ROC analysis in medical imaging: a tutorial review of the literature
- 2k Downloads
- 61 Citations
Abstract
Receiver operating characteristic (ROC) analysis measures the “diagnostic accuracy” of a medical imaging system, which represents the second level of diagnostic efficacy in the hierarchical model described by Fryback and Thornbury (Med Decis Making 11:88–94, 1991). After describing the historical origins of ROC analysis, this paper reviews the importance of sampling cases appropriately, designing an observer study to avoid bias, and collecting data on a useful scale. A variety of methods for fitting ROC curves to observer data and testing the statistical significance of apparent differences are then reported. Finally, generalized forms of ROC analysis that require lesion localization or allow more than two states of truth are surveyed briefly.
Keywords
Receiver operating characteristic analysis ROC analysis Image evaluation Diagnostic accuracy Diagnostic efficacy Observer performanceReferences
- 1.Fryback DG, Thornbury JR. The efficacy of diagnostic imaging. Med Decis Making. 1991;11:88–94PubMedGoogle Scholar
- 2.Metz CE. Basic principles of ROC analysis. Semin Nucl Med. 1978;8:283–98PubMedGoogle Scholar
- 3.Wald A. Statistical decision functions. New York: Wiley; 1950Google Scholar
- 4.Egan JP. Signal detection theory and ROC analysis. New York: Academic; 1975Google Scholar
- 5.Van Meter D, Middleton D. Modern statistical approaches to reception in communication theory. IRE Trans. 1954;PGIT-4:119–41Google Scholar
- 6.Peterson WW, Birdsall TG, Fox WC. The theory of signal detectability. IRE Trans. 1954;PGIT-4:171–212Google Scholar
- 7.Tanner WP Jr, Swets JA. A decision-making theory of visual detection. Psych Rev. 1954;61:401–9Google Scholar
- 8.Swets JA, Birdsall TG. Human use of information III: decision-making in signal detection and recognition situations involving multiple alternatives. IEEE Trans Inf Theory. 1956;IT-2:138–65Google Scholar
- 9.Swets JA, Tanner WP Jr, Birdsall TG. Decision processes in perception. Psych Rev. 1961;68:301–40Google Scholar
- 10.Swets JA, (editor). Signal detection and recognition by human observers: contemporary readings. New York: Wiley; 1964Google Scholar
- 11.Green DM, Swets JA. Signal detection theory and psychophysics. New York: Wiley; 1966. [Reprinted with corrections and an updated topical bibliography by Krieger (Huntington, NY, 1974) and by Peninsula Publishing (Los Altos, CA, 1988)]Google Scholar
- 12.Swets JA. The relative operating characteristic in psychology. Science. 1973;182:990–1000PubMedGoogle Scholar
- 13.Swets JA, Green DM. Applications of signal detection theory. In: Pick HA, Liebowitz HL, Singer A, et al. editors. Psychology: from research to practice. New York: Plenum; 1978. p. 311–331Google Scholar
- 14.Swets JA. Effectiveness of information retrieval methods. Am Doc. 1969;20:72–89Google Scholar
- 15.Griner PF, Mayewski RJ, Mushlin AI, Greenland P. Selection and interpretation of diagnostic tests and procedures: principles and applications. Ann Intern Med. 1981;94:553–92Google Scholar
- 16.Swets JA. Assessment of NDT systems (Parts I and II). Mater Eval. 1983;41:1294–303Google Scholar
- 17.Robertson EA, Zweig MH, Van Steirtghem AC. Evaluating the clinical efficacy of laboratory tests. Am J Clin Path. 1983;79:78–86PubMedGoogle Scholar
- 18.Zweig MH, Campbell G. Receiver-operating characteristic (ROC) plots: a fundamental evaluation tool in clinical medicine. Clin Chem. 1993;39:561–77. (Erratum published in Clin Chem. 1993;39:1589.)PubMedGoogle Scholar
- 19.Swets JA. Signal detection theory and ROC analysis in psychology and diagnostics: collected papers. Mahwah: Lawrence Erlbaum Associates; 1996Google Scholar
- 20.Lusted LB. Personal communication in conversations with CE Metz. circa 1975Google Scholar
