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**|**HHS Author Manuscripts**|**PMC3849723

Stat Med. Author manuscript; available in PMC 2014 February 20.

Published in final edited form as:

Stat Med. 2013 February 20; 32(4): 10.1002/sim.5663.

doi: 10.1002/sim.5663PMCID: PMC3849723

NIHMSID: NIHMS533171

Stuart G. Baker^{*}

Biometry Research Group, National Cancer Institute, Bethesda, MD 20892 USA.

Vickers et al make a valuable contribution to the comparison of two binary diagnostic tests by taking a decision-analytic approach [1]. They introduce relative diagnostic value which yields a threshold probability for selecting the preferred test. Two additional points are worth noting.

First, although the context differs, the equation relating relative diagnostic value to the odds of prevalence and threshold odds of disease is mathematically identical to an equation for finding the optimal slope of a concave Receiver Operating Characteristic (ROC) curve when the two tests correspond to adjacent points on the ROC curve [2, 3]. The relative diagnostic value is derived by setting equal the net benefits of the two tests. The optimal slope of the concave ROC curve is found by setting equal the net benefits of tests corresponding to adjacent points on the ROC curve, which corresponds to maximizing a function by finding where its slope is zero.

Second the asymptotic confidence interval for the threshold probability corresponding to the relative diagnostic value can be computed with a simple formula derived from the Multinomial-Poisson (MP) transformation [4]. The relative diagnostic value is *R*= *n _{0}* (

$$selogR={\{-1\u2215{n}_{0}-1\u2215{n}_{1}+({c}_{0}+{b}_{0})\u2215{({c}_{0}-{b}_{0})}^{2}+({c}_{1}+{b}_{1})\u2215{({c}_{1}-{b}_{1})}^{2}\}}^{{\scriptstyle \frac{1}{2}}}.$$

Let *R _{L}* = exp{log(

1. Vickers AJ, Cronin AM, Göne M. A simple decision analytic solution to the comparison of two binary diagnostic tests. Stat Med. Early view. [PMC free article] [PubMed]

2. Metz CE. Basic principles of ROC analysis. Seminars in Nuclear Medicine. 1978;8:283–298. [PubMed]

3. Baker SG, Cook NR, Vickers A, Kramer BS. Using relative utility curves to evaluate risk prediction. Journal of the Royal Statistical Society Series A. 2009;172:729–748. [PMC free article] [PubMed]

4. Baker SG. The multinomial-Poisson transformation. The Statistician. 1994;43:495–504.

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