lincom (version 1.2)

eum: Empirical performance optimization for specificity (or sensitivity) at a controlled sensitivity (or specificity) level

Description

Linear combination of multiple biomarkers

Usage

eum(mk, n1, s0, w=2, grdpt=10, contract=0.8, fixsens=TRUE, lbmdis=TRUE)

Value

coef

estimated combination coefficient, with unity l1 norm.

hs

empirical estimate of specificity at controlled sensitivity, or vice versa.

threshold

estimated threshold.

init_coef

initial combination coefficient, with unity l1 norm.

init_hs

initial specificity at controlled sensitivity, or vice versa.

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.

s0

controlled level of sensitivity or specificity.

w

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

grdpt

number of grid points in coarse grid search for initial value; if grdpt=0, use logistic regression instead.

contract

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

fixsens

fixing sensitivity if True, and specificity otherwise.

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 maximize specificity at controlled 0.95
## sensitivity
## Require installation of 'MOSEK' to run
if (FALSE) {
lcom <- eum(mk, 100, 0.95, grdpt=0)
}