AROC.sp {AROC} | R Documentation |

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)

`formula.healthy` |
A |

`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. |

`est.surv.h` |
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". |

`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 | \mathbf{X}_{D}) ≤q 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{β}_{\bar{D}} + σ_{\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}}≤ft(\frac{y-\mathbf{x}_{\bar{D}i}^{T}\mathbf{β}_{\bar{D}}}{σ_{\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) = Φ(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).

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). |

`fit.h` |
Object of class |

`est.surv.h` |
The value of the argument |

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`

.

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) 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)

[Package *AROC* version 1.0-3 Index]