American Journal of Epidemiology Advance Access originally published online on August 17, 2006
American Journal of Epidemiology 2006 164(7):708; doi:10.1093/aje/kwj293
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Letter to the Editor |
THE AUTHORS REPLY
Division of Epidemiology, Statistics and Prevention Research, National Institute of Child Health and Human Development, Rockville, MD 20852
(e-mail: schistee{at}mail.nih.gov)
We thank Dr. Zetterberg for his comments (1
) regarding our guidance for using the Youden index, J, in lieu of the closest-to-(0,1) criterion (2). He points out an important additional inconsistency in the literature, where J is calculated using positive and negative predictive values instead of sensitivity, q(t), and specificity, p(t), respectively. Zetterberg argues that using this J based on predictive values is more informative than the traditional J for the purposes of rating diagnostic tests, as predictive values inherently include disease prevalence. We disagree with Zetterberg that this index is more informative.
The traditional Youden index gives equal weight to sensitivity and specificity. If a researcher thinks that different weights are appropriate (based, perhaps, on the costs of different types of error) or the prevalence of the disease should be included when choosing an optimal cutpoint, a generalized Youden index can be used. The generalized J can be determined using an application of decision theory. The expected loss function in classifying a subject can be written as (1 – 
)p(t) + a(1 – q(t)), where a denotes the relative loss (cost) of a false negative as compared with a false positive and is the proportion of diseased persons in the population of interest (prevalence) (3). It is easy to see that minimizing this expected loss over all possible threshold values is the same as maximizing r(1 – p(t)) + q(t), where r = (1 – )/a. In the case where r = 1, this quantity is equivalent to that of the traditional Youden index.
If the goal of rating diagnostic tests is to identify the test with the highest total proportions of people with or without disease given that they provided positive and negative test results, respectively, then we concur with Zetterberg, cautioning that the chosen cutpoint cannot be used in a different population. However, if the goal is to identify the test with the highest total proportions of correctly classified persons, then J, which can incorporate the prevalence, is the most appropriate measure of comparison.
As we held in our evaluation of the closest-to-(0,1) criterion (2), the appropriate measure of comparison and thus the appropriate method for cutpoint selection depends on the goal of the comparison process or the choice of which loss function should be optimized. We agree with Zetterberg that the predictive Youden index can be considered in addition to J when evaluating cutpoints and rating diagnostic tests in clinically relevant populations.
ACKNOWLEDGMENTS
Conflict of interest: none declared.
References
- Zetterberg H. Re: "The inconsistency of ‘optimal’ cut-points obtained using two criteria based on the receiver operating characteristic curve." (Letter). Am J Epidemiol 2006;164:707–8.
[Free Full Text] - Perkins NJ, Schisterman EF. The inconsistency of "optimal" cutpoints obtained using two criteria based on the receiver operating characteristic curve. Am J Epidemiol 2006;163:670–5. (Epub 2006 Jan 12).
[Abstract/Free Full Text] - Schisterman EF, Perkins NJ, Liu A, et al. Optimal cut-point and its corresponding Youden index to discriminate individuals using pooled blood samples. Epidemiology 2005;16:73–81.[CrossRef][ISI][Medline]
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