| Title: | Causal Inference with High-Dimensional Error-Prone Covariates and Misclassified Treatments |
|---|---|
| Description: | We aim to deal with the average treatment effect (ATE), where the data are subject to high-dimensionality and measurement error. This package primarily contains two functions, which are used to generate artificial data and estimate ATE with high-dimensional and error-prone data accommodated. |
| Authors: | Wei-Hsin Hsu [aut, cre], Li-Pang Chen [aut] |
| Maintainer: | Wei-Hsin Hsu <[email protected]> |
| License: | GPL-3 |
| Version: | 0.1.5 |
| Built: | 2025-02-25 04:30:29 UTC |
| Source: | https://github.com/cran/CHEMIST |
The package CHEMIST, referred to Causal inference with High-dimsensional Error- prone Covariates and MISclassified Treatments, aims to deal with the average treatment effect (ATE), where the data are subject to high-dimensionality and measurement error. This package primarily contains two functions: one is Data_Gen that is applied to generate artificial data, including potential outcomes, error-prone treatments and covariates, and the other is FATE that is used to estimate ATE with measurement error correction.
CHEMIST_package()CHEMIST_package()
This package aims to estimate ATE in the presence of high-dimensional and error-prone data. The strategy is to do variable selection by feature screening and general outcome-adaptive lasso. After that, measurement error in covariates are corrected. Finally, with informative and error corrected data obtained, the propensity score can be estimated and can be used to estimate ATE by the inverse probability weight approach.
CHEMIST_package
This function shows the demonstration of data generation based on some specific and commonly used settings, including exponential family distributed potential outcomes, error-prone treatments, and covariates. In this function, users can specify different magnitudes of measurement error and relationship between outcome, treatment, and covariates.
Data_Gen( X, alpha, beta, theta, a, sigma_e, e_distr = "normal", num_pi, delta, linearY, typeY )Data_Gen( X, alpha, beta, theta, a, sigma_e, e_distr = "normal", num_pi, delta, linearY, typeY )
X |
The input of n x p dimensional matrix of true covariates, where n is sample size and p is number of covariates. Users can customize the data structure and distribution. |
alpha |
A vector of the parameters that reflects the relationship between
treatment model and covariates. The dimension of |
beta |
A vector of the parameters that reflects the relationship between
outcome and covariates. The dimension of |
theta |
The scalar of the parameter used to link outcome and treatment. |
a |
A weight of |
sigma_e |
|
e_distr |
Distribution of the noise term in the classical measurement
error model. The input "normal" refers to the normal distribution with mean
zero and covariance matrix with diagonal entries |
num_pi |
Settings of misclassification probability with option 1 or 2.
|
delta |
The parameter that determines number of treatment with measurement
error. |
linearY |
The boolean option that determines the relationship between
outcome and covariates. |
typeY |
The outcome variable with exponential family distribution
"binary", "pois" and "cont". |
Data |
A n x (p+2) matrix of the original data without measurement error, where n is sample size and the first p columns are covariates with the order being Xc (the covariates associated with both treatment and outcome), Xp (the covariates associated with outcome only), Xi (the covariates associated with treatment only), Xs (the covariates independent of outcome and treatment), the last second column is treatment, and the last column is outcome. |
Error_Data |
