Imaging Science Lecture 4.docx

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Western University
Medical Biophysics
Medical Biophysics 3503G
James Lacefield

3503 Imaging Science Lecture 4 January 21 th Receiver Operating Characteristic (ROC) Continued • Applications of ROC Analysis 1. Evaluate diagnostic performance of a single imaging method  If you just have one imaging system to study you can construct its ROC Curve and can ask yourself if it’s close to the chance line or closer to the perfect detector curve. Can make inferences about whether the accuracy of the imaging test is acceptable based on that 2. Compare two methods or implementations of the same imaging modality  i.e. Two or more implementations of MRI, or two or more implementations of CT 3. Compare two different imaging modalities 4. Compare diagnostic performance of human observers  Can find papers where they show that radiologists in one practice are better at interpreting mammograms than radiologists in another practice. Also used to study innovations in radiologist education (new educational techniques vs. old) • Comparing Methods or Modalities oApplication was detecting liver tumours. They had a conventional method which gave the blue ROC curve and new methods A and B. If the curves don’t cross, then it is easy to interpret:  The blue line is almost directly on chance line. Red curve is above and to the left of the orange curve, therefore you could infer the red method outperforms the orange method (same conclusion by comparing their areas) o It is harder to compare if the ROC Curves cross  Curve A is the one you prefer if your priority is to minimize the FPF (A is above and to the left at low false positives and so if you have a medical application in which that is your priority you choose A)  Curve B is higher and to the left than curve A for higher values of false positives which are also higher values of TPF. So if your priority is to maximize true positive fraction, you would prefer B to A  We would like to have a tool that tells us what our priority should be* • Statistical View of ROC Analysis o We imagine that whatever we are using to rate the images, x; if we collect the ratings for all the images we study, we can plot the distribution of the ratings of all the images o Assume the distribution will be Normal (or Gaussian); the distribution will have some mean, μ, and some standard deviation, σ. o We imagine that we could describe separately the distributions of imaging ratings for all of the disease absent patients and distributions of imaging ratings for all of the disease present patients. o Then we must add a decision threshold: a value of x such that all the images whos ratings are greater than the threshold will give a positive diagnosis . And the false positive fraction is then the area under the blue distribution from our threshold to positive infinity (calculating this area under the curve gives us the total number of patients who were disease absent, blue, but an imaging rating of positive) o We can repeat this for other distributions to get multiple pairs of TPF and FPF and again plot them  In this theoretical view the ROC curve is going to be a nice smooth curve rather than the piecewise curve we had before  Why is this useful? An innovation that is going to improve diagnostic accuracy and therefore is going to increase the area under the ROC curve, in terms of the statistical view is going to reduce the overlap between the distribution of image ratings for disease absent and present patients.  Since the two means and standard deviations tell you everything there is to know about the distributions, we reduce overlap by: 1. Increase spacing between peaks (difference between means) 2. Make one or both distributions narrower (reduce standard deviation) 3. Also suggests that this can be improved by improving the SNR. Interesting because the contrast detail curve gave us a way to think about how improving the SNR will affect our ability to detect simple features. So that suggests that this is the key to the bridge between the two: the contrast and ROC curve • From Contrast-Detail Curve to ROC o In terms of the statistical view of the ROC: making it easier to detect large low contrast features is the same thing as reducing the overlap of the
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