lincom (version 1.2)

wmse: Weighted Manski's maximum score estimator

Description

empirical minimization of averaged false positive rate and false negative rate

Usage

wmse(mk, n1, r=1, w=2, contract=0.8, lbmdis=TRUE)

Value

coef

estimated combination coefficient, with unity l1 norm.

obj

empirical objective function: r * false positive rate + false negative rate.

threshold

estimated threshold.

init_coef

initial combination coefficient from logistic regression, with unity l1 norm.

init_obj

empirical objective function for the initial combination coefficient.

init_threshold

estimated threshold for the initial combination coefficient.

Arguments

mk

biomarker values of cases followed by controls, with each row containing multiple markers from an individual.

n1

size of cases.

r

weight of false positive rate relative to false negative rate.

w

weight for l1 norm of combination coefficient in the objective function (w>1 guarantees sound asymptotic properties).

contract

reduction factor in the sequence of approximation parameters for indicator function.

lbmdis

larger biomarker value is more associated with cases if True, and controls otherwise.

Author

Yijian Huang

References

Huang and Sanda (2022). Linear biomarker combination for constrained classification. The Annals of Statistics 50, 2793--2815

Examples

## simulate 3 biomarkers for 100 cases and 100 controls
mk <- rbind(matrix(rnorm(300),ncol=3),matrix(rnorm(300),ncol=3))
mk[1:100,1] <- mk[1:100,1]/sqrt(2)+1
mk[1:100,2] <- mk[1:100,2]*sqrt(2)+1

## linear combination to empirically minimize averaged false positive rate and
## false negative rate
## Require installation of 'MOSEK' to run
if (FALSE) {
lcom <- wmse(mk, 100)
}