Gene_Mean_CenIPWE function

A low-level function for the generic optimization step in estimating Mean-optimal treatment regime for censored data

This function supports the IPWE_mean_IndCen function. It does the genetic algorithm based method with inverse probability weighting for censored data. In the future, if more complicated applications/scenarios is sought after for mean optimality, users may create their own wrapper function based on Gene_Mean_CenIPWE.

Gene_Mean_CenIPWE(data_aug, ph, p_level, regimeClass, Domains = NULL,
  cluster = FALSE, s.tol = 1e-04, it.num = 8, pop.size = 3000)

Arguments

• data_aug: a data.frame of the observed data after preprocessing. It should include be augmented with two new columns: ph for the enstimated propensity scores and ghat for the estimated conditional survival probabilities.

• ph: propensity score estimates. For example, if the treatment is denoted by A, then ph should be P(A=1|X)

• p_level: printing level

• regimeClass: a formula indicating the form of treatment regimes

• Domains: default is NULL. Otherwise, the object should be a nvars *2

  matrix used as the space of parameters, which will be supplied to rgenoud::genoud.

• cluster: default is FALSE. This can also be an object of the 'cluster' class returned by one of the makeCluster commands in the parallel package or a vector of machine names so rgenoud::genoud can setup the cluster automatically.

• 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).

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)

# preprocessing
data_aug <- data
data_aug$ph <- rep(mean(data$a), n)
data_aug$deltaC <- 1 - data_aug$delta
library(survival)
survfit_all <- survfit(Surv(censor_y, event = deltaC)~1, data=data_aug)
survest <- stepfun(survfit_all$time, c(1, survfit_all$surv))
data_aug$ghat <- survest(data_aug$censor_y)

# estimate the mean-optimal treatment regime
meanopt_fit <- Gene_Mean_CenIPWE(data=data_aug, ph = data_aug$ph, p_level=1, regimeClass=a~x1*x2)