- 21.Lusted LB. Logical analysis in roentgen diagnosis. Radiology. 1960;74:178–93PubMedGoogle Scholar
- 22.Lusted LB. Introduction to medical decision making. Springfield: Thomas; 1968Google Scholar
- 23.Lusted LB. Decision-making studies in patient management. New Engl J Med. 1971;284:416–24PubMedCrossRefGoogle Scholar
- 24.Lusted LB. Signal detectability and medical decision-making. Science. 1971;171:1217–9PubMedGoogle Scholar
- 25.Lusted LB. Observer error, signal detectability, medical decision making. In: Jacquez JA, editor. Computer diagnosis and diagnostic methods. Springfield: Thomas; 1972. p. 29–44Google Scholar
- 26.Lusted LB. Receiver operating chararcteristic analysis and its significance in interpretation of radiologic images. In: Potchen E, editor. Current concepts in radiology. St Louis: Mosby; 1975. p. 117–130Google Scholar
- 27.Lusted LB. General problems in medical decision making, with comments on ROC analysis. Semin Nucl Med. 1978;8:299–306PubMedGoogle Scholar
- 28.Goodenough DJ, Rossmann K, Lusted LB. Radiographic applications of signal detection theory. Radiology. 1972;105:199–200PubMedGoogle Scholar
- 29.Goodenough DJ, Rossmann K, Lusted LB. Factors affecting the detectability of a simulated radiographic signal. Invest Radiol. 1973;8:339–44PubMedGoogle Scholar
- 30.Goodenough DJ, Rossmann K, Lusted LB. Radiographic applications of receiver operating characteristic (ROC) analysis. Radiology. 1974;110:89–95PubMedGoogle Scholar
- 31.Swets JA. Signal detection in medical diagnosis. In: Jacquez JA, editor. Computer diagnosis and diagnostic methods. Springfield: Thomas; 1972. p. 8–28Google Scholar
- 32.Morgan RH, Donner MW, Gayler BW, et al. Decision processes and observer error in the diagnosis of pneumoconiosis by chest roentgenography. Am J Roentgenol. 1973;117:757–64Google Scholar
- 33.Kundel HL, Revesz G. The evaluation of radiograghic techniques by observer tests: problems, pitfalls and procedures. Invest Radiol. 1974;9:166–73PubMedGoogle Scholar
- 34.Metz CE, Starr SJ, Lusted LB, Rossmann K. Progress in evaluation of human observer visual detection performance using the ROC curve approach. In: Raynaud C, Todd-Pokropek AE, editors. Information processing in scintigraphy. Orsay, France: Commissariat à l’Energie Atomique, Département de Biologie, Service Hospitalier Frédéric Joliot; 1975. p. 420–439Google Scholar
- 35.Metz CE, Starr SJ, Lusted LB. Quantitative evaluation of visual detection performance in medicine: ROC analysis and determination of diagnostic benefit. In: Hay GA, editor. Medical images: formation, perception and measurement. London: Wiley; 1977. p. 220–240Google Scholar
- 36.Andrus WS, Bird KT. Radiology and the receiver operating characteristic (ROC) curve. Chest. 1975;67:378–9PubMedGoogle Scholar
- 37.McNeil BJ, Keeler E, Adelstein SJ. Primer on certain elements of medical decision making. New Engl J Med. 1975;293:211–5PubMedCrossRefGoogle Scholar
- 38.Turner DA. An intuitive approach to receiver operating chararcteristic curve analysis. J Nucl Med. 1978;19:213–20PubMedGoogle Scholar
- 39.Swets JA. ROC analysis applied to the evaluation of medical imaging techniques. Invest Radiol. 1979;14:109–21PubMedGoogle Scholar
- 40.Swets JA, Pickett RM. Evaluation of diagnostic systems: methods from signal detection theory. New York: Academic; 1982Google Scholar
- 41.Metz CE. ROC methodology in radiologic imaging. Invest Radiol. 1986;21:720–33PubMedGoogle Scholar
- 42.Swets JA. Measuring the accuracy of diagnostic systems. Science. 1988;240:1285–93PubMedGoogle Scholar
- 43.Hanley JA. Receiver operating characteristic (ROC) methodology: the state of the art. CRC Crit Rev Diagn Imaging. 1989;29:307–35Google Scholar
