AROC.kernel {AROC} | R Documentation |

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)

`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 |

`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. |

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.

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 |

`bw.var` |
An object of class |

`fit.mean` |
An object of class |

`fit.var` |
An object of class |

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`

.

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]