Estimates the covariate-adjusted ROC curve (AROC) using the nonparametric kernel-based method proposed by Rodriguez-Alvarez et al. (2011). The method, as it stands now, can only deal with one continuous covariate.
AROC.kernel(marker, covariate, group, tag.healthy, data, p = seq(0, 1, l = 101), B = 1000)A character string with the name of the diagnostic test variable.
A character string with the name of the continuous covariate.
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.
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).
An object of class npregbw with the selected bandwidth for the nonparametric regression function. For further details, see R-package np.
An object of class npregbw with the selected bandwidth for the nonparametric variance function. For further details, see R-package np.
An object of class npreg with the nonparametric regression function estimate. For further details, see R-package np.
An object of class npreg with the nonparametric variance function estimate. For further details, see R-package np.
Estimates the covariate-adjusted ROC curve (AROC) defined as
$$AROC\left(t\right) = Pr\{1 - F_{\bar{D}}(Y_D | X_{D}) \leq t\},$$
where \(F_{\bar{D}}(\cdot|X_{D})\) denotes the conditional distribution function for \(Y_{\bar{D}}\) conditional on the vector of covariates \(X_{\bar{D}}\). In particular, the method implemented in this function estimates the outer probability empirically (see Janes and Pepe, 2008) and \(F_{\bar{D}}(\cdot|X_{\bar{D}})\) is estimated assuming a nonparametric location-scale regression model for \(Y_{\bar{D}}\), i.e.,
$$Y_{\bar{D}} = \mu_{\bar{D}}(X_{\bar{D}}) + \sigma_{\bar{D}}(X_{\bar{D}})\varepsilon_{\bar{D}},$$
where \(\mu_{\bar{D}}\) is the regression funcion, \(\sigma_{\bar{D}}\) is the variance function, and \(\varepsilon_{\bar{D}}\) has zero mean, variance one, and distribution function \(F_{\bar{D}}\). As a consequence, and for a random sample \(\{(x_{\bar{D}i},y_{\bar{D}i})\}_{i=1}^{n_{\bar{D}}}\)
$$F_{\bar{D}}(y_{\bar{D}i} | X_{\bar{D}}= x_{\bar{D}i}) = F_{\bar{D}}\left(\frac{y_{\bar{D}i}-\mu_{\bar{D}}(x_{\bar{D}i})}{\sigma_{\bar{D}}(x_{\bar{D}i})}\right).$$
Both the regression and variance functions are estimated using the Nadaraya-Watson estimator, and the bandwidth are selected using least-squares cross-validation. Implementation relies on the R-package np. No assumption is made about the distribution of \(\varepsilon_{\bar{D}}\), which is empirically estimated on the basis of standardised residuals.
Hayfield, T., and Racine, J. S.(2008). Nonparametric Econometrics: The np Package. Journal of Statistical Software 27(5). URL http://www.jstatsoft.org/v27/i05/.
Inacio de Carvalho, V., and Rodriguez-Alvarez, M. X. (2018). Bayesian nonparametric inference for the covariate-adjusted ROC curve. arXiv preprint arXiv:1806.00473.
Rodriguez-Alvarez, M. X., Roca-Pardinas, J., and Cadarso-Suarez, C. (2011). ROC curve and covariates: extending induced methodology to the non-parametric framework. Statistics and Computing, 21(4), 483 - 499.
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 {
m2 <- AROC.kernel(marker = "l_marker1", covariate = "age",
group = "status", tag.healthy = 0, data = newpsa,
p = seq(0,1,l=101), B = 500)
summary(m2)
plot(m2)
# }
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