- 44.Metz CE. Some practical issues of experimental design and data analysis in radiological ROC studies. Invest Radiol. 1989;24:234–45PubMedGoogle Scholar
- 45.Metz CE, Wagner RF, Doi K, Brown DG, Nishikawa RN, Myers KJ. Toward consensus on quantitative assessment of medical imaging systems. Med Phys. 1995;22:1057–61PubMedGoogle Scholar
- 46.Allisy A, (editor). Medical imaging—the assessment of image quality. ICRU report #54. Bethesda: International Commission for Radiation Units and Measurements, Inc.; 1996Google Scholar
- 47.Metz CE. Evaluation of CAD. In: Doi K, MacMahon H, Giger ML, Hoffmann KR, editors. Computer-aided diagnosis in medical imaging. Amsterdam: Elsevier; 1999. p. 543. (Excerpta Medica International Congress Series, vol. 1182)Google Scholar
- 48.Metz CE. Fundamental ROC analysis. In: Beutel J, Kundel H, Van Metter R, editors. Handbook of medical imaging, vol. 1: physics and psychophysics. Bellingham: SPIE Press; 2000. p. 751Google Scholar
- 49.Wagner RF, Beiden SV, Campbell G, Metz CE, Sacks WM. Assessment of medical imaging and computer-assist systems: lessons from recent experience. Acad Radiol. 2002;8:1264–77Google Scholar
- 50.Metz CE. Receiver operating characteristic (ROC) analysis: a tool for quantitative evaluation of observer performance and imaging systems. JACR. 2006;3:413–22PubMedGoogle Scholar
- 51.Wagner RF, Metz CE, Campbell G. Assessment of medial imaging systems and computer aids: a tutorial review. Acad Radiol. 2007;14:723–48PubMedGoogle Scholar
- 52.Krupinski EA, Jiang Y. Evaluation of medical imaging systems. Med Phys. 2008 (in press)Google Scholar
- 53.Gur D. Objectively measuring and comparing performance levels of diagnostic imaging systems and practices (editorial). Acad Radiol. 2007;14:641–2PubMedGoogle Scholar
- 54.Gur D, Rockette HE, Good W, Slasky BS, Cooperstein LA, Straub WH, et al. Effect of observer instruction on ROC study of chest images. Invest Radiol. 1990;25:230–4PubMedCrossRefGoogle Scholar
- 55.Kobayashi T, Xu X-W, MacMahon H, Metz CE, Doi K. Effect of a computer-aided diagnosis scheme on radiologists’ performance in detection of lung nodules on chest radiographs. Radiology. 1996;199:843–8PubMedGoogle Scholar
- 56.Ransohoff DF, Feinstein AR. Problems of spectrum and bias in evaluating the efficacy of diagnostic tests. New Engl J Med. 1978;299:926–30PubMedCrossRefGoogle Scholar
- 57.Begg CB, Greenes RA. Assessment of diagnostic tests when disease verification is subject to selection bias. Biometrics. 1983;39:207–15PubMedGoogle Scholar
- 58.Revesz G, Kundel HL, Bonitatibus M. The effect of verification on the assessment of imaging techniques. Invest Radiol. 1983;18:194–8PubMedGoogle Scholar
- 59.Gray R, Begg CB, Greenes RA. Construction of receiver operating characteristic curves when disease verification is subject to selection bias. Med Decis Making. 1984;4:151–64PubMedGoogle Scholar
- 60.Begg CB, McNeil BJ. Assessment of radiologic tests: control of bias and other design considerations. Radiology. 1988;167:565–9PubMedGoogle Scholar
- 61.Gur D, Rockette HE, Armfield DR, et al. Prevalence effect in a laboratory environment. Radiology. 2003;228:10–4PubMedGoogle Scholar
- 62.Gur D, Bandos AI, Fuhrman CR, Klym AH, King JL, Rockette HE. The prevalence effect in a laboratory environment: changing the confidence ratings. Acad Radiol. 2007;14:49–53PubMedGoogle Scholar
- 63.Rockette HE, Gur D, Metz CE. The use of continuous and discrete confidence judgments in receiver operating characteristic studies of diagnostic imaging techniques. Invest Radiol. 1992;27:169–72PubMedGoogle Scholar
- 64.King JL, Britton CA, Gur D, Rockette HE, Davis PL. On the validity of continuous and discrete confidence rating scales in receiver operating characteristic studies. Invest Radiol. 1993;28:962–3PubMedGoogle Scholar
