Assessing the additional value of diagnostic markers: a comparison of traditional and novel measures Ewout W. Steyerberg Professor of Medical Decision Making Dept of Public Health, Erasmus MC, Rotterdam, the Netherlands Birmingham, July 2, 2010

Introduction: additional value of a diagnostic marker  Usefulness / Clinical utility: what do we mean exactly?  Evaluation of predictions  Ordering: concordance statistic (c, or AUC)  Evaluation of decisions  Net Reclassification Index (NRI), very popular  Net Benefit (NB): decision-analytic, not popular  Adding a marker to a model  Statistical significance? Simple LR testing; not an issue  Clinical usefulness: measurement worth the costs?

Overview  Hypotheses:  NRI is closely related to AUC  NRI may be misleading

Addition of a marker to a model  Typically small improvement in discriminative ability according to c statistic  c stat blamed for being insensitive

 Net Reclassification Index:  (move up | event– move down | event) + (move down | non-event – move up | non-event ) = improvement in sensitivity + improvement in specificity

Pencina example

/183=12% 1/3081=0.03%

Enthusiasm

History of NRI 1.Many object to AUC 2.Cook: Reclassification provides insight 3.Pencina: Net reclassification is what counts 4.Many: Enthusiasm 5.Objections, 8 LTTEs Stat Med 2008 a) Relationships to other measures Reply: agree b) Greenland +Vickers/Steyerberg: Need to weight consequences Reply: implicit weighting by prevalence

5a) NRI ‘a better measure’?  NRI requires classification  Simplest case: binary (high vs low risk)  If binary, easy to calculate sensitivity and specificity  NRI = delta sens + delta spec, reminds us of Youden Index  Youden Index = sens + spec – 1  NRI = delta Youden Index

NRI better than AUC?  Binary ROC curve  AUC = (sens+spec) / 2  NRI = delta sens + delta spec  NRI = 2 x delta AUC !  Conclusion: NRI misleading in claiming being ‘better’ than AUC 1. from predictions to classification 2. 2 x delta AUC

5b) Weighting ‘absurd”

Chapter 16 - Google books - Order

Evaluation of decisions  Clinically meaningful cut-off (or threshold) for the probability: p t  p t reflects relative true-positive vs weight false-positive decisions e.g. if p t = 50%, wTP=wFP if p t = 20%, wTP = 4 times wFP  Net Benefit: (TP – w FP) / N, with w = harm / benefit = p t / (1 – p t ) (Pierce 1884, Vickers 2006)  If p t = 50%, w =.5 / (1 –.5) = 1 if p t = 20%, w =.2 / (1 –.2) = 1/4  Net Reclassification Index:  NRI = improvement in sens + improvement in spec  Implicit weighting by non-event odds: (1 – Prevalence) / Prevalence  Hence inconsistent if p t ≠ Prevalence

Overview

Case study  Testicular cancer: prediction of residual tumor after chemotherapy  N=544, 299 tumor (55%)  Reference models  Postchemotherapy mass size  … + reduction in size + primary histology  3 tumor markers  AFP: abnormal vs normal  HCG: abnormal vs normal  LDH: abnormal vs normal and continuous: log(LDH)

Evaluation of predictions  LR and AUC (c) same pattern  Reference model matters; dichotomization harms

Evaluation of decisions at 20% and 55% thresholds  Net Benefit and NRI consistent at 55% (=prevalence) threshold, not 20%

Conclusions 1.Judgment of additional value depends on the measure chosen; the reference model; coding of the marker. 2.A decision-analytic perspective is not compatible with an overall judgment as obtained from the AUC in ROC analysis nor with NRI. 3.The current practice of reporting AUC and NRI as measures of usefulness needs to be replaced by routinely reporting net benefit analyses. 4.Further work: - NRI and NB for 2 decisions, e.g. CVD 5% and 20% thresholds - link to decision analysis / cost-effectiveness analysis

References  Vickers AJ, Elkin EB: Decision curve analysis: a novel method for evaluating prediction models. Med Decis Making 26:565-74, 2006  Steyerberg EW, Vickers AJ: Decision Curve Analysis: A Discussion. Med Decis Making 28; 146, 2008  Steyerberg EW, Vickers AJ, Cook NR, et al. Assessing the performance of prediction models: a framework for some traditional and novel measures. Epidemiology, Jan 2010

From 1 cutoff to consecutive cutoffs  Sensitivity and specificity  ROC curve  Net benefit  decision curve

ROC curves

Decision curves