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Partial area under ROC curve

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Introduction

The partial area under the ROC curve summarizes a portion of the ROC curve over a pre-specified interval of interest. This interval can be a specificity or sensitivity interval.

The partial area under the ROC curve for a pre-specified specifity interval

Partial area under the ROC curve for a pre-specified specififity interval

The partial area pAUC for a pre-specified specifity interval is given by the area ABCD. The partial area corresponding to a random model is the area ABgh. The partial area corresponding to a perfect model is the area ABef.

The random model area ABgh is the minimum pAUC ($pAUC_{min}$), and the perfect model area ABef is the maximum pAUC ($pAUC_{max}$).

The partial area pAUC can be interpreted as the average sensitivity in the pre-specified specificity interval (Zhou et al., 2002).

The partial area under the ROC curve for a pre-specified sensitivity interval

Partial area under the ROC curve for a pre-specified sensitivity interval

For calculating the partial area under the ROC curve for a pre-specified sensitivity interval, MedCalc takes the right border (Specificity = 0%; or False Positive Rate FPR = 1 ) as the baseline. The pAUC calculated this way is sometimes called the horizontal partial area under the curve pAUCx (Walter, 2005).

Therefore, analogous to the definitions for the pAUC for a specificity interval, the partial area pAUC for a pre-specified sensitivity interval is given by the area ABCD. The partial area corresponding to a random model is the area ABgh. The partial area corresponding to a perfect model is the area ABef.

Again, the random model area ABgh is the minimum pAUC ($pAUC_{min}$), and the perfect model area ABef is the maximum pAUC ($pAUC_{max}$).

The partial area pAUC can be interpreted as the average specificity in the pre-specified sensitivity interval (Zhou et al., 2002).

Methodology

MedCalc calculates the pAUC non-parametrically using the trapezoidal method.

Confidence intervals are calculated using bootstrapping (Efron, 1987; Efron & Tibshirani, 1993).

Standardized pAUC

The Standardized pAUC (pAUCs) is defined as (McCLish, 1989):

$$ pAUCs = \frac {1} {2} \left( 1 + \frac {pAUC - pAUC_{min}} { pAUC_{max} - pAUC_{min} } \right) $$

The Standardized pAUC (pAUCs) has a maximum value of 1 and a minimum value 0.5. Therefore it allows to view the partial area on the same scale as the total area under the ROC curve.

Required input

Dialog box for Partial area under ROC curve

Results - Specificity interval

The following report is displayed:

Partial area under ROC curve statistics (specificity interval)

First MedCalc shows the parameters of the analysis.

Next, the following are reported:

Partial area under ROC curve graph (specificity interval)

Results - Sensitivity interval

The results for the partial area under the ROC curve for a pre-specified sensitivity interval are anologous to the results for a specifiity interval.

Partial area under ROC curve statistics (sensitivity interval)

Partial area under ROC curve graph (sensitivity interval)

Literature

See also

External links

Recommended book

Statistical Methods in Diagnostic Medicine
Xiao-Hua Zhou, Nancy A. Obuchowski, Donna K. McClish

Buy from Amazon US - CA - UK - DE - FR - ES - IT

Statistical Methods in Diagnostic Medicine provides a comprehensive approach to the topic, guiding readers through the necessary practices for understanding these studies and generalizing the results to patient populations.

Following a basic introduction to measuring test accuracy and study design, the authors successfully define various measures of diagnostic accuracy, describe strategies for designing diagnostic accuracy studies, and present key statistical methods for estimating and comparing test accuracy.