The perceived clinical value of NMR measurements on biopsy specimens. Part I. Interval estimates of diagnostic error rates and a note on an effect of the law of small numbers.
There are currently two conflicting views concerning the value of NMR measurements (in vivo and in vitro) of the proton T1 and T2 relaxation times in tissues, in discriminating between normal (Ca) and malignant (Ca) conditions. Damadian repeatedly asserted that a linear combination of these two measurements, the so-called malignancy index, can, "...discriminate between normal and cancer tissue on a case-by-case basis...considerably better than 90%" and thus "...the technique is now ready for use by pathologists as an adjunct to present methods of diagnosing malignancy." On the other hand, Hollis countered that, "Neither nmr nor any other method requiring surgical biopsy is likely to replace or even supplement the standard histopathological techniques." Part I of the present paper examines the relation between the first of these two views and the sample data presented in their support. Part I is a "cautionary tale" in which the procedures used by Koutcher to obtain point estimates of the misclassification rates from these data are shown to be incorrect. (These procedures are identical to those used two decades earlier by Ternberg in an advocacy of the diagnostic use of EPR measurements on biopsied tissues.) It is also shown that the interval estimates of the misclassification rates obtained from these data, which have not previously been reported, are large enough to embrace both views; these data are "user-friendly"--a characteristic of small samples. It is shown that, in accordance with the Tversky-Kahneman (1971) Law of Small Numbers, the disparity in the two views can be accounted for by, "...underestimates of the breadth of confidence intervals" (due to the small sample sizes) by each group. The appropriate statistical procedures for determining point and interval estimates of such misclassification rates are also described and illustrated with the Koutcher, data. Part II describes a Discriminant Analysis of these data. It is, of course, still possible that proton T1 and T2 measurements can be used to reliably distinguish between normal and malignant tissues since absence of evidence is not always evidence of absence for an effect.
Herbert
D E
DE
Dept. of Radiology, University of South Alabama, College of Medicine, Mobile 36688.
D000465:Algorithms; D001706:Biopsy; D003951:Diagnostic Errors; D006801:Humans; D066298:In Vitro Techniques; D009682:Magnetic Resonance Spectroscopy; D009369:Neoplasms / Q000175:diagnosis*; D013223:Statistics as Topic