| Title: | Linear Biomarker Combination: Empirical Performance Optimization |
|---|---|
| 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. |
| Authors: | Yijian Huang <[email protected]> |
| Maintainer: | Yijian Huang <[email protected]> |
| License: | GPL (>= 2) |
| Version: | 1.2 |
| Built: | 2024-11-28 06:39:40 UTC |
| Source: | CRAN |
Linear combination of multiple biomarkers
eum(mk, n1, s0, w=2, grdpt=10, contract=0.8, fixsens=TRUE, lbmdis=TRUE)eum(mk, n1, s0, w=2, grdpt=10, contract=0.8, fixsens=TRUE, lbmdis=TRUE)
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. |
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. |
Yijian Huang
Huang and Sanda (2022). Linear biomarker combination for constrained classification. The Annals of Statistics 50, 2793–2815
## 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)## 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)
empirical minimization of averaged false positive rate and false negative rate
wmse(mk, n1, r=1, w=2, contract=0.8, lbmdis=TRUE)wmse(mk, n1, r=1, w=2, contract=0.8, lbmdis=TRUE)
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. |
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. |
Yijian Huang
Huang and Sanda (2022). Linear biomarker combination for constrained classification. The Annals of Statistics 50, 2793–2815
## 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)## 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)