Description Usage Arguments Details Value Author(s) References See Also Examples

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

1 | ```
maximin(B, c0)
``` |

`B` |
An |

`c0` |
The common marginal treatment effect shared by all subgroups. It can be computed by |

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.

A vector of maximin effects.

Chengchun Shi

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.

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)
``` |

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