In WaverlyWei/debiased.subgroup: Sharp Inference on Selected Subgroup in Observational Studies

Introduction

debiased.subgroup is a package that implements two bootstrap-assisted estimators: bootstrap-assisted desparsified Lasso and R-split. The two methods remove the subgroup selection bias and regularization bias indeced by high-dimensional covariates.

Installation

devtools::install_github("WaverlyWei/debiased.subgroup")

Quick start

First we load the debiased.subgroup package:

library(debiased.subgroup)

We generate high-dimensional data with 2 subgroups of interest. We predefine a set of tuning parameters, denoted as $r$.

  library(MASS)
  library(glmnet)

  p <- 200 # number of confounders

  n <- 100 # sample size

  ngroups <- 2 # number of subgroups/treatments;

  s0 <- 4

  m <- ngroups

  Sigma <- matrix(0,p,p)

  for (i in 1:n){
      for(j in 1:p){
        Sigma[i,j] <- 0.5^(abs(i-j))
      }
    }

    # generate X 
    X <- mvrnorm( n = n, mu = rep(0,p), Sigma = Sigma )

    Z <- matrix(0,n,m)

    for(i in 1:n){
      for(j in 1:m){
        Z[i,j] <- rbinom(1,1,exp(X[i,2*j-1] + X[i,2*j])/(1+exp(X[i,2*j-1] + X[i,2*j])))
      }
    }


    # noise: heter/homo
    noise.y <- 1

    betas <- 1

    #index of the subgroups
    w.index <- seq(1, m, 1) 

    x <- cbind(Z,X)


    ## Model: Y = Z * beta + X * gamma + noise

    # Generate coefficients
    beta <- c(rep(0,m-1),betas) 

    gamma <- c(rep(1, s0), rep(0, p-s0)) 

    beta0 <- c(beta, gamma)

    # Generate noise 
    noise <- mvrnorm( n = 1, mu = rep(0,n), Sigma = diag(n) * noise.y )

    # Generate response Y 
    Y <- 0.5 + x %*% beta0 + noise

    ## parameters in the function
    r <- 1/(3*1:10)

Bootstrap-calibrated Desparsified Lasso

Bootstrap iterations are recommended to be B = 200. Here we use B = 5 for demonstration purpose.

desparse_res <- BSDesparseLasso(y = Y,
                                x = x, 
                                r = r, 
                                G = w.index,
                                B = 5)

Result summary

The tuning parameter is selected through cvDesparse.

desparse_res$LowerBound

desparse_res$UpperBound

betaMax is the bias-reduced maximum beta estimate.

desparse_res$betaMax

betaEst contains the beta estimate for each subgroup.

desparse_res$betaEst

op is the cross-validated optimal tuning.

desparse_res$op

Bootstrap-calibrated R-Split

Bootstrap iterations are recommended to be B = 200, BB = 1000. Here we use B = 5 and BB = 10 as demo. The tuning parameter is selected through cvSplit.

rsplit_res <- BSSplitLasso(y = Y,
                           x = x, 
                           r = r, 
                           G = w.index,
                           B = 5, BB = 10)

Result summary

rsplit_res$LowerBound

rsplit_res$UpperBound

betaMax is the bias-reduced maximum beta estimate.

rsplit_res$betaMax

betaEst contains the beta estimate for each subgroup.

rsplit_res$betaEst

modelSize contains the R-split model size for each bootstrap iteration.

summary(rsplit_res$modelSize)

op is the cross-validated optimal tuning paramter

rsplit_res$op

WaverlyWei/debiased.subgroup documentation built on June 27, 2022, 7:22 p.m.