rocbc (version 3.2.0)

comparebcAUC: Performs inference to compare the AUCs of two correlated (or uncorrelated) Box-Cox transformed biomarkers at a given nominal level

Description

This function provides a comparison of two correlated markers in terms of their AUCs (areas under the Box-Cox based ROC curves). Markers measurements are assumed to be taken on the same individuals for both markers.

Usage

comparebcAUC(marker1, marker2, D, alpha, plots)

Value

resultstable

A summary table of the comparison that contains the AUC of each marker, the p-value of the difference using the probit transformation, the p-value of the difference, and the confidence interval of the difference.

AUCmarker1

The AUC of the first marker.

AUCmarker2

The AUC of the second marker.

pvalue_probit_difference

The p-value for the comparison of the AUCs. It employs the probit transformation that has greater power than when not using it (as in pvalue_difference).

pvalue_difference

The p-value for the comparisons of the AUC (without the probit transformation). Simulations have shown that this is inferior to the ‘pvalue_probit_difference’.

CI_difference

The confidence interval for the difference of the AUCs.

roc1

A function that refers to the ROC of the first marker. It allows the user to feed in FPR values and the corresponding TPR values.

roc2

A function that refers to the ROC of the first marker. It allows the user to feed in FPR values and the corresponding TPR values.

transx1

The Box-Cox transformed scores for the first marker and the healthy group.

transy1

The Box-Cox transformed scores for the first marker and the diseased group.

transformation.parameter.1

The estimated Box-Cox transformation parameter (lambda) for marker 1.

transx2

The Box-Cox transformed scores for the second marker and the healthy group.

transy2

The Box-Cox transformed scores for the second marker and the diseased group.

transformation.parameter.2

The estimated Box-Cox transformation parameter (lambda) for marker 2.

Arguments

marker1

A vector of length n that contains the biomarker scores of all individuals for the first marker.

marker2

A vector of length n that contains the biomarker scores of all individuals for the second marker.

D

A vector of length n that contains the true disease status of an individual. It is a binary vector containing 0 for the healthy/control individuals and 1 for the diseased individuals.

alpha

Nominal level used to calculate the confidence intervals. A common choice is 0.05.

plots

Valid inputs are "on" and "off". When set to "on" it returns the Box-Cox based ROC along with informative information about the two AUCs in the legend of the plot.

Author

Leonidas Bantis

References

Bantis LE, Feng Z. (2016). Comparison of two correlated ROC curves at a given specificity or sensitivity level. Statistics in Medicine, 35(24):4352-4367. https://doi.org/10.1002/sim.7008

Examples

#GENERATE SOME BIVARIATE DATA===

set.seed(123)

nx <- 100
Sx <- matrix(c(1,   0.5,
               0.5,  1),
             nrow = 2, ncol = 2)

mux <- c(X = 10, Y = 12)
X=mvtnorm::rmvnorm(nx, mean = mux, sigma = Sx)

ny <- 100
Sy <- matrix(c(1.1,   0.6,
               0.6,  1.1),
             nrow = 2, ncol = 2)

muy <- c(X = 11, Y = 13.7)
Y=mvtnorm::rmvnorm(ny, mean = muy, sigma = Sy)

dx=pracma::zeros(nx,1)
dy=pracma::ones(ny,1)

markers=rbind(X,Y);
marker1=markers[,1]
marker2=markers[,2]
D=c(rbind(dx,dy))

#===COMPARE THE AUCs of Marker 1 vs Marker 2

out=comparebcAUC(marker1, marker2, D, alpha=0.05,  plots="on")