IPWE_mean_IndCen {QTOCen}

Estimate the mean-optimal treatment regime for data with independently censored response

Description

This function estimates the Mean-optimal Treatment Regime with censored response. The implemented function only works for scenarios in which treatment is binary and the censoring time is independent of baseline covariates, treatment group and all potential survival times.

Usage

IPWE_mean_IndCen(data, regimeClass, moPropen = "BinaryRandom",
  Domains = NULL, cluster = FALSE, p_level = 1, s.tol = 1e-04,
  it.num = 8, pop.size = 3000)

Arguments

data

a data.frame, containing variables in the moPropen and RegimeClass and also the response variables, namely censor_y as the censored response, and delta as the censoring indicator.

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.

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.

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. nvars is the total number of parameters.

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).

Value

This function returns an object with 6 objects:

• coefficients the estimated parameter indexing the mean-optimal treatment regime. Since we focus the space of linear treatment regimes, the estimated decision rule cannot be uniquely identified without scale normalized. In this package, we normalized by |\beta_1| = 1, which was proposed in Horowitz (Horowitz 1992).

• hatQ the estimated optimal marginal mean response

• moPropen log of the input argument of moPropen

• regimeClass log of the input argument of regimeClass

• data_aug Training data with additional columns used in the algorithm. Note that data_aug is used for plotting of survival function of the censoring time

• survfitCensorTime the estimated survival function of the censoring time

References

Zhou Y (2018). Quantile-Optimal Treatment Regimes with Censored Data. Ph.D. thesis, University of Minnesota.

Horowitz JL (1992). “A smoothed maximum score estimator for the binary response model.” Econometrica: journal of the Econometric Society, 505–531.

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 <- exp(-0.5+1*(x1+x2))/(1+exp(-0.5 + 1*(x1+x2)))
  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 <- 400

D <- GenerateData(n)
fit1 <- IPWE_mean_IndCen(data = D, regimeClass = a~x1+x2)