AROC.sp {AROC} | R Documentation |

## Semiparametric frequentist inference of the covariate-adjusted ROC curve (AROC).

### Description

Estimates the covariate-adjusted ROC curve (AROC) using the semiparametric approach proposed by Janes and Pepe (2009).

### Usage

```
AROC.sp(formula.healthy, group, tag.healthy, data,
est.surv.h = c("normal", "empirical"), p = seq(0, 1, l = 101), B = 1000)
```

### Arguments

`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. |

### Details

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).

### 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). |

`fit.h` |
Object of class |

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

### References

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.

### 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)
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)
```

*AROC*version 1.0-4 Index]