AROC.kernel {AROC}R Documentation

Non parametric kernel-based estimation of the covariate-adjusted ROC curve (AROC).

Description

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.

Usage

AROC.kernel(marker, covariate, group, tag.healthy, data, p = seq(0, 1, l = 101), B = 1000)

Arguments

marker

A character string with the name of the diagnostic test variable.

covariate

A character string with the name of the continuous covariate.

group

A character string with the name of the variable that distinguishes healthy from diseased individuals.

tag.healthy

The value codifying the healthy individuals in the variable group.

data

Data frame representing the data and containing all needed variables.

p

Set of false positive fractions (FPF) at which to estimate the covariate-adjusted ROC curve.

B

An integer value specifying the number of bootstrap resamples for the construction of the confidence intervals. By default 1000.

Details

Estimates the covariate-adjusted ROC curve (AROC) defined as

AROC≤ft(t\right) = Pr\{1 - F_{\bar{D}}(Y_D | X_{D}) ≤q 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}} = μ_{\bar{D}}(X_{\bar{D}}) + σ_{\bar{D}}(X_{\bar{D}})\varepsilon_{\bar{D}},

where μ_{\bar{D}} is the regression funcion, σ_{\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}}≤ft(\frac{y_{\bar{D}i}-μ_{\bar{D}}(x_{\bar{D}i})}{σ_{\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.

Value

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

call

The matched call.

p

Set of false positive fractions (FPF) at which the pooled ROC curve has been estimated

ROC

Estimated covariate-adjusted ROC curve (AROC), and 95% pointwise confidence intervals (if required)

AUC

Estimated area under the covariate-adjusted ROC curve (AAUC), and 95% pointwise confidence intervals (if required).

bw.mean

An object of class npregbw with the selected bandwidth for the nonparametric regression function. For further details, see R-package np.

bw.var

An object of class npregbw with the selected bandwidth for the nonparametric variance function. For further details, see R-package np.

fit.mean

An object of class npreg with the nonparametric regression function estimate. For further details, see R-package np.

fit.var

An object of class npreg with the nonparametric variance function estimate. For further details, see R-package np.

References

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.

See Also

AROC.bnp, AROC.bsp, AROC.sp, AROC.kernel, pooledROC.BB or pooledROC.emp.

Examples

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)

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)



[Package AROC version 1.0-3 Index]