The classification accuracy of a marker (

*Y*) is most commonly described by the receiver operating characteristic (ROC) curve, a plot of the true positive rate (TPR) versus the false positive rate (FPR) for the set of rules which classify an individual as “test-positive” if

*Y ≥ c*, where the threshold

*c* is varied over all possible values (

Pepe et al., 2001;

Baker, 2003). Equivalently, the ROC curve can be represented as the cumulative distribution function (CDF) of the case marker observations, standardized with respect to the control distribution (

Pepe and Cai, 2004;

Pepe and Longton, 2005). The standardized marker observations, or percentile values, are written as

*pv*_{D} =

*F*(

*Y*_{D}), where

*F* is the right-continuous CDF of

*Y* among controls and

*Y*_{D} denotes a case marker observation. The ROC curve at a FPR of

*f* is

In many settings, covariates should be incorporated into the ROC analysis. First, there are covariates which impact the marker distribution among controls. For example, “center effects” in multi-center studies may affect marker observations. In Section 2, we describe methods for adjusting the ROC curve for such covariates. The associated Stata programs are called
`roccurve` and
`comproc`. Other covariates may affect the inherent discriminatory accuracy of the marker (i.e. the ROC curve). For example, disease severity often impacts marker accuracy, with less severe cases being more difficult to distinguish from controls. In Section 3 we describe an ROC regression method which allows the ROC curve to depend on covariates. The associated Stata program is called
`rocreg`. Finally, there are covariates which contribute to discrimination. For example, baseline risk factors for disease provide some ability to discriminate between cases and controls. A common question is how much discriminatory accuracy the marker adds to the known classifiers (i.e. incremental value). In Section 4 we describe methods for evaluating incremental value.

This paper is a companion to another article in this journal (

Pepe et al., 2007) which describes the use of the programs

`roccurve` and

`comproc` for estimating and comparing ROC curves without incorporating covariate information.