RIIM (version 2.0.0)

IPPW: Randomization-based inference using inverse post-matching probability weighting (IPPW)

Description

This function implements the inverse post-matching probability weighting (IPPW) method proposed in Zhu, Zhang, Guo and Heng (2024). It can be used for conducting randomization-based inference for the sample average treatment effect in potentially inexactly matched observational studies. 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(Y, Z, X, min.controls = 0.0001,max.controls = 10000, caliper = TRUE, 
     calipersd = 0.2, dim = FALSE, gamma = 0.1, alpha = 0.05)

Value

estimate

The estimate for the sample average treatment effect using the IPPW estimator.

var

The variance for the sample average treatment effect using the IPPW estimator.

low

The lower bound for the sample average treatment effect using the IPPW estimator.

up

The upper bound for the sample average treatment effect using the IPPW estimator.

CI

The confidence interval for the sample average treatment effect using the IPPW estimator.

balance

The pre- and post-matching covariate balance table.

Arguments

Y

The observed outcome vector.

Z

The treatment indicator vector.

X

The covariates matrix. Each row is an individual.

min.controls

The minimum ratio of controls to treatments permitted within a matched set. The default is 0.0001.

max.controls

The maximum ratio of controls to treatments 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.

dim

Whether using difference-in-means estimator to estimate the average treatment effect. The default is FALSE.

gamma

The regularization threshold. The default is 0.1.

alpha

The prespecified level alpha for the 1-alpha condifence 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])
}

# Generate Y 
Y_0 = 0.2*(X_d[,1])^3 + 0.2*abs(X_d[,2]) + 0.5*abs(X_d[,3]) + rnorm(n,0,1)
Y_1 = Y_0 + 1 + 0.3*X_d[,1] + 0.2*X_d[,3]^3
Y = (1-Z)*Y_0 + Z*Y_1

# The output
est = IPPW(Y,Z,X_d,min.controls = 0.01,max.controls = 100,caliper=FALSE,  
calipersd = 0.2,dim=FALSE,gamma=0.1,alpha=0.05)$estimate
est