Type: Package
Title: Causal Inference with High-Dimensional Error-Prone Covariates and Misclassified Treatments
Version: 0.1.5
Maintainer: Wei-Hsin Hsu <anson60214@gmail.com>
Depends: R (≥ 3.3.1),MASS
Imports: stats,XICOR,LaplacesDemon
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.
License: GPL-3
Encoding: UTF-8
RoxygenNote: 7.2.1
NeedsCompilation: no
Packaged: 2023-05-01 09:14:04 UTC; anson
Author: Wei-Hsin Hsu [aut, cre], Li-Pang Chen [aut]
Repository: CRAN
Date/Publication: 2023-05-01 14:15:38 UTC

Causal Inference with High-Dimensional Error-Prone Covariates and Misclassified Treatments

Description

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.

Usage

CHEMIST_package()

Details

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.

Value

CHEMIST_package

Generation of Artificial Data

Description

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.

Usage

Data_Gen(
  X,
  alpha,
  beta,
  theta,
  a,
  sigma_e,
  e_distr = "normal",
  num_pi,
  delta,
  linearY,
  typeY
)

Arguments

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 alpha should be equal to the dimension of beta. If alpha and beta have the same nonzero components, then we call them Xc (covariates associated with both outcome and treatment). If components in alpha are zero but the same components in beta are nonzero, we call them Xp (covariates associated with outcome only), If components in alpha are nonzero but the same components in beta are zero, we call them Xi (covariates associated with treatment only). For example, if alpha = c(2,2,0,0,1,1) and beta = c(3,3,1,1,0,0), then the first two components are Xc, the middle two components are Xp, and the last two components are Xi.

beta

A vector of the parameters that reflects the relationship between outcome and covariates. The dimension of alpha should be equal to the dimension of beta. If alpha and beta have the same nonzero components, then we call them Xc (covariates associated with both outcome and treatment). If components in alpha are zero but the same components in beta are nonzero, we call them Xp (covariates associated with outcome only), If components in alpha are nonzero but the same components in beta are zero, we call them Xi (covariates associated with treatment only). For example, if alpha = c(2,2,0,0,1,1) and beta = c(3,3,1,1,0,0), then the first two components are Xc, the middle two components are Xp, and the last two components are Xi.

theta

The scalar of the parameter used to link outcome and treatment.

a

A weight of cov_e in the measurement error model W = cov_e*a + X + e, where W is observed covariates with measurement error, X is actual covariates, and e is noise term with covaraince matrix cov_e.

sigma_e

sigma_e is the common diagonal entries of covariance matrix in the measurement error model.

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 sigma_e. The scalar input "v" represents t-distribution with degree of freedom v.

num_pi

Settings of misclassification probability with option 1 or 2. num_pi = 1 gives that pi_01 equals pi_10, and num_pi = 2 refers to that pi_01 is not equal to pi_10.

delta

The parameter that determines number of treatment with measurement error. delta = 1 has equal number of treatment with and without measurement error. We set default = 0.5 since it has smaller number of treatment who has measurement error.

linearY

The boolean option that determines the relationship between outcome and covariates. linearY = TRUE gives linear relationship with a vector of parameters alpha, linearY = FALSE refers to non linear relationship between outcome and covariates, where the sin function is specified on Xc and the exponential function is specified on Xp.

typeY

The outcome variable with exponential family distribution "binary", "pois" and "cont". typeY = "binary" refers to binary random variables, typeY = "pois" refers to Poisson random variables, and typeY = "cont" refers to normally distributed random variables.

Value

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.

Examples

##### 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")

Estimation of ATE under high-dimensional error-prone data

Description

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.

Usage

FATE(Data, cov_e, Consider_D, pi_10, pi_01)

Arguments

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. Conidser_D = TRUE refers to feature screening with A and (1-A) incorporated. Consider_D = FALSE will not multiply with A and (1-A).

pi_10

Misclassifcation probability is P(Observed Treatment = 1 | Actual Treatment = 0).

pi_01

Misclassifcation probability is P(Observed Treatment = 0 | Actual Treatment = 1).

Value

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.

Examples

##### 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])