COMPROBACIÓN DE HIPÓTESIS

To compare the quality of the approximation k-MLIQ search to existing methods and therefore to demonstrate the superiority of considering corre- lations between features, we conducted three additional methods. The first method was glioma grading which was based on the presence of contrast en- hancement executed by neuroradiologist experts. The second method was a

k-MLIQ search not considering correlations which we will call axis-parallel

k-MLIQ search and the third one was ak-NN approach using Euclidean dis- tances of the weighted mean values of the nGMMs as a distance measure, which will be called k-NN search in the following.

5.2.2.1 Glioma Grading Based On Contrast Enhancement

Glioma grading based on conventional MRI sequences was performed by two independent neuroradiologists in consensus who were blinded to the histo- logical information. They visually inspected FLAIR as well as pre- and post contrast T1-weighted images. Tumors that showed any pathological contrast enhancement in the contrast-enhanced T1-weighted sequence were diagnosed as high-grade gliomas. In the absence of any contrast enhancement a low- grade glioma was diagnosed.

5.2.2.2 Axis-parallel k-MLIQ Search

To test, whether the non-axis parallel k-MLIQ method is superior to a k- MLIQ method not considering feature correlations a k-MLIQ of axis parallel GMMs was carried out, not considering feature correlations of the GMMs.

Instead of using the entire covariance matrix Σi of the Gaussian compo-

covariance matrices. Therefore, the joint Probability Density Value for the axis-parallel k-MLIQ search can be defined by the following formula:

P DVap(G∗,G0) = m∗ X i=1 m0 X j=1 w∗_iw0_j·N(µ_i∗, σ∗_i +σ_j0, µ0_j) ! . (5.17)

As for the non-axis parallel method, the theorem of Bayes is used to convert joint P DVaps to absolute probabilities with |DB|=n.

Pap(G∗,G0) =

P DVap(G∗,G0)

Pn

i=1P DVap(Gi∗,G0)

(5.18)

The T Score is obtained the same way as for the approximation k-MLIQ search using T Score(_G∗, k₋MLIQ) = X G∗_∈k−MLIQ I/II⊆k−MLIQ Pap(G∗,G0)− X G∗_∈k−MLIQ III⊆k−MLIQ Pap(G∗,G0). (5.19)

5.2.2.3 k-Nearest Neighbor Search

The k-NN search approach was solely based on the weighted mean values of the Gaussian components. Euclidean distances of these weighted means were used to determine the distances between the tumor patients. In contrast to the k-MLIQ results the k-NN search did not provide any probabilities but rather distances corresponding to the dissimilarity between two objects. Hence, thekobjects having the smallest distance were returned by thek-NN search.

To distinguish the predicted grade returned by thek-NN search the most frequently predicted grade in the set of k-NN was chosen.

5.2.3

Quality Measures

In order to receive quality measures for the three presented methods (ap- proximationk-MLIQ search, axis-parallel k-MLIQ search, andk-NN search) we used leave-one-out cross validation, which is a special case of the X-fold cross validation [Koh95] with X = n which is the number of observations (= patients in the database). The validation was performed for each of the n

patients by completely excluding the respective patient from the database (resulting in a new database size of (n-1)). The test patient p was then used as query object in the k-MLIQ/k-NN. In total, n = 37 (number of patients in our database) MLIQs/NNs were executed for obtaining quality measures of the methods.

Since the k-MLIQ and the k-NN methods include a parameter k which had to be assigned we executed nested leave-one-out cross validation to ad- equately evaluate the methods [RHPM04]. Thereby, having excluded the test patient p from the database resulting in a database size of (n-1), each remaining patient had to be excluded to determine the best fitting value for the parameter k. This particular value for k was then assigned to the

k-MLIQ/k-NN search for grading patient p. Thus, using nested leave-one- out cross validation we obtained an independent validation set, since the

k-MLIQ/k-NN only considered those patients which were presently located in the database. All algorithms concerning the k-MLIQ/k-NN search were implemented in Java and run on a 2.4 GHz Intel Core 2 Duo Macintosh computer.

The accuracy, sensitivity, specificity, positive predicted value (PPV), and negative predicted value (NPV) were calculated for the grading results of all four methods. Tumors which were histologically grade III and subse- quently found as grade III tumors, were considered as True Positive findings; grade I/II tumors which were identified as low-grade gliomas and found at histological examination to be grade I/II, were considered as True Negative findings.

For statistical analysis SPSS 18.0 for Macintosh (SPSS Inc, Chicago, IL, USA) was used. To compare the quality of all glioma grading methods, the Area Under the Curve (AUC) of the Receiver Operating Characteristic (ROC) curve was carried out. After drawing the ROC curves (one for each method) the AUC can be obtained. Thereby, the AUC values can range from 0 to 1, where a diagonal ROC curve (lower left corner to upper right corner) having an AUC of 0.5 (worst possible value) corresponds to random guessing and a AUC of 1 (most desired value) corresponds to a perfect grading result. The considered method had discriminatory power if the curve is significantly different from the diagonal.