- 65.Walsh SJ. Limitations to the robustness of binormal ROC curves: effects of model misspecification and location of decision thresholds on bias, precision, size and power. Stat Med. 1997;16:669–79PubMedGoogle Scholar
- 66.Wagner RF, Beiden SV, Metz CE. Continuous vs. categorical data for ROC analysis: some quantitative considerations. Acad Radiol. 2001;8:328–34PubMedGoogle Scholar
- 67.Hadjiiski L, Chan H-P, Sahiner B, Helvie MA, Roubidoux MA. Quasi-continuous and discrete confidence rating scales for observer performance studies: effects on ROC analysis. Acad Radiol. 2007;14:38–48PubMedGoogle Scholar
- 68.Swets JA. Form of empirical ROCs in discrimination and diagnostic tasks: implications for theory and measurement of performance. Psychol Bull. 1986;99:181–98PubMedGoogle Scholar
- 69.Hanley JA. The robustness of the “binormal” assumptions used in fitting ROC curves. Med Decis Making. 1988;8:197–203PubMedGoogle Scholar
- 70.Hanley JA. The use of the “binormal” model for parametric ROC analysis of quantitative diagnostic tests. Stat Med. 1996;15:1575–85PubMedGoogle Scholar
- 71.Dorfman DD, Alf E. Maximum likelihood estimation of parameters of signal detection theory and determination of confidence intervals—rating method data. J Math Psych. 1969;6:487–96Google Scholar
- 72.Grey DR, Morgan BJT. Some aspects of ROC curve-fitting: normal and logistic models. J Math Psych. 1972;9:128–39Google Scholar
- 73.Metz CE, Herman BA, Shen J-H. Maximum-likelihood estimation of ROC curves from continuously-distributed data. Stat Med. 1998 17:1033–53PubMedGoogle Scholar
- 74.Dorfman DD, Berbaum KS. Degeneracy and discrete receiver operating characteristic rating data. Acad Radiol. 1995;2:907–15PubMedGoogle Scholar
- 75.Dorfman DD, Berbaum KS, Metz CE, Lenth RV, Hanley JA, Dagga HA. Proper ROC analysis: the bigamma model. Acad Radiol. 1997;4:138–49PubMedGoogle Scholar
- 76.Pan X, Metz CE. The “proper” binormal model: parametric ROC curve estimation with degenerate data. Acad Radiol. 1997;4:380–9PubMedGoogle Scholar
- 77.Metz CE, Pan X. “Proper” binormal ROC curves: theory and maximum-likelihood estimation. J Math Psych. 1999;43:1–33Google Scholar
- 78.Pesce LL, Metz CE. Reliable and computationally efficient maximum-likelihood estimation of “proper” binormal ROC curves. Acad Radiol. 2007;14:814–29PubMedGoogle Scholar
- 79.Tosteson A, Begg C. A general regression methodology for ROC curve estimation. Med Decis Making. 1988;8:204–15PubMedGoogle Scholar
- 80.Toledano AY, Gatsonis C. Ordinal regression methodology for ROC curves derived from correlated data. Stat Med. 1996;15:1807–26PubMedGoogle Scholar
- 81.Hellmich M, Abrams KR, Jones DR, Lambert PC. A Bayesian approach to a general regression model for ROC curves. Med Decis Making. 1998;18:436–43PubMedGoogle Scholar
- 82.Pepe MS. The statistical evaluation of medical tests for classification and prediction. New York: Oxford University Press; 2004Google Scholar
- 83.Metz CE. Quantification of failure to demonstrate statistical significance: the usefulness of confidence intervals. Invest Radiol. 1993;28:59–63PubMedGoogle Scholar
- 84.Metz CE, Kronman HB. Statistical significance tests for binormal ROC curves. J Math Psych. 1980;22:218–43Google Scholar
- 85.Hanley JA, McNeil BJ. The meaning and use of the area under a receiver operating characteristic (ROC) curve. Radiology. 1982;143:29–36PubMedGoogle Scholar
- 86.McClish DK. Analyzing a portion of the ROC curve. Med Decis Making. 1989;9:190–5PubMedGoogle Scholar
- 87.Jiang Y, Metz CE, Nishikawa RM. A receiver operating characteristic partial area index for highly sensitive diagnostic tests. Radiology. 1996;201:745–50PubMedGoogle Scholar
- 88.Halpern EJ, Alpert M, Krieger AM, Metz CE, Maidment AD. Comparisons of ROC curves on the basis of optimal operating points. Acad Radiol. 1996;3:245–53PubMedGoogle Scholar
