Androcentrismo

In the previous section, I defined a classifier m for anesthetic depth, and showed qualitative results. Here, its discrimination power is quantified, from the perspective of a possible appli- cation as a real-time monitor for anesthetic depth. Since the classifier was defined locally (i. e. for single electrode pairs), its discrimination power can be studied in a spatially resolved way, relating the differences between the conscious and unconscious state to regions of the scalp.

The quantification was done in terms of thereceiver operating characteristic(ROC), which I introduce briefly. It deals with the question to distinguish two populations of samples, referred to as positive and negative here. Suppose that a scalar classifier m is given, which defines a ranking among the samples. A higher ranking means that a sample is more likely to come from the positive population. The aim of ROC analysis is to quantify how useful the classifier is for separating the two populations.

The probably most straightforward quantitative measure is the error probabilities of a statistical test. Such a test is defined by the choice of a threshold T, assigning the samples with m(x) ≥T to the positive population, and the others to the negative one. Since there is no canonic threshold, a measure for the discrimination potential of the classifier should take into account every possible threshold. Peterson et al. [75] propose a graph of the true positive rate (or sensitivity)

p(m(x)≥T |x∈X1) (5.3)

versus the false positive rate (or 1-specificity)

p(m(x)≥T |x∈X0), (5.4)

which they call the ROC curve. Since both quantities grow monotonically as a function ofT, the ROC curve is monotonically increasing.

As a scalar quantity for the discrimination power of a classifier, Peterson et al. propose the area under the curve (AUC). The AUC equals the probability that a randomly chosen positive sample is ranked higher than a randomly chosen negative sample. Note that the ROC curve is invariant with respect to monotonic transformations of the scalar classifier, i. e. it only depends on the ranking of the samples. It is straightforward to see that a perfect classifier has an AUC of 1, a random one has 0.5 and the inverse of a ranking with AUC=x has an AUC of 1−x.

I used the AUC for a large set of observations (all probands), as well as for subsets (a single proband). Let us take a look at the relations of these quantities. When combining data sets, the union can have an AUC far from the average of its subsets. Fig. 5.10 illustrates two examples with opposite effects. If a classifier is perfect on one subset and random on another, the discrimination can be better than the average AUC (fig. 5.10a). On the other hand, a bias of the classifier on one subset can lower the performance of the union considerably (fig. 5.10b). I analyzed the classifier m from the preceding section in terms of the ROC. Using the average ofm over all pairs of neighboring electrodes, aglobal AUC (over all probands and all electrodes) of 0.99 (baseline-unconsciousness), 0.97 (awake-unconsciousness), and 0.93 (awake- unconsciousness with common template for awake) was attained.

A spatially resolved ROC analysis (fig. 5.11) showed a good separation, especially in the frontal and temporal regions. There are regions where the separation fails, which depend on the individual and mainly appear in the occipital region of the scalp.

Fig. 5.10:The ROC for merged data sets. a) The global AUC can be larger than the average over the merged sets. b) An individual bias can reduce the discrimination power considerably.

The comparison of fig. 5.11 b and c shows that the personalized template is an effective means to increase the discrimination power. While technically not possible with the awake regime, it is in principle applicable to the beginning of the descent regime.

Some of the individuals presented in fig. 5.11 show isolated zones of low discrimination, which are often related to mis-classifications in fig. 5.9. These areas are generally well defined and not changing over time. Thus, these were probably not random fluctuations but pecu- liarities of the individual. The affected areas are situated mainly in the occipital region. The locations of the individual areas of low discrimination are generally similar for the baseline and the awake reference regime.

The baseline regime is the primary choice for the conscious reference and can in principle be measured directly before a surgery, allowing to generate a personalized template. In the context of monitoring anesthetic depth however, the aim is to detect intra-operative awareness. It is therefore not clear which regime is an appropriate representation for those intermittent moments of consciousness. I expect those moments to be more similar to the awake regime, hence for the measuring of anesthetic depth the awake regime would be the preferred reference regime.

From the ROC results, the classifier based on the the baseline regime shows the highest discrimination power (with proband #11 being the exception from the rule). Under identical conditions (i. e. when used with a personalized template), the awake regime gives a slightly lower performance. Since a sample of the awake regime can generally not be recorded in ad- vance, fig. 5.11c probably gives the most realistic approach for the detection of intra-operative awareness in a surgery situation (awake with common template versus unconsciousness), with an AUC of 0.93.

For ease of application, it is preferable to restrict the measurement to a small set of elec- trodes, ideally located in the frontal area. In this study, the four front electrodes Fp1, Fp2,

Fig. 5.11: Left: Topogram of the discrimination power (AUC) over all individuals. Right: Discrimina- tion power for each individual. a) Baseline versus unconsciousness (global AUC 0.99) b) Awake versus unconsciousness (global AUC 0.97) c) Awake versus unconsciousness (common template for awake, global AUC 0.93). The EEG data was digitally filtered (0.5−50 Hz), equidistant sampling pattern with sequence lengthn= 5 and delayτ = 6 ms. The classification was based on samples with a length of 6 s. For every pair of neighboring electrodes, the population comprised 52 samples per individual, for the conscious and unconscious reference regimes, respectively. The numbers beneath the topograms refer to the probands.

reference regimes

common template pers. template

ev

aluation

regimes

bl/un aw/un bl/aw bl/un aw/un bl/aw bl/un 0.926 0.922 0.986 0.928

aw/un 0.926 0.932 0.875 0.974

bl/aw 0.760 0.975

Table 5.1:Discrimination power of different measures, evaluated on different pairs of regimes in terms of the global AUC. The baseline, unconsciousness and awake regimes are abbreviated asbl, unandaw. As mentioned, ’personalized template’ only refers to the conscious states.

F3 and F4 performed as well as the complete set of electrodes (AUC 0.985 versus 0.986, see fig. 5.12). There is a range of high specificity (>0.95) where the measure based on the front electrodes performed better. However, the difference was small and could be an artifact of the small sample size. The AUC values given here refer to sliding windows of length 6s, which determines the reaction time in which a case of intra-operative awareness would be detected with the given sensitivity and specificity.

Fig. 5.12:ROC curve for single elec- trode pairs (gray, average AUC 0.92), the whole data set (red, AUC 0.99), and combinations of the frontal elec- trodes FP1, FP2, F3 and F4 (green, AUC 0.98). The reference regimes are baseline (personalized template) and unconsciousness.

It should be noted that the global AUC values are larger than the average of the AUC topogram in fig. 5.11. To understand this, note that when averaging over a spatially resolved classifierm, the electrode pairs with|m| 1 have a small weight. For instance, the average of a perfect classifier (AUC= 1, with |m| ≈1) and one that fluctuates around zero (AUC= 0.5) is still perfect for sufficiently small fluctuations.

Table 5.1 gives a summary of the global AUC for the proposed measures, evaluated on pairs from the baseline, unconsciousness and awake regimes. A personalized template for the awake states (which is not possible in practice) increased the AUC considerably. Note that some of the combinations are not reasonable, like distinguishing between bl/aw using a measure with reference regimes bl/un.

In conclusion, the transfer symbols of neighboring channels, which have proven themselves as a powerful description in the application to the coupled map lattice of chapter 4, are a promising description for the EEG of different states of consciousness and the transitions between them. There are practical calibration difficulties and individual exceptions, but the results support the general conclusion that the symbolic description depends on the state of consciousness in a systematic and consistent way.