical = FALSE,gamma = 0.1,lower.bound=0,upper.bound=3,
      by=0.01,alpha=0.05)$estimate
est