×

Medical diagnostic test based on the potential test result approach: bounds and identification. (English) Zbl 1514.62649

Summary: Evaluating the performance of a medical diagnostic test is an important issue in disease diagnosis. W. J. Youden [“Index for rating diagnostic tests”, Cancer 3, No. 1, 32–35 (1950; doi:10.1002/1097-0142(1950)3:1<32::AID-CNCR2820030106>3.0.CO;2-3)] stated that the ideal measure of performance is to ensure that the control group resembles the diseased group as closely as possible in all respects except for the presence of the disease. To achieve this aim, this paper introduces the potential test result approach and proposes a new measure to evaluate the performance of medical diagnostic tests. This proposed measure, denoted as \(\operatorname{pr}(T_{d_1}\geq t\), \(T_{d_0}<t)\), can be interpreted as a probability that a test result \(T\) would respond to a disease status \(D\) (\(d \in\{d_0, d_1\}\)) for a given threshold \(t\), and therefore evaluates both the sufficiency and necessity of the performance of a medical diagnostic test. This new measure provides a total different interpretation for the Youden index and thus helps us to better understand the essence of the Youden index and its properties. We further propose non-parametric bounds on the proposed measure based on a variety of assumptions and illustrate our results with an example from the neonatal audiology study.

MSC:

62-XX Statistics

Software:

