The document describes using support vector machines (SVMs) to improve assessment of deep vein thrombosis (DVT) compared to the standard Wells Score method. An SVM model was trained on 159 anonymous patient records containing Wells Score information and DVT findings. The SVM with an RBF kernel achieved 100% sensitivity and 58% accuracy, outperforming the Wells Score method. This demonstrates that machine learning can enhance clinical decision-making for DVT.

1. DVT assessment using SVM
Daniel Öberg

2. Introduction
Implementation of a thrombus reporting system
Deep vein thrombosis (DVT) assessment using Support Vector
Machines

3. Why?
Every year 1.6 per 1000 inhabitants suffer from venous
thrombosis, blood cloths in their veins.
Commonly assessed by a combination of D-Dimer tests and a
questionnaire.
Can we make a system that makes the assessment better?

4. D-Dimer
A small protein fragment present in the blood after a blood
clot is degraded. High concentration of D-Dimer correlates
with thrombosis, but false positive readings can occur from
liver disease, high rheumatoid factor, inflammation, and many
other factors which makes the sensitivity low.

5. Wells Score
Gold standard for DVT clinical assessment, named Wells Score.
A simple scoring system and a yes or no questionnaire
regarding the patients medical history.
Very quick assessment as it only has 9 significant variables.

6. Assessment in real world
A combination of Wells Score and a D-dimer test reliably
excludes DVT
Often no need for painful imaging studies such as compression
ultrasonography

7. Compression Ultrasonography
Compressing the veins
Send pulses of ultrasound into the leg to find material with
different density
Note absence or presence of occluded veins
Needed to be reported

8. Compression Ultrasonography
Figure 1:Compression Ultrasonography

9. Deep Vein Thrombosis
Blood is constantly coagulating and dissolving.
This balance between the stimulating and inhibitory is sensitive.
Coagulated blood could produce blood clots
Dangerous internal bleeding otherwise

10. Rate of occurrence
If part of a cloth breaks free and is allowed to travel to the lung , we
call it a pulmonary embolism . A serious condition that 1000
patients a year die from just in Sweden. These figures should be
compared to the ~4000 who gets diagnosed with pulmonary
embolism or ~8000 patients who gets diagnosed with deep vein
thrombosis.

11. Costs
The Swedish hospitals costs of venous thromboembolism alone
was estimated to 0.375 billion SEK in 1999.
Difficulty to confirm diagnosis without thrombosonography

12. Pretest
The decision to order thrombosonography is, in several
guidelines, in large part done based entirely on pretest risk
assessment like Wells Score . The patients with low risk get
D-dimer blood test and only go on to ultrasonography if the
test is positive. The ones with high risk goes straight to
ultrasonography without getting a D-dimer test.

13. Technical Background

14. Can we improve Wells Score?
With machine learning algorithms we can figure out how to
assess deep vein thrombosis by generalising from examples.
As more data would become available in the reporting system
the better the assessment would become.

15. Support Vector Machines
Developed by Cortes & Vapnik for classification.
Finding the maximal margin of separation between two classes,
which can be seen as the generalisation, for linearly separable
patterns.

16. Support Vector Machines
With support vector classifiers the hyperplane can be described by
the unknown, u, and the margin-vector, w (see figure 2):
w · u ≥ C (1)

17. Support Vector Machines
Figure 2:Optimal hyperplane

18. Support Vector Machines
We are interested in which side the u vector is in so we project the
u onto w and if this is bigger than some constant C then we say
that u a positive sample.

19. Support Vector Machines
By setting b = −C we get our decision rule:
(w · u) + b = 0, w ∈ RN
, u ∈ RN
, b ∈ R (2)
which corresponds to the decision function:
f (x) = sign((w · u) + b) (3)

20. Support Vector Machines
The problem is that we do not know neither the w nor the b.
However adding additional constraints we can calculate them.
Taking a positive and negative sample and arbitrary setting it to
bigger and smaller than one respectively:
w · x+ ≥ 1 (4)
w · x− ≤ 1 (5)

21. Support Vector Machines
Then introducing a variable yi that is +1 for positive samples and
−1 for negative samples we can combine these into:
yi ∗ (xi · w + b) ≥ 1 (6)

22. Support Vector Machines
And with that we can add the extra constraint that:
yi ∗ (xi · w + b) − 1 = 0 (7)
should be were xi is on the margin.

