Estimates the covariate-adjusted ROC curve (AROC) using the semiparametric approach proposed by Janes and Pepe (2009).
AROC.sp(formula.healthy, group, tag.healthy, data,
est.surv.h = c("normal", "empirical"), p = seq(0, 1, l = 101), B = 1000)A formula object specifying the location regression model to be fitted in healthy population (see Details).
A character string with the name of the variable that distinguishes healthy from diseased individuals.
The value codifying the healthy individuals in the variable group.
Data frame representing the data and containing all needed variables.
A character string. It indicates how the conditional distribution function of the diagnostic test in healthy population is estimated. Options are "normal" and "empirical" (see Details). The default is "normal".
Set of false positive fractions (FPF) at which to estimate the covariate-adjusted ROC curve.
An integer value specifying the number of bootstrap resamples for the construction of the confidence intervals. By default 1000.
As a result, the function provides a list with the following components:
The matched call.
Set of false positive fractions (FPF) at which the pooled ROC curve has been estimated
Estimated covariate-adjusted ROC curve (AROC), and 95% pointwise confidence intervals (if required)
Estimated area under the covariate-adjusted ROC curve (AAUC), and 95% pointwise confidence intervals (if required).
Object of class lm with the fitted regression model in the healthy population.
The value of the argument est.surv.h used in the call.
Estimates the covariate-adjusted ROC curve (AROC) defined as
$$AROC\left(t\right) = Pr\{1 - F_{\bar{D}}(Y_D | \mathbf{X}_{D}) \leq t\},$$
where \(F_{\bar{D}}(\cdot|\mathbf{X}_{\bar{D}})\) denotes the conditional distribution function for \(Y_{\bar{D}}\) conditional on the vector of covariates \(\mathbf{X}_{\bar{D}}\). In particular, the method implemented in this function estimates the outer probability empirically (see Janes and Pepe, 2008) and \(F_{\bar{D}}(\cdot|\mathbf{X}_{\bar{D}})\) is estimated assuming a semiparametric location regression model for \(Y_{\bar{D}}\), i.e.,
$$Y_{\bar{D}} = \mathbf{X}_{\bar{D}}^{T}\mathbf{\beta}_{\bar{D}} + \sigma_{\bar{D}}\varepsilon_{\bar{D}},$$
such that, for a random sample \(\{(\mathbf{x}_{\bar{D}i})\}_{i=1}^{n_{\bar{D}}}\) from the healthy population, we have
$$F_{\bar{D}}(y | \mathbf{X}_{\bar{D}}=\mathbf{x}_{\bar{D}i}) = F_{\bar{D}}\left(\frac{y-\mathbf{x}_{\bar{D}i}^{T}\mathbf{\beta}_{\bar{D}}}{\sigma_{\bar{D}}}\right),$$
where \(F_{\bar{D}}\) is the distribution function of \(\varepsilon_{\bar{D}}\). In line with the assumptions made about the distribution of \(\varepsilon_{\bar{D}}\), estimators will be referred to as: (a) "normal", where Gaussian error is assumed, i.e., \(F_{\bar{D}}(y) = \Phi(y)\); and, (b) "empirical", where no assumption is made about the distribution (in this case, the distribution function \(F_{\bar{D}}\) is empirically estimated on the basis of standardised residuals).
Janes, H., and Pepe, M.S. (2009). Adjusting for covariate effects on classification accuracy using the covariate-adjusted receiver operating characteristic curve. Biometrika, 96(2), 371 - 382.
AROC.bnp, AROC.bsp, AROC.sp, AROC.kernel, pooledROC.BB or pooledROC.emp.
# 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 {
m3 <- AROC.sp(formula.healthy = l_marker1 ~ age,
group = "status", tag.healthy = 0, data = newpsa,
p = seq(0,1,l=101), B = 500)
summary(m3)
plot(m3)
# }
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