# A low-level function for the generic optimization step in estimating dynamic Quanilte-optimal treatment regime for censored data This function supports wrapper functions for two stage Quantile-optimal treatment regime estimation, namely `IPWE_Qopt_DTR_IndCen`. ```r Gene_Quantile_CenIPWE_DTR(data, max, tau, regimeClass.stg1, regimeClass.stg2, s_Diff_Time, txVec1, txVec2, nvars.stg1, nvars.stg2, p.data1, p.data2, sign_beta1.stg1, sign_beta1.stg2, p_level, cluster, s.tol, it.num, pop.size, Domains1 = NULL, Domains2 = NULL, Penalty.level = 0) ``` ## Arguments - `data`: raw data.frame - `max`: Maximization (TRUE) or Minimizing (FALSE). Determines if genoud minimizes or maximizes the objective function. - `tau`: a quantile level of interest - `regimeClass.stg1`: the class of treatment regimes for stage one - `regimeClass.stg2`: the class of treatment regimes for stage two - `s_Diff_Time`: the length of time between the first stage treatment and the second stage treatment - `txVec1`: the vector of treatment received at the first stage - `txVec2`: the vector of treatment received at the second stage, it expects entries to be `NA` for patients who did not receive the second treatment - `nvars.stg1`: number of coeffients for the decision rule of the first stage - `nvars.stg2`: number of coeffients for the decision rule of the second stage - `p.data1`: the design matrix to be used for decision in stage one - `p.data2`: the design matrix to be used for decision in stage two - `sign_beta1.stg1`: Is sign of the coefficient for the first non-intercept variable for the first stage known? Default is NULL, meaning user does not have contraint on the sign; FALSE if the coefficient for the first continuous variable is fixed to be `-1`; TRUE if `1`. We can make the search space discrete because we employ $|\beta_1| = 1$ scale normalizaion. - `sign_beta1.stg2`: Default is NULL. Similar to `sign_beta1.stg1`. - `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). - `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`). - `Domains1`: This is optional. If not NULL, please provide the two-column matrix for the searching range of coeffients in stage one. The coefficient taking value of positive/negative one should not be included. - `Domains2`: This is optional. If not NULL, please provide the two-column matrix for the searching range of coeffients in stage two. The coefficient taking value of positive/negative one should not be included. - `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 ```r library(survival) # Simulate data n=200 s_Diff_Time = 1 D <- simJLSDdata(n, case="a") # give regime classes regimeClass.stg1 <- as.formula(a0~x0) regimeClass.stg2 <- as.formula(a1~x1) # extract columns that matches each stage's treatment regime formula p.data1 <- model.matrix(regimeClass.stg1, D) # p.data2 would only contain observations with non-null value. p.data2 <- model.matrix(regimeClass.stg2, D) txVec1 <- D[, "a0"] txVec2 <- D[, "a1"] # Eligibility flag ELG <- (D$censor_y > s_Diff_Time) # Build weights D$deltaC <- 1 - D$delta survfit_all <- survfit(Surv(censor_y, event = deltaC)~1, data=D) survest <- stepfun(survfit_all$time, c(1, survfit_all$surv)) D$ghat <- survest(D$censor_y) g_s_Diff_Time <- survest(s_Diff_Time) D$w_di_vec <- rep(-999, n) for(i in 1:n){ if (!ELG[i]) { D$w_di_vec[i] <- 0.5 * D$ghat[i]} else { D$w_di_vec[i] <- 0.5* D$ghat[i] * 0.5 } } fit1 <- Gene_Quantile_CenIPWE_DTR(data=D, max=TRUE, tau=0.3, regimeClass.stg1 = regimeClass.stg1, regimeClass.stg2 = regimeClass.stg2, s_Diff_Time = s_Diff_Time, txVec1 = txVec1, txVec2 = txVec2, nvars.stg1=2, nvars.stg2=2, p.data1=p.data1, p.data2=p.data2, sign_beta1.stg1=FALSE, sign_beta1.stg2=NULL, p_level=1, cluster=FALSE, s.tol=1e-6, it.num=5, pop.size=6000, Domains1 = NULL, Domains2 = NULL, Penalty.level = 0 ) ```

Gene_Quantile_CenIPWE_DTR function