comproc; Stata
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Balke, A. and Pearl, J. 1997. Bounds on treatment effects from studies with imperfect compliance. J. Am. Stat. Assoc., 92: 1171-1176. (doi:10.1080/01621459.1997.10474074) · Zbl 0888.62049
[2] Bellamy, S. L., Lin, J. Y. and Ten Have, T. R. 2007. An introduction to causal modeling in clinical trials. Clin. Trials, 4: 58-73. (doi:10.1177/1740774506075549) · doi:10.1177/1740774506075549
[3] Biggersta, B. J. 2000. Comparing diagnostic tests: A simple graphic using likelihood ratios. Stat Med., 19: 649-663. (doi:10.1002/(SICI)1097-0258(20000315)19:5<649::AID-SIM371>3.0.CO;2-H) · doi:10.1002/(SICI)1097-0258(20000315)19:5<649::AID-SIM371>3.0.CO;2-H
[4] Broemeling, L. D. 2007. “Bayesian Biostatistics and Diagnostic Medicine”. Boca Raton, FL: Chapman & Hall/CRC. · Zbl 1123.62079 · doi:10.1201/9781584887683
[5] Cai, Z., Kuroki, M., Pearl, J. and Tian, J. 2008. Bounds on direct effects in the presence of confounded intermediate variables. Biometrics, 64: 695-701. (doi:10.1111/j.1541-0420.2007.00949.x) · Zbl 1274.62737 · doi:10.1111/j.1541-0420.2007.00949.x
[6] Cai, Z., Kuroki, M. and Sato, T. 2007. Nonparametric bounds of treatment effects with noncompliance by covariate adjustment. Stat. Med., 26: 3188-3204. (doi:10.1002/sim.2766) · doi:10.1002/sim.2766
[7] Gardner, I. A. 2002. The utility of Bayes’ theorem and Bayesian inference in veterinary clinical practice and research. Aust. Vet. J., 80: 758-761. (doi:10.1111/j.1751-0813.2002.tb11347.x) · doi:10.1111/j.1751-0813.2002.tb11347.x
[8] Geller, N. L. 2004. “Advances in Clinical Trial Biostatistics”. New York: Marcel Dekker. · Zbl 1039.62101
[9] Greenland, S. 1989. Modeling and variable selection in epidemiologic analysis. Am. J. Public Health, 79: 340-349. (doi:10.2105/AJPH.79.3.340) · doi:10.2105/AJPH.79.3.340
[10] Greer, A. L. and Collins, J. P. 2007. Sensitivity of a diagnostic test for amphibian ranavirus varies with sampling protocol. J. Wildl. Dis., 43: 525-532.
[11] Hilden, J. and Glasziou, P. 1996. Regret graphs, diagnostic uncertainty and Youden’s index. Stat. Med., 15: 969-986. (doi:10.1002/(SICI)1097-0258(19960530)15:10<969::AID-SIM211>3.0.CO;2-9) · doi:10.1002/(SICI)1097-0258(19960530)15:10<969::AID-SIM211>3.0.CO;2-9
[12] Janes, H., Longston, G. and Pepe, M. S. 2009. Accommodating covariates in ROC analysis. Stata J., 9: 17-39.
[13] Janes, H. and Pepe, M. S. 2008. Adjusting for covariates in studies of diagnostic, screening, or prognostic markers: An old concept in a new setting. Am. J. Epidemiol., 168: 89-97. (doi:10.1093/aje/kwn099) · doi:10.1093/aje/kwn099
[14] Janes, H. and Pepe, M. S. 2009. Adjusting for covariate effects on classification accuracy using the covariate-adjusted receiver operating characteristic curve. Biometrika, 96: 371-382. (doi:10.1093/biomet/asp002) · Zbl 1163.62046 · doi:10.1093/biomet/asp002
[15] Joseph, L., Gyorkos, T. and Coupal, L. 1995. Bayesian estimation of disease prevalence and the parameters of diagnostic tests in the absence of a gold standard. Am. J. Epidemiol., 141: 263-272. · doi:10.1093/oxfordjournals.aje.a117428
[16] MacLehose, R. F., Kaufman, S., Kaufman, J. S. and Poole, C. 2005. Bounding causal effects under uncontrolled confounding using counterfactuals. Epidemiology, 16: 548-555. (doi:10.1097/01.ede.0000166500.23446.53) · doi:10.1097/01.ede.0000166500.23446.53
[17] Martinez, E. Z., Achcar, J. A. and Louzada Neto, F. 2005. Bayesian estimation of diagnostic tests accuracy for semi-latent data with covariates. J. Biopharm. Stat., 15: 809-821. (doi:10.1081/BIP-200067912)
[18] Mickey, R. M. and Greenland, S. 1989. Modeling and variable selection in epidemiologic analysis. Am. J. Epidemiol., 129: 125-137. · doi:10.1093/oxfordjournals.aje.a115101
[19] Norton, S. J., Gorga, M. P., Widen, J. E., Folsom, R. C., Sininger, Y., Cone-Wesson, B., Vohr, B. R., Mascher, K. and Fletcher, K. 2000. Identification of neonatal hearing impairment: Evaluation of transient evoked otoacoustic emission, distortion product otoacoustic emission, and auditory brain stem response test performance. Ear Hearing, 21: 508-528. (doi:10.1097/00003446-200010000-00013) · doi:10.1097/00003446-200010000-00013
[20] Pearl, J. 2009. “Causality: Models of Reasoning and Inference”. In , 2, New York: Cambridge University Press. · Zbl 1188.68291 · doi:10.1017/CBO9780511803161
[21] Pencina, M. J., D’Agostino, R. B. Sr., D’Agostino, R. B. Jr. and Vasan, R. S. 2008. Evaluating the added predictive ability of a new marker: From area under the ROC curve to reclassification and beyond. Stat. Med., 27: 157-172. (doi:10.1002/sim.2929) · doi:10.1002/sim.2929
[22] Pepe, M. S. 2003. “The Statistical Evaluation of Medical Tests for Classification and Prediction”. New York: Oxford University Press. · Zbl 1039.62105
[23] Pepe, M. S., Feng, Z. and Gu, J. W. 2008. Comments on ‘Evaluating the added predictive ability of a new marker: From area under the ROC curve to reclassification and beyond’ by M. J. Pencina, R. B. D’Agostino Sr, R. B. D’Agostino Jr, R. S. Vasan. Stat. Med., 27: 173-181. (doi:10.1002/sim.2991) · doi:10.1002/sim.2991
[24] Robins, J. M. 1986. A new approach to causal inference in mortality studies with sustained exposure periods – application to control of the healthy worker survivor effect. Math. Model., 7: 1393-1512. (doi:10.1016/0270-0255(86)90088-6) · Zbl 0614.62136 · doi:10.1016/0270-0255(86)90088-6
[25] Robins, J. M., Hernan, M. A. and Brumback, B. 2000. Marginal structural models and causal inference in epidemiology. Epidemiology, 11: 550-560. (doi:10.1097/00001648-200009000-00011) · doi:10.1097/00001648-200009000-00011
[26] Rosenbaum, P. R. and Rubin, D. B. 1983. The central role of the propensity score in observational studies for causal effects. Biometrika, 70: 41-55. (doi:10.1093/biomet/70.1.41) · Zbl 0522.62091 · doi:10.1093/biomet/70.1.41
[27] Rothman, K. J., Greenland, S. and Lash, T. L. 2008. “Modern Epidemiology”. In , 3, Philadelphia, PA: Lippincott Williams & Wilkins.
[28] Sato, T. 1994. Confounding and effect modification in epidemiologic studies. Proc. Inst. Stat. Math., 42: 83-101.
[29] Schisterman, E. F., Faraggi, D., Reiser, B. and Hu, J. 2008. Youden Index and the optimal threshold for markers with mass at zero. Stat. Med., 27: 297-315. (doi:10.1002/sim.2993) · doi:10.1002/sim.2993
[30] Youden, W. J. 1950. Index for rating diagnostic tests. Cancer, 3: 32-35. (doi:10.1002/1097-0142(1950)3:1<32::AID-CNCR2820030106>3.0.CO;2-3) · doi:10.1002/1097-0142(1950)3:1<32::AID-CNCR2820030106>3.0.CO;2-3
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.