# maximin: Maixmin projection learning for optimal individualized... In ITRLearn: Statistical Learning for Individualized Treatment Regime

## Description

Derives a meaningful and reliable individualized treatment regime for future patients based on estimated groupwise contrast function.

## Usage

 1 maximin(B, c0) 

## Arguments

 B An p_1*G matrix containing parameters in the groupwise contast function. Here p_1 is the dimension of x.tau and G is the number of subgroups. It does not contain the intercept term. It can be computed by MPL. c0 The common marginal treatment effect shared by all subgroups. It can be computed by MPL. maximin to compute the maximin effects.

## Details

Denoted by β_g the g-th column of B. This function computes

\arg\max_{\|(β^T,c)^T\|=1} \min_{g\in\{1,…,G\}} (β_g^T β+c_0 c).

The above optimaization problem can be efficiently computed based on quadratic programming.

## Value

A vector of maximin effects.

Chengchun Shi

## References

Shi, C., Song, R., Lu, W., and Fu, B. (2018). Maximin Projection Learning for Optimal Treatment Decision with Heterogeneous Individualized Treatment Effects. Journal of the Royal Statistical Society, Series B, 80: 681-702.

MPL

## Examples

  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 set.seed(12345) X <- matrix(rnorm(1600), 800, 2) A <- rbinom(800, 1, 0.5) h <- 1+sin(0.5*pi*X[,1]+0.5*pi*X[,2]) tau <- rep(0, 800) B <- matrix(0, 2, 4) B[,1] <- c(2,0) B[,2] <- 2*c(cos(15*pi/180), sin(15*pi/180)) B[,3] <- 2*c(cos(70*pi/180), sin(70*pi/180)) B[,4] <- c(0,2) for (g in 1:4){ tau[((g-1)*200+1):(g*200)] <- X[((g-1)*200+1):(g*200),]%*%B[,g] } ## mean and scale of the subgroup covariates are allowed to be different X[1:200,1] <- X[1:200,1]+1 X[201:400,2] <- 2*X[201:400,2]-1 X[601:800,] <- X[601:800,]/2 Y <- h+A*tau+0.5*rnorm(800) G <- c(rep(1,200), rep(2,200), rep(3,200), rep(4,200)) result <- MPL(Y~X|A|G) maximin(result$B, result$c0) 

ITRLearn documentation built on May 2, 2019, 11:03 a.m.