- 89.Hanley JA, McNeil BJ. A method of comparing the areas under receiver operating characteristic curves derived from the same cases. Radiology. 1983;148:839–43PubMedGoogle Scholar
- 90.DeLong ER, DeLong DM, Clarke-Pearson DL. Comparing the areas under two or more correlated receiver operating characteristic curves: a nonparametric approach. Biometrics. 1988;44:837–45PubMedGoogle Scholar
- 91.Wieand S, Gail MH, James BR, James KL. A family of nonparametric statistics for comparing diagnostic markers with paired or unpaired data. Biometrika. 1989;76:585–92Google Scholar
- 92.Thompson ML, Zucchini W. On the statistical analysis of ROC curves. Stat Med. 1989;8:1277–90PubMedGoogle Scholar
- 93.Zhou XH, Gatsonis CA. A simple method for comparing correlated ROC curves using incomplete data. Stat Med. 1996;15:1687–93PubMedGoogle Scholar
- 94.Metz CE, Wang P-L, Kronman HB. A new approach for testing the significance of differences between ROC curves measured from correlated data. In: Deconinck F, editor. Information processing in medical imaging. The Hague: Nijhoff; 1984. p. 432–445Google Scholar
- 95.Metz CE. Statistical analysis of ROC data in evaluating diagnostic performance. In: Herbert D, Myers R, editors. Multiple regression analysis: applications in the health sciences. New York: American Institute of Physics; 1986. p. 365–384Google Scholar
- 96.Metz CE, Herman BA, Roe CA. Statistical comparison of two ROC curve estimates obtained from partially-paired datasets. Med Decis Making. 1998;18:110–21PubMedGoogle Scholar
- 97.Hajian-Tilaki KO, Hanley JA, Joseph L, Collet J-P. A comparison of parametric and nonparametric approaches to ROC analysis of quantitative diagnostic tests. Med Decis Making. 1997;17:94–102PubMedGoogle Scholar
- 98.Hsieh F, Turnbull BW. Nonparametric and semiparametric estimation of the receiver operating characteristic curve. Ann Stat. 1996;24:25–40Google Scholar
- 99.Roe CA, Metz CE. Variance-component modeling in the analysis of receiver operating characteristic index estimates. Acad Radiol. 1997;4:587–600PubMedGoogle Scholar
- 100.Dorfman DD, Berbaum KS, Metz CE. Receiver operating characteristic rating analysis: generalization to the population of readers and patients with the jackknife method. Invest Radiol. 1992;27:723–31PubMedGoogle Scholar
- 101.Dorfman DD, Metz CE. Multi-reader multi-case ROC analysis: comments on Begg’s commentary. Acad Radiol. 1995;2 Suppl 1:S76Google Scholar
- 102.Dorfman DD, Berbaum KS, Lenth RV. Multireader, multicase receiver operating characteristic methodology: a bootstrap analysis. Acad Radiol. 1995;2:626–33Google Scholar
- 103.Roe CA, Metz CE. The Dorfman–Berbaum–Metz method for statistical analysis of multi-reader, multi-modality ROC data: validation by computer simulation. Acad Radiol. 1997;4:298–303PubMedGoogle Scholar
- 104.Dorfman DD, Berbaum KS, Lenth RV, Chen Y-F, Donaghy BA. Monte Carlo validation of a multireader method for receiver operating characteristic discrete rating data: factorial experimental design. Acad Radiol. 1998;5:591–602PubMedGoogle Scholar
- 105.Hillis SL, Berbaum KS. Power estimation for the Dorfman–Berbaum–Metz method. Acad Radiol. 2004;11:1260–73PubMedGoogle Scholar
- 106.Hillis SL, Berbaum KS. Monte Carlo validation of the Dorfman–Berbaum–Metz method using normalized pseudovalues and less data-based model simplification. Acad Radiol. 2005;12:1534–42PubMedGoogle Scholar
- 107.Obuchowski NA, Rockette HE. Hypothesis testing of the diagnostic accuracy for multiple diagnostic tests: an ANOVA approach with dependent observations. Commun Stat Simul Comput. 1995;24:285–308Google Scholar
