# find.I2DR: Estimating the Individualized Interval-valued Dose Rule via... In JQL: Jump Q-Learning for Individualized Interval-Valued Dose Rule

## Description

This function estimates the optimal Individualized Interval-valued Dose Rule (I2DR), and calculates a Wald-type confidence interval for the value function under the estimated optimal I2DR via Bootstrap.

## Usage

 ```1 2 3 4``` ``` find.I2DR(Y,A,X,cm=6,method='JQL',Gamma.list=seq(from=1,to=20,by=2)/5, Lambda.list=seq(from=1,to=20,by=2)/5,RF_A.list=c(0,0.25,0.5,0.75,1), folds_num=5,alpha=0.95,nboots=500) ```

## Arguments

 `Y` The patient’s associated response/outcome, the larger the better by convention. `A` The dose level received by each patient, should be continuous. `X` The patient’s baseline covariates, could be a matrix, including continous or discrete covariates. `cm` The constent cm in m=n/cm, where m is the number of total subinterval that diverges with sample size n. The default value is 6. `method` Two methods are available, Jump Q-learning ('JQL') and Residual Jump Q-learning ('RJQL'). The default method is 'JQL'. `Gamma.list` The candidate tuning paramter space for c1 in penalty term gamma=c1 log(n)/n. The default value is seq(from=1,to=20,by=2)/5. If the length of Gamma.list is 1, then the tuning process will be skipped. `Lambda.list` The candidate tuning paramter space for c2 in penalty term lambda=c2 log(n)/n. The default value is seq(from=1,to=20,by=2)/5. If the length of Lambda.list is 1, then the tuning process will be skipped. `RF_A.list` The candidate tuning paramter space for A in fitted E(Y|A=a,X) by Random Forest Regression for method 'RJQL' only. The default value is c(0,0.25,0.5,0.75,1). If the length of RF_A.list is 1, then the tuning process will be skipped. `folds_num` The number of the folds in the cross-validation process. The default value is 5. `alpha` The Confidence level. The default level is 0.95. `nboots` The number of Bootstrap. The default number is 500.

## Value

An object of class "I2DR" which is a list with components:

 `Partition` A partition of the entire dose range. `Beta` The regression coefficients for each partition. `Value` The estimated value function under our proposed I2DR. `low_bd` The lower bound of the confidence interval. `up_bd` The upper bound of the confidence interval. `method` The method used to find the I2DR.

## References

Jump Q-learning for Individualized Interval-valued Dose Rule.

## Examples

 ```1 2 3 4 5 6``` ```n=50 d=4 x=matrix(runif(n*(d-1),-1,1),nrow=n,ncol=d-1) a=runif(n,0,1) y=(1+x[,1])*(a>=0&a<0.35)+(x[,1]-x[,2])*(a>=0.35&a<0.65)+(1-x[,2])*(a>=0.65&a<=1)+rnorm(n,0,1) find.I2DR(Y=y,A=a,X=x) ```

JQL documentation built on Nov. 16, 2019, 1:07 a.m.