BIOE420 Bioimaging
Name:_____________________________ UID: _______________________________
Homework #2 (Due: 3/1/2018 in class)
Note: In your solution,
... [Show More] please be as detailed as possible. We will breakdown the points
for each step.
Question #1 (20%):
Consider the data for a study of 100 patients undergoing CT colonography, where the tumor size
is used for diagnosis of colon cancer:
Table 1
Tumor size (mm) | # with cancer | # without cancer
>10 | 15 | 3
8-10 | 17 | 6
6-8 | 10 | 9
4-6 | 5 | 20
<4 | 2 | 13(a) By choosing a threshold value of tumor size, we can calculate sensitivity and specificity
for this diagnostic test. Please compute the sensitivity and specificity using a threshold
value of 10mm, 8mm, 6mm and 4mm, respectively.
Hint: For each threshold value, reduce Table 1 to a 2×2 table of conditional
probabilities.
10mm
negative | positive
CT negative | 48 | 34
CT positive | 3 | 15Sensitivity = 15/49
Specificity = 48/51
8mm
negative | positive
CT negative | 42 | 17
CT positive | 9 | 32Sensitivity = 32/49
Specificity = 42/51
6mm
negative | positive
CT negative | 33 | 7
CT positive | 18 | 42Sensitivity = 42/49
Specificity = 33/51
BIOE420 Bioimaging
Name:_____________________________ UID: _______________________________
4mm
negative | positive
CT negative | 13 | 2
CT positive | 38 | 47Sensitivity = 47/49
Specificity = 13/51
(b) | Using the results in (a), plot the ROC curve for this test by Matlab or by hand.
Hint: A ROC curve would always pass through (0, 0) and (1, 1).
BIOE420 Bioimaging
Name:_____________________________ UID: _______________________________
Question #2 (20%):
Suppose the probability distributions of a test result for patients with and without a disease are
modeled as Gaussian distributions with different mean values and variances, as shown in Figure
1. We design a diagnostic test by selecting a threshold t0 . For a patient whose test value is below
t0 , we call it normal. Otherwise, we call it diseased. Denote the means and variances of the test
result of the normal and diseased subjects as 0 , 0 2 and 1 , 12 . Given that 0 2, 0 2 1
, 1 8,12 4 , with arbitrary unit.
Figure 1
(a). For threshold value t0 in the interval 0 t0 1 , plot the curve of sensitivity against
1-specificity (ROC) using Matlab. The sensitivity and specificity are defined: [Show Less]