This presentation will emphasize the estimation of the combined accuracy of two or more tests when verification bias is present. Verification bias occurs when some of the subjects are not subject to the gold standard. The approach is Bayesian where the estimation of test accuracy is based on the posterior distribution of the relevant parameter. Accuracy of two combined binary tests is estimated employing either “believe the positive” or “believe the negative” rule, then the true and false positive fractions for each rule are computed for two tests. In order to perform the analysis, the missing at random assumption is imposed, and an interesting example is provided by estimating the combined accuracy of CT and MRI to diagnose lung cancer. The Bayesian approach is extended to two ordinal tests when verification bias is present, and the accuracy of the combined tests is based on the ROC area of the risk function. An example involving mammography with two readers with extreme verification bias illustrates the estimation of the combined test accuracy for ordinal tests.
References
[1]
Johnson, D.; Sandmire, D.; Klein, D. Medical Tests that Can Save Your Life, Tests Your Doctor Won't Order Unless You Know To Ask; Rodale Inc.: Emmaus, PA, USA, 2004.
[2]
Buscombe, J.R.; Cwikla, J.B.; Holloway, B.; Hilson, A.J.W. Prediction and usefulness of combined mammography and scintimmaography in suspected primary breast cancer using ROC curves. J. Nuclear Medicine 2001, 42, 3.
[3]
Berg, W.A.; Gutierrez, L.; NessAlver, M.S.; Carter, W.B.; Bhargavan, M.; Lewis, R.S.; Loffe, O.B. Diagnostic accuracy of mammography, clinical examination, US and MR, imaging in preoperative assessment of breast cancer. Radiology 2004, 233, 830–849.
[4]
Van Overhagen, H.; Brakel, K.; Heijenbrok, M.W.; van Kasteren, J.H.L.M.; van de Moosdijk, C.N.F.; Roldann, A.C.; van Gils, A.P.; Hansen, B.E. Metastasis in supraclavicular lymph nodes in lung cancer: Assessment in palpation, US, and CT. Radiology 2004, 232, 75–80.
[5]
Pauleit, D.; Zimmerman, A.; Stoffels, G.; Bauer, D.; Risse, J.; Fluss, M.O.; Hamacher, K.; Coenene, H.H.; Langen, K.J. 18F-FET PET compared with 18F-FEG PET ad CT in patients with head and neck cancer. J. Nuclear Med. 2006, 47, 256–261.
[6]
Schaffler, G.J.; Wolf, G.W.; Schoellnast, H.; Groell, R.; Maier, A.; Smolle-Juttner, F.M.; Woltsche, M.; Fasching, G.; Nicolletti, R.; Aigner, R.M. Non-small cell lung cancer: Evaluation of pleural abnormalities on CT scans with 18F-FET PET. Radiology 2004, 231, 858–865.
[7]
Pepe, M.S. The Statistical Evaluation of Medical Tests for Classification and Prediction; Oxford University Press: Oxford, UK, 2004.
[8]
Zhou, X.H.; Obuchowski, N.A.; McClish, D.K. Statistical Methods in DiagnosticMedicine; John Wiley & Sons Inc.: New York, NY, USA, 2002.
[9]
Zhou, X.H. Maximum likelihood estimators of sensitivity and specificity corrected for verification bias. Commun. Stat. Theory Methods 1993, 22, 3177–3198.
[10]
Zhou, X.H. Nonparametric ML estimate of the ROC area corrected for verification bias. Biometrics 1996, 52, 310–316.
[11]
Zhou, X.H.; Castelluccio, P. Nonparametric analysis for the ROC curves of two diagnostic tests in the presence of non ignorable verification bias. J. Stat. Plan. Infer. 2002, 115, 193–213.
[12]
Broemeling, L.D. Bayesian Biostatistics and Diagnostic Medicine; Chapman & Hall/CRC Taylor & Francis: Boca Raton, FL, USA, 2007.
[13]
Broemeling, L.D. Advanced Bayesian Methods for Medical Test Accuracy; Chapman & Hall/CRC Taylor & Francis: Boca Raton, FL, USA, 2011.
[14]
Begg, C.B.; Greenes, R.A. Assessment of diagnostic tests when disease verification is subject to selection bias. Biometrics 1983, 39, 207–215.
[15]
Gray, R.; Begg, C.; Greenes, R. Construction of receiver operating characteristic curve when disease verification is subject to selection bias. Med. Decis. Making 1984, 4, 151–164.
[16]
Liu, D.; Zhou, X.H. A model for adjusting for nonignorable verification bias in estimation of the ROC curve and its area with likelihood-based approach. Biometrics 2010, 66, 1119–1128.
[17]
Zhang, Z. Likelihood-based confidence sets for partially identified parameters. J. Stat. Plan. Infer. 2009, 139, 696–710.
[18]
Alonzo, T.A. Comparing accuracy in an unpaired post-market device study with incomplete disease assessment. Biom. J. 2009, 51, 491–503.
[19]
He, H.; Lyness, J.M.; McDermott, M.P. Direct estimation of the area under the receiver operating characteristic curve in the presence of verification bias. Stat. Med. 2009, 28, 361–376.
[20]
Buzoianu, M.; Kadane, J.B. Adjusting for verification bias in diagnostic test evaluation: A Bayesian approach. Stat. Med. 2008, 27, 2453–2473.
