IPWE_Qopt_DTR_IndCen function

Function to estimate the two-stage quantile-optimal dynamic treatment regime for censored data: the independent censoring Case

This function inplements the estimator of two-stage quantile-optimal treatment regime with censored outcome by inverse probability of weighting, which is proposed in Chapter 3 of if(!exists(".Rdpack.currefs")) .Rdpack.currefs <-new.env();Rdpack::insert_citeOnly(keys="zhou2018quantile",package="QTOCen",cached_env=.Rdpack.currefs) . We assume the censoring is independent of everything else, including the treatment covariates, and potential outcomes.

Specifically, we do grid search on the sign of the coefficient for the first non-intercept variables in stage 1 and stage 2 and apply genetic algorithm on the remaining coeffients simultaneously. So if stage one has d1 covariates excluding the intercept, stage two has d2, the resulting coefficient has dimension d1+d2+2.

IPWE_Qopt_DTR_IndCen(data, tau, regimeClass.stg1, regimeClass.stg2,
  s_Diff_Time = 1, moPropen1 = "BinaryRandom",
  moPropen2 = "BinaryRandom", sign_beta1.stg1 = NULL,
  sign_beta1.stg2 = NULL, Penalty.level = 0, s.tol = 1e-06,
  it.num = 4, max = TRUE, Domains1 = NULL, Domains2 = NULL,
  cluster = FALSE, p_level = 1, pop.size = 10000)

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.

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

• regimeClass.stg1: a formula specifying the class of treatment regimes for the first stage. For details of the general formulation of a linear treatment regime see regimeClass in IPWE_Qopt_IndCen.

• regimeClass.stg2: a formula specifying the class of treatment regimes for the second stage

• s_Diff_Time: Numeric. The fixed length of time between the first stage treatment and the second stage treatment

• moPropen1: the first stage propensity score model. Default is "BinaryRandom".

• moPropen2: the second stage propensity score model. Default is "BinaryRandom".

• 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.

• Penalty.level: 0: stop if the marginal quantiles cannot be further optimized; 1: continue the search among treatment regimes with with same value for the TR with the smallest intended proportion of treatment.

• 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

• max: logical. TRUE if the goal is maximization of the quantile. FALSE is the goal is minimization of the quantile.

• 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.

• 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).

• 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).

Details

In our setting, if a subject was censored or had experienced the event of interest before s_Diff_Time units of time had elapsed after the first stage of treatment, s/he would not be eligible to receive a second stage treatment.

Examples

D <- simJLSDdata(400, case="a")
fit_2stage <-IPWE_Qopt_DTR_IndCen(data=D, tau= 0.3, regimeClass.stg1 = a0~x0,
                     regimeClass.stg2 = a1~x1,
                     sign_beta1.stg1 = FALSE,
                     sign_beta1.stg2 = FALSE)

References

Rdpack::insert_ref(key="zhou2018quantile",package="QTOCen")

Author(s)

Yu Zhou, zhou0269@umn.edu