AROC (version 1.0-4)

compute.threshold.AROC.bsp: AROC-based threshold values.

Description

Estimates AROC-based threshold values using the semiparametric Bayesian normal linear regression model discussed in Inacio de Carvalho and Rodriguez-Alvarez (2018).

Usage

compute.threshold.AROC.bsp(object, newdata, FPF = 0.5)

Arguments

object

An object of class AROC as produced by AROC.bsp.

newdata

Data frame with the covariate values at which threshold values are required.

FPF

Numeric vector with the FPF at which to calculate the AROC-based threshold values. Atomic values are also valid.

Value

As a result, the function provides a list with the following components:

thresholds.est

A matrix with the posterior mean of the AROC-based threshold values. The matrix has as many columns as different covariate vector values, and as many rows as different FPFs.

thresholds.ql

A matrix with the posterior 2.5% quantile of the AROC-based threshold values. The matrix has as many columns as different covariate vector values, and as many rows as different FPFs.

thresholds.qh

A matrix with the posterior 97.5% quantile of the AROC-based threshold values. The matrix has as many columns as different covariate vector values, and as many rows as different FPFs.

Details

Estimation of the covariate-adjusted ROC curve (AROC) using the semiparametric Bayesian normal linear regression model discussed in Inacio de Carvalho and Rodriguez-Alvarez (2018) involves the estimation of the conditional distribution function for the diagnostic test outcome in the healthy population

$$F_{\bar{D}}(y|\mathbf{X}_{\bar{D}}) = Pr\{Y_{\bar{D}} \leq y | \mathbf{X}_{\bar{D}}\}.$$

This function makes use of this estimate in order to calculate AROC-based threshold values. In particular, for a covariate value \(\mathbf{x}\) and a FPF = t, the AROC-based threshold value at the \(s\)-th posterior sample (\(s = 1,\ldots,S\)) is calculated as follows

$$c^{(s)}_{\mathbf{x}} = \hat{F}^{-1(s)}_{\bar{D}}(1-t|\mathbf{X}_{\bar{D}} = \mathbf{x}).$$

from which the posterior mean can be computed

$$\hat{c}_{\mathbf{x}} = \frac{1}{S}\sum_{s = 1}^{S}c^{(s)}_{\mathbf{x}}.$$

References

Inacio de Carvalho, V., and Rodriguez-Alvarez, M. X. (2018). Bayesian nonparametric inference for the covariate-adjusted ROC curve. arXiv preprint arXiv:1806.00473.

See Also

AROC.bsp

Examples

# NOT RUN {
library(AROC)
data(psa)
# Select the last measurement
newpsa <- psa[!duplicated(psa$id, fromLast = TRUE),]

# Log-transform the biomarker
newpsa$l_marker1 <- log(newpsa$marker1)
# }
# NOT RUN {
m1 <- AROC.bsp(formula.healthy = l_marker1 ~ age,
group = "status", tag.healthy = 0, data = newpsa, scale = TRUE,
p = seq(0,1,l=101), compute.lpml = TRUE, compute.WAIC = TRUE,
a = 2, b = 0.5, nsim = 5000, nburn = 1500)

# Compute the threshold values
FPF = c(0.1, 0.3)
newdata <- data.frame(age = seq(52, 80, l = 50))

th_bsp <- compute.threshold.AROC.bsp(m1, newdata, FPF)
names(th_bsp)
# }