find.I2DR {JQL}

Estimating the Individualized Interval-valued Dose Rule via (Residual) Jump Q-learning.

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

  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

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)