Assessing the incremental value of diagnostic and prognostic markers: a review and illustration

Abstract

Background: New markers may improve prediction of diagnostic and prognostic outcomes. We review various measures to quantify the incremental value of markers over standard, readily available characteristics.

Methods: Widely used traditional measures include the improvement in model fit or in the area under the receiver operating characteristic (ROC) curve (AUC). New measures include the net reclassification index (NRI) and decision-analytic measures, such as the fraction of true-positive classifications penalized for false-positive classifications [net benefit (NB)]. For illustration, we discuss a case study on the presence of residual tumour vs. benign tissue in 544 patients with testicular cancer. We assessed three tumour markers [Alpha-fetoprotein (AFP), Human chorionic gonadotropin (HCG) and Lactate dehydrogenase (LDH)] for their incremental value over currently standard clinical predictors.

Results: AUC and R(2) values suggested adding continuous LDH and AFP whereas NB only favoured HCG as a potentially promising marker at a clinically defendable decision threshold of 20% risk. The NRI suggested reclassification potential of all three markers.

Conclusions: The improvement in standard discrimination measures, which focus on finding variables that might be promising across all decision thresholds, may not detect the most informative markers at a specific threshold of particular clinical relevance. When a marker is intended to support decision-making, calculation of the improvement in a decision-analytic measure, such as NB, is preferable over an overall judgment as obtained from the AUC in ROC analysis.

Fig 1

Relationship of LDH to presence of residual tumor at resection in testicular cancer patients. A restricted cubic spline function was used with 5 knots (shown with 95% confidence intervals), a dichotomized version (LDH elevated vs normal), and a logarithmic transformation. Note that the x-axis is log transformed such that a straight line is shown for log(LDH). The distribution of LDH values is indicated by spikes at the bottom of the graph.

Fig 2

Receiver operating characteristic (ROC) curves for adjustment with postchemotherapy size (A) or postchemotherapy size, reduction in size, and primary histology (B).

Fig 3

Decision curves showing the Net Benefit (NB) in comparison to a logistic regression model with postchemotherapy size (A) or postchemotherapy size, reduction in size, and primary histology (B).