BACKWARD_EXPOSURE {VARSELECTEXPOSURE}

Performs deviance-based backwards variable selection in logistic regression with an exposure.

Description

Returns the estimated Average Treatment Effect and estimated Relative Treatment Effect calculated by the optimal model chosen via backward selection including an exposure variable.

Usage

BACKWARD_EXPOSURE(Data)

Arguments

Data

Data frame containing outcome variable (Y), exposure variable (E), and candidate covariates.

Value

List containing (1) the estimated Average Treatment Effect, (2) estimated Relative Treatment Effect, (3) summary of the selected model, and (4) the first 6 rows of the data frame containing backward-selected covariates.

References

[1] **will contain our paper later**

Examples

###Generate data with n rows and p covariates, can be any number but we'll choose 750 rows
###and 7 covariates for this example
set.seed(3)

p = 7
n = 750
beta0 = rnorm(1, mean = 0, sd = 1)
betaE = rnorm(1, mean = 0, sd = 1)
beta0_E = rnorm(1, mean = 0, sd = 1)
betaX_E = c()
betaX_Y = c()
Y = rep(NA, n)
E = rep(NA, n)
pi0 = rep(NA, n)
pi1 = rep(NA, n)
data = data.frame(cbind(Y, E, pi0, pi1))
j = round(runif(1, 0, p))
for(i in 1:p){
  betaX_Y[i] = rnorm(1, mean = 0, sd = 0.5)
  betaX_E[i] = rnorm(1, mean = 0, sd = 0.5)
}
zeros = sample(1:p, j, replace =  FALSE)
betaX_Y[zeros] = 0
betaX_E[zeros] = 0
mu = 0
sigma = 1
for(i in 1:p){
  covar = rnorm(n, 0, 1)
  data[,i+4] = covar
  names(data)[i+4] = paste("X", i, sep = "")
}
for(i in 1:n){
  p.event_E = beta0_E + sum(betaX_E*data[i,5:(p+4)])
  pi1_E = exp(p.event_E)/(1+exp(p.event_E))
  data[i,2] = rbinom(1, 1, prob = pi1_E)
}
for(i in 1:n){
  p.event = beta0 + betaE + sum(betaX_Y*data[i,5:(p+4)])
  p.noevent = beta0 + sum(betaX_Y*data[i,5:(p+4)])
  pi0 = exp(p.noevent)/(1+exp(p.noevent))
  pi1 = exp(p.event)/(1+exp(p.event))
  data[i,3] = pi0
  data[i,4] = pi1
  if(data[i,2] == 1){
    data[i,1] = rbinom(1, 1, prob = pi1)
  }else{
    data[i,1] = rbinom(1, 1, prob = pi0)
  }
}
for(i in 1:n){
  p.event_E = beta0_E + sum(betaX_E*data[i,5:(p+4)])
  pi1_E = exp(p.event_E)/(1+exp(p.event_E))
  data[i,2] = rbinom(1, 1, prob = pi1_E)
}

###Raw data includes pi0 and pi1 columns used to fill Y and E, so to test
###the function we'll remove these

testdata = data[,-c(3,4)]

BACKWARD_EXPOSURE(testdata)