A n x (p+2) matrix of the data with measurement error in covariates and treatment, where n is sample size and the first p columns are covariates with the order being Xc (the covariates associated with both treatment and outcome), Xp (the covariates associated with outcome only), Xi (the covariates associated with treatment only), Xs (the covariates independent of outcome and treatment), the last second column is treatment, and the last column is outcome. |
Pi |
A n x 2 matrix containing two misclassification probabilities pi_10 = P(Observed Treatment = 1 | Actual Treatment = 0) and pi_01 = P(Observed Treatment = 0 | Actual Treatment = 1) in columns. |
cov_e |
A covariance matrix of the measurement error model. |
##### Example 1: A multivariate normal continuous X with linear normal Y ##### ## Generate a multivariate normal X matrix mean_x = 0; sig_x = 1; rho = 0 Sigma_x = matrix( rho*sig_x^2,nrow=120 ,ncol=120 ) diag(Sigma_x) = sig_x^2 Mean_x = rep( mean_x, 120 ) X = as.matrix( mvrnorm(n = 60,mu = Mean_x,Sigma = Sigma_x,empirical = FALSE) ) ## Data generation setting ## alpha: Xc's scale is 0.2 0.2 and Xi's scale is 0.3 0.3 ## so this refers that there is 2 Xc and Xi ## beta: Xc's scale is 2 2 and Xp's scale is 2 2 ## so this refers that there is 2 Xc and Xp ## rest with following setup Data_fun <- Data_Gen(X, alpha = c(0.2,0.2,0,0,0.3,0.3), beta = c(2,2,2,2,0,0) , theta = 2, a = 2, sigma_e = 0.75, e_distr = 10, num_pi = 1, delta = 0.8, linearY = TRUE, typeY = "cont") ##### Example 2: A uniform X with non linear binary Y ##### ## Generate a uniform X matrix n = 50; p = 120 X = matrix(NA,n,p) for( i in 1:p ){ X[,i] = sample(runif(n,-1,1),n,replace=TRUE ) } X = scale(X) ## Data generation setting ## alpha: Xc's scale is 0.1 and Xi's scale is 0.3 ## so this refers that there is 1 Xc and Xi ## beta: Xc's scale is 2 and Xp's scale is 3 ## so this refers that there is 1 Xc and Xp ## rest with following setup Data_fun <- Data_Gen(X, alpha = c(0.1,0,0.3), beta = c(2,3,0) , theta = 1, a = 2, sigma_e = 0.5, e_distr = "normal", num_pi = 2, delta = 0.5, linearY = FALSE, typeY = "binary")##### Example 1: A multivariate normal continuous X with linear normal Y ##### ## Generate a multivariate normal X matrix mean_x = 0; sig_x = 1; rho = 0 Sigma_x = matrix( rho*sig_x^2,nrow=120 ,ncol=120 ) diag(Sigma_x) = sig_x^2 Mean_x = rep( mean_x, 120 ) X = as.matrix( mvrnorm(n = 60,mu = Mean_x,Sigma = Sigma_x,empirical = FALSE) ) ## Data generation setting ## alpha: Xc's scale is 0.2 0.2 and Xi's scale is 0.3 0.3 ## so this refers that there is 2 Xc and Xi ## beta: Xc's scale is 2 2 and Xp's scale is 2 2 ## so this refers that there is 2 Xc and Xp ## rest with following setup Data_fun <- Data_Gen(X, alpha = c(0.2,0.2,0,0,0.3,0.3), beta = c(2,2,2,2,0,0) , theta = 2, a = 2, sigma_e = 0.75, e_distr = 10, num_pi = 1, delta = 0.8, linearY = TRUE, typeY = "cont") ##### Example 2: A uniform X with non linear binary Y ##### ## Generate a uniform X matrix n = 50; p = 120 X = matrix(NA,n,p) for( i in 1:p ){ X[,i] = sample(runif(n,-1,1),n,replace=TRUE ) } X = scale(X) ## Data generation setting ## alpha: Xc's scale is 0.1 and Xi's scale is 0.3 ## so this refers that there is 1 Xc and Xi ## beta: Xc's scale is 2 and Xp's scale is 3 ## so this refers that there is 1 Xc and Xp ## rest with following setup Data_fun <- Data_Gen(X, alpha = c(0.1,0,0.3), beta = c(2,3,0) , theta = 1, a = 2, sigma_e = 0.5, e_distr = "normal", num_pi = 2, delta = 0.5, linearY = FALSE, typeY = "binary")
This function aims to estimate ATE by selecting informative covariates and correcting for measurement error in covariates and misclassification in treatments. The function FATE reflects the strategy of estimation method: Feature screening, Adaptive lasso, Treatment adjustment, and Error correction for covariates.
