Description Usage Arguments Details Author(s) References Examples

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 \insertCitezhou2018quantileQTOCen. 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.

1 2 3 4 5 6 | ```
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)
``` |

`data` |
a data.frame, containing variables in the |

`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.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 |

`sign_beta1.stg2` |
Default is NULL. Similar to |

`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 |

`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 ( |

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.

Yu Zhou, zhou0269@umn.edu

zhou2018quantileQTOCen

1 2 3 4 5 | ```
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)
``` |

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