- 108.Obuchowski NA. Multireader, multimodality receiver operating characteristic curve studies: hypothesis testing and sample size estimation using an analysis of variance approach with dependent observations. Acad Radiol. 1995;2:522–9Google Scholar
- 109.Obuchowski NA. Sample size tables for receiver operating characteristic studies. Am J Roentgenol. 2000;175:603–8Google Scholar
- 110.Toledano AY, Gatsonis C. GEEs for ordinal categorical data: arbitrary patterns of missing responses and missingness in a key covariate. Biometrics. 1999;22:488–96Google Scholar
- 111.Beiden SV, Wagner RF, Campbell G. Components-of-variance models and multiple-bootstrap experiments: an alternative method for random-effects, receiver operating characteristic analysis. Acad Radiol. 2000;7:341–9PubMedGoogle Scholar
- 112.Beiden SV, Wagner RF, Campbell G, Chan HP. Analysis of uncertainties in estimates of components of variance in multivariate ROC analysis. Acad Radiol. 2001;8:616–22PubMedGoogle Scholar
- 113.Beiden SV, Wagner RF, Campbell G, Metz CE, Jiang Y. Components-of-variance models for random-effects ROC analysis: the case of unequal variance structures across modalities. Acad Radiol. 2001;8:605–15PubMedGoogle Scholar
- 114.Beiden SV, Wagner RF, Campbell G, Chan H-P. Analysis of uncertainties in estimates of components of variance in multivariate ROC analysis. Acad Radiol. 2001;8:616–22PubMedGoogle Scholar
- 115.Obuchowski NA, Beiden SV, Berbaum KS, Hillis SL, Ishwaran H, Song HH, et al. Multireader, multicase receiver operating characteristic analysis: an empirical comparison of five methods. Acad Radiol. 2004;11:980–95PubMedGoogle Scholar
- 116.Hillis SL, Obuchowski NA, Schartz KM, Berbaum KS. A comparison of the Dorfman–Berbaum–Metz and Obuchowski–Rockette methods for receiver operating characteristic (ROC) data. Stat Med. 2005;24:1579–607PubMedGoogle Scholar
- 117.Hillis, SL: Sample size estimates for DBM MRMC based on analysis of published data. http://perception.radiology.uiowa.edu/SampleSize/tabid/182/Default.aspx
- 118.Dorfman DD. RSCORE II. In: Swets JA, Pickett RM, editors. Evaluation of diagnostic systems: methods from signal detection theory. New York: Academic; 1982. p. 208–232Google Scholar
- 119.University of Chicago Receiver Operating Characteristic program software downloads. http://xray.bsd.uchicago.edu/krl/KRL_ROC/software_index6.htm
- 120.University of Iowa Receiver Operating Characteristic program software downloads. http://perception.radiology.uiowa.edu/
- 121.Cleveland Clinic Receiver Operating Characteristic program software downloads. http://www.bio.ri.ccf.org/html/obumrm.html
- 122.Obuchowski, NA: Research activities: ROC analysis. http://www.bio.ri.ccf.org/html/rocanalysis.html
- 123.Starr SJ, Metz CE, Lusted LB, Goodenough DJ. Visual detection and localization of radiographic images. Radiology. 1975;116:533–8PubMedGoogle Scholar
- 124.Starr SJ, Metz CE, Lusted LB. Comments on generalization of receiver operating characteristic analysis to detection and localization tasks (Letter to the Editor). Phys Med Biol. 1977;22:376–9PubMedGoogle Scholar
- 125.Swensson RG. Unified measurement of observer performance in detecting and localizing target objects on images. Med Phys. 1996;23:1709–25PubMedGoogle Scholar
- 126.Egan JP, Greenberg GZ, Schulman AI. Operating characteristics, signal detection, and the method of free response. J Acoust Soc Am. 1961;33:993–1007Google Scholar
- 127.International Atomic Energy Agency. IAEA co-ordinated research programme on the intercomparison of computer-assisted scintigraphic techniques: third progress report. In: Medical radionuclide imaging, vol. 1. Vienna: IAEA; 1977. p. 585–615Google Scholar
- 128.Bunch PC, Hamilton JF, Sanderson GK, Simmons AH. A free response approach to the measurement and characterization of radiographic observer performance. Proc SPIE. 1977;127:124–35Google Scholar
