IPWE_Qopt_DTR_IndCen {QTOCen}

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

Description

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 (Zhou 2018). 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.

Usage

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.

Author(s)

Yu Zhou, [e-mail]

References

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

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)