comparebcJ {rocbc}

Performs inference to compare the Youden Indices 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 J (Youden indices for Box-Cox based ROC curves). Marker measurements are assumed to be taken on the same individuals for both markers.

Usage

comparebcJ(marker1, marker2, D, 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.

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 maximized Youden Index 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.

J1

The maximized Youden Index of the first marker.

J2

The maximized Youden Index of the second marker.

pvalue_probit_difference

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

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, Nakas CT, Reiser B. (2021). Statistical inference for the difference between two maximized Youden indices obtained from correlated biomarkers. Biometrical Journal, 63(6):1241-1253. https://doi.org/10.1002/bimj.202000128

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 Js of Marker 1 vs Marker 2

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