- 129.Bunch PC, Hamilton JF, Sanderson GK, Simmons AH. A free response approach to the measurement and characterization of radiographic observer performance. J Appl Photogr Eng. 1978;4:166–72Google Scholar
- 130.Chakraborty DP. Maximum likelihood analysis of free-response receiver operating characteristic (FROC) data. Med Phys. 1989;16:561–8PubMedGoogle Scholar
- 131.Chakraborty DP, Winter LHL. Free-response methodology: alternate analysis and a new observer-performance experiment. Radiology. 1990;33:873–81Google Scholar
- 132.Obuchowski NA, Lieber ML, Powell KA. Data analysis for detection and localization of multiple abnormalities with application to mammography. Acad Radiol. 2000;7:516–25PubMedGoogle Scholar
- 133.Chakraborty DP. Statistical power in observer performance studies: a comparison of the ROC and free-response methods in tasks involving localization. Acad Radiol. 2002;9:147–56PubMedGoogle Scholar
- 134.Edwards DC, Kupinski MA, Metz CE, Nishikawa RM. Maximum-likelihood fitting of FROC curves under an initial-detection-and-candidate-analysis model. Med Phys. 2002;29:2861–70PubMedGoogle Scholar
- 135.Chakraborty DP, Berbaum KS. Observer studies involving detection and localization: modeling, analysis, and validation. Med Phys. 2004;31:2313–30PubMedGoogle Scholar
- 136.Chakraborty DP. A search model and figure of merit for observer data acquired according to the free-response paradigm. Phys Med Biol. 2006;51:3449–62PubMedGoogle Scholar
- 137.Chakraborty DP. Analysis of location specific observer performance data: validated extensions of the jackknife free-response (JAFROC) method. Acad Radiol. 2006;13:1187–93PubMedGoogle Scholar
- 138.Chakraborty D, Yoon H-J, Mello-Thoms C. Spatial localization accuracy of radiologists in free-response studies: inferring perceptual FROC curves from mark-rating data. Acad Radiol. 2007;14:4–18PubMedGoogle Scholar
- 139.Edwards DC, Metz CE, Kupinski MA. Ideal observers and optimal ROC hypersurfaces in N-class classification. IEEE Trans Med Imaging. 2004;23:891–5PubMedGoogle Scholar
- 140.Edwards DC, Metz CE, Nishikawa RM. The hypervolume under the ROC hypersurface of “near-guessing” and “near-perfect” observers in N-class classification tasks. IEEE Trans Med Imaging. 2005;24:293–9PubMedGoogle Scholar
- 141.Edwards DC, Lan L, Metz CE, Giger ML, Nishikawa RM. Estimating three-class ideal observer decision variables for computerized detection and classification of mammographic mass lesions. Med Phys. 2004;31:81–90PubMedGoogle Scholar
- 142.Edwards DC, Metz CE. Review of several proposed three-class classification decision rules and their relation to the ideal observer decision rule. Proc SPIE. 2005;5749:128–37Google Scholar
- 143.Edwards DC, Metz CE. Restrictions on the three-class ideal observer’s decision boundary lines. IEEE Trans Med Imaging. 2005;24:1566–73PubMedGoogle Scholar
- 144.Edwards DC, Metz CE. Analysis of proposed three-class classification decision rules in terms of the ideal observer decision rule. J Math Psych. 2006;50:478–87Google Scholar
- 145.He X, Metz CE, Tsui BMW, Links JM, Frey EC. Three-class ROC analysis—I: a decision theoretic approach under the ideal observer framework. IEEE Trans Med Imaging. 2006;25:571–81PubMedGoogle Scholar
- 146.He X, Fry EC. An optimal three-class linear observer derived from decision theory. IEEE Trans Med Imaging. 2007;26:77–83PubMedGoogle Scholar
- 147.Chan H-P, Sahiner B, Hadjiiski LM, Petrick N, Zhou C. Design of three-class classifiers in computer-aided diagnosis: Monte Carlo simulation study. Proc SPIE. 2003;5032:567–78Google Scholar
- 148.Sahiner B, Chan H-P, Hadjiiski LM. Performance analysis of 3-class classifiers: properties of the 3D ROC surface and the normalized volume under the surface. Proc SPIE. 2006;6146:87–93Google Scholar