FATE(Data, cov_e, Consider_D, pi_10, pi_01)FATE(Data, cov_e, Consider_D, pi_10, pi_01)
Data |
A n x (p+2) matrix of the data, where n is sample size and the first p columns are covariates with the order being Xc (the covariates associated with both treatment and outcome), Xp (the covariates associated with outcome only), Xi (the covariates associated with treatment only), Xs (the covariates independent of outcome and treatment), the last second column is treatment, and the last column is outcome. |
cov_e |
Covariance matrix in the measurement error model. |
Consider_D |
Feature screening with treatment effects accommodated.
|
pi_10 |
Misclassifcation probability is P(Observed Treatment = 1 | Actual Treatment = 0). |
pi_01 |
Misclassifcation probability is P(Observed Treatment = 0 | Actual Treatment = 1). |
ATE |
A value of the average treatment effect. |
wAMD |
A weighted absolute mean difference. |
Coef_prop_score |
A table containing coefficients of propensity score. |
Kersye_table |
The selected covariates by feature screening. |
Corr_trt_table |
A summarized table containing corrected treatment. |
##### Example 1: Input the data without measurement correction ##### ## Generate a multivariate normal X matrix mean_x = 0; sig_x = 1; rho = 0; n = 50; p = 120 Sigma_x = matrix( rho*sig_x^2 ,nrow=p ,ncol=p ) diag(Sigma_x) = sig_x^2 Mean_x = rep( mean_x, p ) X = as.matrix( mvrnorm(n ,mu = Mean_x,Sigma = Sigma_x,empirical = FALSE) ) ## Data generation setting ## alpha: Xc's scale is 0.2 0.2 and Xi's scale is 0.3 0.3 ## so this refers that there is 2 Xc and Xi ## beta: Xc's scale is 2 2 and Xp's scale is 2 2 ## so this refers that there is 2 Xc and Xp ## rest with following setup Data_fun <- Data_Gen(X, alpha = c(0.2,0.2,0,0,0.3,0.3), beta = c(2,2,2,2,0,0) , theta = 2, a = 2, sigma_e = 0.75, e_distr = 10, num_pi = 1, delta = 0.8, linearY = TRUE, typeY = "cont") ## Extract Ori_Data, Error_Data, Pi matrix, and cov_e matrix Ori_Data=Data_fun$Data Pi=Data_fun$Pi cov_e=Data_fun$cov_e Data=Data_fun$Error_Data pi_01 = pi_10 = Pi[,1] ## Input data into model without error correction Model_fix = FATE(Data, matrix(0,p,p), Consider_D = FALSE, 0, 0) ##### Example 2: Input the data with measurement correction ##### ## Input data into model with error correction Model_fix = FATE(Data, cov_e, Consider_D = FALSE, Pi[,1],Pi[,2])##### Example 1: Input the data without measurement correction ##### ## Generate a multivariate normal X matrix mean_x = 0; sig_x = 1; rho = 0; n = 50; p = 120 Sigma_x = matrix( rho*sig_x^2 ,nrow=p ,ncol=p ) diag(Sigma_x) = sig_x^2 Mean_x = rep( mean_x, p ) X = as.matrix( mvrnorm(n ,mu = Mean_x,Sigma = Sigma_x,empirical = FALSE) ) ## Data generation setting ## alpha: Xc's scale is 0.2 0.2 and Xi's scale is 0.3 0.3 ## so this refers that there is 2 Xc and Xi ## beta: Xc's scale is 2 2 and Xp's scale is 2 2 ## so this refers that there is 2 Xc and Xp ## rest with following setup Data_fun <- Data_Gen(X, alpha = c(0.2,0.2,0,0,0.3,0.3), beta = c(2,2,2,2,0,0) , theta = 2, a = 2, sigma_e = 0.75, e_distr = 10, num_pi = 1, delta = 0.8, linearY = TRUE, typeY = "cont") ## Extract Ori_Data, Error_Data, Pi matrix, and cov_e matrix Ori_Data=Data_fun$Data Pi=Data_fun$Pi cov_e=Data_fun$cov_e Data=Data_fun$Error_Data pi_01 = pi_10 = Pi[,1] ## Input data into model without error correction Model_fix = FATE(Data, matrix(0,p,p), Consider_D = FALSE, 0, 0) ##### Example 2: Input the data with measurement correction ##### ## Input data into model with error correction Model_fix = FATE(Data, cov_e, Consider_D = FALSE, Pi[,1],Pi[,2])