Gene_Quantile_CenIPWE {QTOCen}

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

Description

This function supports several user facing functions for Quantile-optimal treatment regime estimation, namely

IPWE_Qopt_IndCen(), IPWE_Qopt_DTR_IndCen(), IPWE_Qopt_DepCen_trt(), and IPWE_Qopt_DepCen_general().

It implements the genetic algorithm based policy-search method with inverse probability weighting for censored data, such that the estimator is cube root consistent under the assumption that the propensity score model and the model for the survival distriution of the censoring time variable are both correct.

Usage

Gene_Quantile_CenIPWE(data_aug, tau, p_level, regimeClass,
  cluster = FALSE, s.tol = 1e-04, it.num = 8, pop.size = 5000,
  Domains = NULL, sign_beta1 = NULL, Penalty.level = 0)

Arguments

data_aug

a data.frame of the observed data after preprocessing. It should include be augmented with a new column: epsi for the composite weights.

tau

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

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).

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.

cluster

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

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).

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.

sign_beta1

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

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)

# 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)
data_aug$epsi <- (data_aug$ph * data_aug$a + (1 - data_aug$ph) * (1 - data_aug$a)) * data_aug$ghat

# estimate the median-optimal treatment regime

quantopt_fit <- Gene_Quantile_CenIPWE(data_aug=data_aug,tau=0.5,
                                      p_level=1, regimeClass=a~x1+x2^2, 
                                      sign_beta1=FALSE)