obj_value {DTRKernSmooth}

Estimate the average response value of the input data given a treatment regime

Description

This function estimates the average response value of the input data given a 'DTR.KernSmooth' / 'DTR.Boots.KernSmooth' model object or an estimated optimal treatment regime vector, with doubly robust correction

Usage

obj_value(
  X,
  y,
  a,
  object,
  beta,
  prob = 0.5,
  m0 = mean(y[a == 0]),
  m1 = mean(y[a == 1])
)

Arguments

X

Input matrix, of dimension n_obs x n_vars; each row is an observation vector.

y

Response variable to be maximized on average if every subject follows the treatment recommended by the optimal regime.

a

Received treatments for n_obs subjects. Must be bivariate, and labeled as {0,1}.

object

Fitted "DTR.KernSmooth" or "DTR.Boots.KernSmooth" model object.

beta

The treatment regime vector. Cannot be missing if "object" is not provided.

prob

The propensity score for n_obs subjects, i.e., P(a=1|X). If NULL, it would be estimated by logistic regression a~X.

m0

The estimated response values if the subjects receive treatment 0. The default is the average response value of all subjects who receive treatment 0.

m1

The estimated response values if the subjects receive treatment 1. The default is the average response value of all subjects who receive treatment 1.

Details

object and beta cannot be both missing. If the input data (X, y, a) is missing but object is provided, the function will return the optimal value of the input object.

Value

The estimated average response value if all n_obs subjects follows the treatment recommendations according to the fitted model or the estimated treatment regime.

Author(s)

Yunan Wu and Lan Wang
Maintainer: Yunan Wu <[e-mail]>

References

Wu, Y. and Wang, L. (2021), Resampling-based Confidence Intervals for Model-free Robust Inference on Optimal Treatment Regimes, Biometrics, 77: 465– 476, doi:10.1111/biom.13337.

See Also

DTR.KernSmooth, DTR.Boots.KernSmooth

Examples

n <- 500; p <- 3
beta <- c(0.2,1,-0.5,-0.8)*0.7
beta1 <- c(1,-0.5,-0.5,0.5)

set.seed(12345)
X <- matrix(rnorm(n*p),n)
a <- rbinom(n,1,0.7)
mean1 <- exp(cbind(1,X) %*% beta1)
mean2 <- 8/(1 + exp(-cbind(1,X) %*% beta)) - 4
y <- mean1 + a * mean2 + rnorm(n)

smooth_model <- DTR.KernSmooth(X, y, a, prob = 0.3 + 0.4*a)
boots_smooth_model <- DTR.Boots.KernSmooth(X, y, a, prob = 0.3 + 0.4*a, B = 100)

newn <- 1e4
newX <- matrix(rnorm(newn*p),newn)
newa <- rbinom(newn,1,0.5)
newmean1 <- exp(cbind(1,newX) %*% beta1)
newmean2 <- 8/(1 + exp(-cbind(1,newX) %*% beta)) - 4
newy <- newmean1 + newa * newmean2 + rnorm(newn)

obj_value(newX, newy, newa, smooth_model)
obj_value(newX, newy, newa, boots_smooth_model)
obj_value(newX, newy, newa, beta = smooth_model$beta_smooth)