IPWE_Qopt_DepCen_trt {QTOCen}

Estimate the Quantile-opt Treatment Regime under the assumption that the censoring time's distribution only depends on treatment level

Description

Here we assume the censoring variable is independent of covariates and potential outcomes given the treatment assignment. For example, if evidence shows that patients at certain treatment level are prone to experience censoring earlier.

Usage

IPWE_Qopt_DepCen_trt(data, regimeClass, tau, moPropen = "BinaryRandom",
  cluster = FALSE, p_level = 1, s.tol = 1e-04, it.num = 8,
  pop.size = 6000)

Arguments

data

raw data.frame

regimeClass

a formula specifying the class of treatment regimes to search, e.g. if regimeClass = a~x1+x2, and then this function will search the class of treatment regimes of the form

d(x) = I \left(\beta_0 +\beta_1 x_1 + \beta_2 x_2 > 0\right).

Polynomial arguments are also supported.

tau

the quantile of interest

moPropen

The propensity score model for the probability of receiving treatment level 1. When moPropen equals the string "BinaryRandom", the proportion of observations receiving treatment level 1 in the sample will be plugged in as an estimate of the propensity. Otherwise, this argument should be a formula/string, based on which this function will fit a logistic regression on the treatment level. e.g. a1~x1.

cluster

default is FALSE, meaning do not use parallel computing for the genetic algorithm(GA).

p_level

choose between 0,1,2,3 to indicate different levels of output from the genetic function. Specifically, 0 (minimal printing), 1 (normal), 2 (detailed), and 3 (debug).

s.tol

tolerance level for the GA algorithm. This is input for parameter solution.tolerance in function rgenoud::genoud.

it.num

the maximum GA iteration number

pop.size

an integer with the default set to be 3000. This is roughly the number individuals for the first generation in the genetic algorithm (rgenoud::genoud).

Details

data is a dataframe that contains: a(observed treatment assignment), censor_y, and delta

Examples

GenerateData_DepCen_trt <- 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 <- exp(-0.5+1*(x1+x2))/(1+exp(-0.5 + 1*(x1+x2)))
  a <- rbinom(n = n, size = 1, prob=ph)
  c <- 1 + 1*a + runif(n = n, min=0, max=2)
   # distribution of `c' depends on treatment level `a'
  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 <- 400
data <- GenerateData_DepCen_trt(n)
fit1 <- IPWE_Qopt_DepCen_trt(data = data, regimeClass = a~x1+x2, moPropen = a~x1+x2,
                                 tau = 0.2)