comparebcSpec {rocbc}

Performs inference to compare the specificities of two correlated (or uncorrelated) Box-Cox transformed biomarkers at a given sensitivity and a given nominal level

Description

This function provides a comparison of two correlated markers in terms of their specificity at a given sensitivity (for Box-Cox based ROC curves). Marker measurements are assumed to be taken on the same individuals for both markers.

Usage

comparebcSpec(marker1, marker2, D, atSens, alpha, plots)

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, where 0 denotes a healthy/control individual, and 1 denotes a diseased individual.

alpha

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

atSens

The value of sensitivity at which the comparison of specificities will take place.

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.

Value

resultstable

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

Spec1

The specificity at the selected sensitivity for the first marker.

Spec2

The specificity at the selected sensitivity for the second marker.

pvalue_probit_difference

The p-value for the comparison of the specificities. 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 specificities (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 specificities.

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.

Author(s)

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 Specificities of Marker 1 vs Marker 2

out=comparebcSpec(marker1=marker1, marker2=marker2, D=D, alpha =0.05, atSens=0.8, plots="on")
summary(out)