# Estimate the mean-optimal treatment regime for data with independently censored response 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. ```r 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 $$ d(x) = I \left(\beta_0 +\beta_1 x_1 + \beta_2 x_2 > 0\right).d(x)=I(\beta_0 +\beta_1 * x1 + \beta_2 * x2 > 0). $$ 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`). ## Returns 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 if(!exists(".Rdpack.currefs")) .Rdpack.currefs \\<-new.env();Rdpack::insert_citeOnly(keys="horowitz1992smoothed",package="QTOCen",cached_env=.Rdpack.currefs) . * `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 ## Examples ```r 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) ``` ## References Rdpack::insert_ref(key="zhou2018quantile",package="QTOCen") Rdpack::insert_ref(key="horowitz1992smoothed",package="QTOCen")

IPWE_mean_IndCen function