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

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 p_1G 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.

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.

MPL

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)