T4LB: Tuning for Local Balance (T4LB) Algorithm

In fiona19832008/PSLB: Propensity Score Analysis with Local Balance

Tuning for Local Balance (T4LB) Algorithm

Description

The T4LB algorithm optimze the balancing property of the estimated propensity score by minimizing a local balance criteria, while still controlling for the global balance. In addition to the the absolute standardized difference (S/D) of the covariates in the whole population, the T4LB selects the model with the minimum "mean" or "max" of the S/D in the pre-specified local neighborhoods. Hence, the selected model would have the best balancing property among the candidate models, and the estimated scores retain the interpretation as an appropriate propensity score, and the weights have the intepretation as an inverse probability weights (IPW). T4LB can be used in propensity score estimation approaches that requires parameter tuning, such as using machine learning approaches to estimate propensity scores.

Usage

T4LB(ps, weight, X, Z, ej, para, criteria = "mean")

Arguments

ps	A matrix contains the estimated propensity scores from candidate models. Each column of the "ps" matrix is the propensity scores estimated from each candidate model corresponding to each set of parameters.
weight	A matrix contains the weight calculated from the corresponding input propensity score. Each column of the "weight" matrix should correspond to each column of the "ps" matrix. If weight = NULL, the IPW of ATE will be calculated using the input propensity scores.
X	The covariate matrixes used for balance evaluation. It can be one or a list of covariate matrixes. If one covariate matrix is provided, this matrix will be used for balance evaluation for all candidate models. If a list of covariate matrixes are provided, each element of the list will be used for balance evaluation for each candidate models. The length of the "X" list must equal to the number of column of the "ps"/"weight" matrix. The rows of "X" matrix correspond to the subjects/participants, and the columns of the "X" matrix correspond to the covariates.
Z	The binary treatment indicator vector. A vector with 2 unique numeric values in 0 = untreated and 1 = treated.
ej	The matrix of the local neighborhoods, which contains two columns of positive values greater or equal to 0 and less or equal to 1. The rows of ej represent the neighborhoods. The first column is the start point of the local neighborhoods. The second column is the end point of the local neighborhoods.
para	The matrix whose each row contains the set of parameters for each candidate model.
criteria	Choose "mean" to use the mean of the absolute S/D among all covariates and neighborhoods as the criteria of local balance; choose "max" to use the max of the absolute S/D among all covariates and neighborhoods as the criteria of local balance. Default is "mean".

Value

A list containing the following components:

• "weight": The optimal weight from the selected model with the best local balance.

• "propensity.score": The optimal propensity score from the selected model with the best local balance.

• "parameter": The set of parameters of the selected model with the best local balance.

• "balance": The matrix containing the global and local balance of the selected propensity score model. The first row contains the absolute S/D of each covariates in the whole study population, which represents the global covariate balance. The rest rows contain the absolute S/D of the covariates in the PS-stratified sub-population corresponding to the loal neighborhoods of "ej", which represent the local covariate balance.

References

Lee, B. K., Lessler, J. and Stuart, E. A. (2009) Improving propensity score weighting using machine learning. Statistics in Medicine, 29, 337-346.

Examples

KS = Kang_Schafer_Simulation(n = 1500, seeds = 371834)
# Misspecified propensity score model
X = KS$Data[,7:10]
Z = KS$Data[,2]
# Local neighborhoods
ej = cbind(seq(0,0.8,0.2), seq(0.2,1,0.2))
print(ej)
# Transform X with Gaussian kernel using 10 sigma
x.k = Gaussian_Kernel_feature(X = X, n_sigma = 10)
sigma = rep(x.k$sigma_seq, each = 3)
r = as.vector(t(x.k$r))
para = cbind("sigma" = sigma, "l" = r)
# Fitting the kernelized logistic regression model
m = matrix(seq(1,30), nrow = 10, ncol = 3, byrow = T)
k.ps = matrix(nrow = nrow(X), ncol = nrow(para))
k.w = k.ps
for (i in 1:10) {
  for (j in 1:3) {
    log.fit = glm(Z~x.k$features[[i]][[j]], family = "binomial")
    A = weight.calculate.ps(Z, log.fit$fitted.values, standardize = T)
    k.ps[,m[i,j]] = A$ps
    k.w[,m[i,j]] = A$weight
  }
}
rm(A,log.fit,i,j,m)
best.glm = T4LB(ps = k.ps, weight = k.w, X = X, Z = Z, ej = ej, para = para)
str(t4lb.find)
best.glm$balance

fiona19832008/PSLB documentation built on April 14, 2022, 12:41 a.m.