gROC_param {movieROC}

Build a binormal ROC curve for a univariate marker

Description

This function builds a univariate ROC curve (standard or general) assuming the binormal scenario with parameters being the sample estimates. It returns a ‘groc’ object, a list of class ‘groc’.

Usage

gROC_param(X, D, side = c("right", "left", "both", "both2"), N = NULL, ...)

Arguments

X

Vector of marker values.

D

Vector of response values. Two levels; if more, the two first ones are used.

side

Type of ROC curve. One of "right" (\mathcal{R}_r(\cdot)), "left" (\mathcal{R}_l(\cdot)), "both" (\mathcal{R}_g(\cdot)) or "both2" (\mathcal{R}_{g'}(\cdot)). Default: "right".

N

Number indicating the length of the vector of FPR considered to build the ROC curve: t \in \{ 0, 1/N, 2/N, \dots, 1 \}. Default: 1000.

...

Other parameters to be passed. Not used.

Details

This function's main job is to estimate an ROC curve for a univariate marker under one of these considerations: larger values of the marker are associated with a higher probability of being positive (resulting in the right-sided ROC curve, \mathcal{R}_r (\cdot)), the opposite (left-sided ROC curve, \mathcal{R}_l (\cdot)), when both smaller and larger values of the marker are associated with having more probability of being positive (gROC curve, \mathcal{R}_g(\cdot)), the opposite (opposite gROC curve, \mathcal{R}_{g'}(\cdot)).

Value

A list of class ‘groc’ with the following fields:

controls, cases

Marker values of negative and positive subjects, respectively.

levels

Levels of response values.

side

Type of ROC curve.

t

Vector of false-positive rates.

roc

Vector of values of the ROC curve for t.

c

Vector of marker thresholds resulting in (t, roc) if side = "right" | "left".

xl, xu

Vectors of marker thresholds resulting in (t, roc) if side = "both" | "both2".

auc

Area under the curve estimate.

a, b

Estimates for parameters a and b considered for the ROC curve estimation: \hat{a} = \left[ \overline{\xi_n} - \overline{\chi_m} \right]/\hat{s}_\xi and \hat{b} = \hat{s}_\chi / \hat{s}_\xi.

p0

Estimate of the "central value", \mu^*, about to which the thresholds x^L and x^U are symmetrical.

References

P. Martínez-Camblor and J. C. Pardo-Fernández (2019) “Parametric estimates for the receiver operating characteristic curve generalization for non-monotone relationships”. Statistical Methods in Medical Research, 28(7): 2032–2048. DOI: doi:10.1177/0962280217747009.

Examples

data(HCC)

# ROC curve estimates for gene 03515901 and response tumor assuming the binormal scenario
gROC_param(X = HCC[,"cg03515901"], D = HCC$tumor) # Standard right-sided ROC curve
gROC_param(X = HCC[,"cg03515901"], D = HCC$tumor, side = "left") # Left-sided ROC curve 
gROC_param(X = HCC[,"cg03515901"], D = HCC$tumor, side = "both") # gROC curve