Version: 1.2
Date: 2024-06-30
Title: Linear Biomarker Combination: Empirical Performance Optimization
Author: Yijian Huang <yhuang5@emory.edu>
Maintainer: Yijian Huang <yhuang5@emory.edu>
Depends: R (≥ 3.6.0)
Imports: SparseM, Rmosek, methods, stats
SystemRequirements: MOSEK (>= 6), MOSEK License (>= 6)
Suggests: knitr, rmarkdown
VignetteBuilder: knitr
Description: Perform two linear combination methods for biomarkers: (1) Empirical performance optimization for specificity (or sensitivity) at a controlled sensitivity (or specificity) level of Huang and Sanda (2022) <doi:10.1214/22-aos2210>, and (2) weighted maximum score estimator with empirical minimization of averaged false positive rate and false negative rate. Both adopt the algorithms of Huang and Sanda (2022) <doi:10.1214/22-aos2210>. 'MOSEK' solver is used and needs to be installed; an academic license for 'MOSEK' is free.
License: GPL-2 | GPL-3 [expanded from: GPL (≥ 2)]
NeedsCompilation: yes
Packaged: 2024-06-30 23:09:40 UTC; eugene
Repository: CRAN
Date/Publication: 2024-06-30 23:30:02 UTC

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)

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.

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.

Author(s)

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
## Not run: 
lcom <- eum(mk, 100, 0.95, grdpt=0)

## End(Not run)

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)

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.

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.

Author(s)

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
## Not run: 
lcom <- wmse(mk, 100)

## End(Not run)