23. Support Vector Machines
Now if we want the widest margin possible we could take the
difference of a negative and positive sample on the margins and
project it onto a unit normal.
WIDTH = (x+ − x−) ·
w
w
(8)

24. Support Vector Machines
Which can be simplified further to
(x+ − x−) ·
w
w
=
2
w
(9)

25. Support Vector Machines
The way one maximize this in the support vector machines
algorithm is to use Lagrange multipliers.

26. Radial Basis Function
But with the so called kernel-trick , were we map data into a richer
feature space then construct a hyperplane in that space, we are able
to classify points that were not linearly separable in its previous
space.
We call the function that maps from the vector x to another input
space φ(x).

27. Radial Basis Function
By doing this simple transformation we know need to maximize:
K(x, y) = φ(x) · φ(y) (10)

28. Radial Basis Function
Don’t need φ(x) on its own but can instead focus on K(x, y) which
we call our kernel function.
By using the radial basis kernel (RBF):
K(x, y) = e−γ x−y 2
(11)
where γ is a chosen constant, we get a great and fast nonlinear
kernel.

29. Environment
Apple iOS
C++ and Objective-C
OpenCV developed by Intel Russia research center in Nizhny
Novgorod for realtime computer vision. This library contains
implementations for both RBF and linear kernels as it adopted
the SVM/C++ library libsvm.

30. Preprocessing
159 anonymous patients DVT journals
From the journals we extracted the Wells score information and
whether a DVT or occlusion were found.
Table 1:Count of each label in dataset
DVT Nothing found
33 126
Already gone through a Wells score, heavy bias.
Yes and no converted to 1.0 and -1.0 respectively.

31. Training
Optimized C and gamma values
5 folds
C-values between 2−5 and 215
Gamma-values between 2−15 and 23

32. Baseline
Wells Score by Philip S. Wells
Gold standard for DVT assessment.

33. Baseline
Table 2:Wells score
Variable
Points
Cancer treatment during the past 6 months +1
Lower leg paralysis or plastering +1
Bed rest > 3 days or surgery < 4 weeks +1
Pain on palpation of deep veins +1
Swelling of entire leg +1
Diameter difference on affected calf > 3 cm +1
Pitting oedema (affected side only) +1
Dilated superficial veins (affected side) +1
Alternative diagnosis at least as probable as DVT -2

34. Baseline
Table 3:Clinical probability for Wells score
Low 0 total
Intermediate 1-2 total
High > 2 total

35. Results
Figure 3:Assessment Model

36. Results
Figure 4:Assessment Statistics

37. Results
Figure 5:Features

38. Results
Figure 6:Feature Statistics

39. Results
Figure 7:Journal

40. Results
Figure 8:Journal Questions

41. Results
Figure 9:Sonography

42. Results
Figure 10:Linear SVM with soft margins and different error costs compared
to Wells Score. C : 12.5

43. Results
Figure 11:SVM with RBF kernel compared to Wells Score.

44. RoC
Figure 12:

45. Results
Class Weight Accuracy
SVM RBF 0.9226 58.49%
Wells Score - MEDIUM N/A 23.12%
SVM RBF 0.8196 81.11%
SVM Linear 0.9193 65.40%
Wells Score - HIGH N/A 58.49%

46. Results
Class Weight Sensitivity Specificity
SVM RBF 0.9226 100.00% 35.71%
Wells Score - MEDIUM N/A 97.05% 3.17%
SVM RBF 0.8196 66.66% 84.92%
SVM Linear 0.9193 63.63% 65.87%
Wells Score - HIGH N/A 60.60% 57.93%

47. Balanced Error Rate
BER =
FP/(TN + FP) + FN/(FN + TP)
2
Average of both the error rate of the positive class and the error
rate of the negative class.

48. Diagnostic Odds Ratio
DOR =
TP/FP
FN/TN
Ratio of the odds of the test being positive if the subject has a
disease relative to the odds of the test being positive if the subject
does not have the disease.

49. Results
Class Weight BCR DOR
SVM RBF 0.9226 67.85% ∞
Wells Score - MEDIUM N/A 50.11% 01.08
SVM RBF 0.8196 75.79% 11.26
SVM Linear 0.9193 64.75% 03.37
Wells Score - HIGH N/A 59.27% 02.11

50. Conclusion
Possible to improve DVT assessment by using SVMs.
Able to get 100% sensitivity with 58% accuracy.
Balanced Classification Rate for Well Score was at most 02.11
whilst our highest benchmarked was 11.26 .
Using different error costs (DEC) we can tweak the sensitivity
and specificity.