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Lecture 4

# Imaging Science Lecture 4.docx

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Western University

Medical Biophysics

Medical Biophysics 3503G

James Lacefield

Winter

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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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