est_quant_ipwe {QTOCen}

Estimate the marginal quantile response of a linear static treatment regime

Description

Assume we have binary treatment options for each subject in the target population. This function evaluates a given treatment regime by the estimated marginal mean response. We assume the space of treatment regimes are linear decision functions indexed by parametric coefficients.

This R function is an empirical value function in the literature of optimal treatment regime estimation. Since the goal here is to maximize population's marginal quantile, this function, which estimates the perforamce of a set of parameters in terms of marginal quantile, is the objective function in a nonparametric policy-search method.

The user facing application which utilizes this function is IPWE_Qopt_IndCen.

Usage

est_quant_ipwe(beta, sign_beta1, x, censor_y, delta, epsi, a, tau,
  check_complete = TRUE, Penalty.level = 0)

Arguments

beta

Numerical vector. Exclude the coefficient for the first nontrivial covariate. So if there are k covariates, the length of beta should equal k+1-1=k because the intercept needs one coefficient as well.

sign_beta1

logical. FALSE if the coefficient for the first continuous variable is fixed to be negative one; TRUE if positive one.

x

Numeric Matrix. The baseline covariates from all observed data.

censor_y

Numeric vector. The censored survival times from all observed data, i.e. censor_y = min(Y, C)

delta

Numeric vector. The censoring indicators from all observed data. We use 1 for uncensored, 0 for censored.

epsi

the product of (1) the probability of being assigned the observed treatment level through the original treatment assignment mechanism and (2) the conditional survival probability of the censoring variable at censor_y.

a

Numeric vector. The vector of observed treatment level for all observed data. Treatment levels should be coded as 0/1.

tau

a value between 0 and 1. This is the quantile of interest.

check_complete

logical. Since this value estimation method is purely nonparametric, we need at least one unit in collected data such that the observed treatment assignment is the same what the regime parameter suggests. If check_complete is TRUE. It will check if any observation satisfies this criterion. When none observation satisfies, a message is printed to console to raise users awareness that the input regime parameter beta does not agree with any observed treatment level assignment. Then a sufficiently small number is returned from this function, to keep the genetic algorithm running smoothly.

Penalty.level

the level that determines which objective function to use. Penalty.level = 0 indicates no regularization; Penalty.level = 1 indicates the value function estimation minus the means absolute average coefficient is the output, which is useful trick to achieve uniqueness of estimated optimal TR when resolution of input response is low.

Examples

GenerateData <- function(n)
{
  x1 <- runif(n, min=-0.5,max=0.5)
  x2 <- runif(n, min=-0.5,max=0.5)
  error <- rnorm(n, sd= 1)
  ph <- rep(0.5,n)
  a <- rbinom(n = n, size = 1, prob=ph)
  c <- 1.5 +  + runif(n = n, min=0, max=2)
  cmplt_y <-  pmin(2+x1+x2 +  a*(1 - x1 - x2) +  (0.2 + a*(1+x1+x2)) * error, 4.4)
  censor_y <- pmin(cmplt_y, c)
  delta <- as.numeric(c > cmplt_y)
  return(data.frame(x1=x1,x2=x2,a=a, censor_y = censor_y, delta=delta))
}
n <- 100
data <- GenerateData(n)

# here the value for argument epsi uses 0.5 vector for brevity in notation.
quant_hat <- est_quant_ipwe(beta=c(-1,2), sign_beta1=TRUE, x=cbind(1, data$x1, data$x2), 
                            censor_y = data$censor_y, delta = data$delta, tau=0.5,
                            epsi = rep(0.5,n), a = data$a)