Depressive symptoms were quantified by the MADRS, administered by the attending physician, and the BDI which was completed by patients. The assessment of depressive symptoms was done at baseline and Day 28 of the trial. The response to treatment was defined as a reduction of the final MADRS score by more than 50 %. A final MADRS score less than, or equal to, 10 corresponded to remission.

The EEG recording was done at baseline and Days 7 and 28 of the trial. In this work we analyzed the baseline recording. The 10–20 international standard was used to position 21 Ag/AgCl electrodes (impedance below 5 kΩ). The ground electrode was placed between Fpz and Fz. Two referential montages were used: the conventional linked mastoid (LM) and the referential (REF) montage for which the reference electrode was mounted between Fz and Cz. The EEG was recorded through a Grass Telefactor Comet data acquisition system with the sampling frequency of 200 Hz and bandpass of 0.3–70 Hz (Natus Medical Inc., Pleasanton, CA). The EEG waveforms corresponding to two referential montages were recorded simultaneously. We also generated the average reference (ARE) montage using the instantaneous average of all 21 electrodes as a common reference. The subjects remained in the supine position in a quiet room. The measurement consisted of three 5-min intervals. During the first interval, subjects had the eyes-open. The eyes-closed intervals were separated by a short (approximately 10 s) blinking interval.

The continuous wavelet transform of signal s(t), such as EEG record, was defined as:
(Latka et al. 2003, 2005). In the above formula, a is the scale and t ₀ indicates the localization of the wavelet. We refer to the square of the complex modulus of Ws as the wavelet power. In this work we will use the wavelet power averaged over time interval:
The dual localization of wavelets in time and frequency enables us to associate a pseudo-frequency f _a with the scale a
where f _c is the center frequency and δt is the sampling period of the signal s(t). Thus, the value of wavelet coefficient reflects the local properties of the signal at a given scale (pseudo-frequency). From the plethora of existing mother functions one should judiciously choose one that is effective in extracting the features of a signal that are important for the problem to be resolved. Herein, we employ the complex Morlet
where center frequency f _c and bandwidth parameter f _b may be independently adjusted. In Fig. 1, we present the time averaged wavelet power w(f) of a monochromatic wave with frequency 10 Hz (value close to the average frequency of alpha waves in healthy adult subjects) plotted as a function of wavelet transform pseudofrequency f _a. It is apparent that for f _c  = 1.8 and f _b  = 1 the width of the wavelet power distribution essentially covers the alpha band (8–13 Hz). For this choice of the complex Morlet parameters and pseudo-frequency f _a  = 10 Hz, the wavelet power is just the weighted average of power in the entire alpha band. In other words, wavelet smooths out the alpha band spectrum. The use of a just single pseudo-frequency to characterize the power in the alpha range is not by all means obvious. In this work we were interested in the topography of the alpha wave power. Therefore, we normalize power w(f;i) in the i-th EEG channel by the total power

Even if the dominant alpha frequency of the subject is different than the chosen value of 10 Hz, the wavelet power is approximately proportionally reduced in all channels, preserving the topography of the normalized wavelet power. The dominant alpha frequency, averaged over all channels and patients, was equal to 9.7 Hz for responders and 9.3 Hz for non-responders. Moreover, there were no statistically significant differences between responders and non-responders in any of the analyzed channels.

Many authors advocate the use of a narrow Fourier band cantered around the dominant alpha frequency to characterize the resting state or task-related changes in alpha rhythm (Klimesch 1997, 1999). In Fig. 1, we provide an example of Fourier spectrum of a depressive patient with broad distribution of alpha power without a distinctive dominant frequency. These traits of Fourier spectrum are common in patients and motivated us to use a broad analysing wavelet.

Log transformation is frequently used in analysis of physiological data. The question arises as to whether logarithm of wavelet power should be used in Eq. (5). The justification of such transformation is the assumption that susceptibility to antidepressant treatment is multiplicatively related to EEG alpha wavelet power. Although there is no a priori justification of such relation, the application of log transformation is a viable modification of the presented prediction algorithm.

In the eyes-open condition, we calculated alpha wavelet power for contiguous EEG data segments without manual or software excising of eye blinks. Therefore, it is worth mentioning that the average number of blinks per minute in the eyes-open interval was similar for responders and non-responders (28 ± 15 vs. 25 ± 21).

A neurophysiologist selected a 2 min data segment from the eyes-open interval which, apart from eye blinks, was free from artefacts. The 2 min artefact-free EEG segment was also extracted from the first eyes-closed interval. Until the end of study, neither the neurophysiologist nor the persons who performed data analyses had access to patients’ treatment records. For both referential montages (LM and REF) and average reference, we calculated the continuous wavelet transform using the Morlet mother function with parameters f _c  = 1 and f _b  = 1.8. The calculations were performed for the pseudo-frequency 10 Hz. The wavelet power over the entire data segment was averaged for each EEG channel. Finally, the averaged wavelet power in each channel was normalized for the total averaged wavelet power from all 21 channels. Consequently, the normalized wavelet power was independent of the subject’s EEG amplitude. Wavelet transforms, in stark contrast to traditional Fourier methods, are intrinsically more robust with respect to eye movement or blink artefacts. This property enabled to calculate the alpha wavelet power for continuous EEG data segments without manual or software excising of eye blinks.

The frequency of a peak value of wavelet power in the interval 8–13 Hz is referred to as a dominant alpha wave frequency. We defined the alpha power ratio as a ratio of the sum of alpha wavelet power at frontal (Fp1, Fp2, Fpz) sites to the sum of alpha power at occipital (O1, O2, Oz) sites.

From the mathematical point of view, prediction of treatment response is equivalent to binary classification based upon a single criterion (such as normalized alpha wavelet power or alpha power ratio). The receiver operating characteristic (ROC) provides a rigorous framework for such classification (Hanley 1989). This framework enables to determine an optimal classification threshold and a qualitative assessment of statistical significance. The area under the receiver operating characteristic curve (AUC) was used to quantify the performance of the binary classifier. When the classification was feasible we calculated the optimal threshold value (cut-off point) as well as the sensitivity, specificity, and accuracy.

It turns out that regardless of the chosen montage prediction of antidepressant treatment, the response is usually possible at several EGG sites. Therefore, we elected to test the prediction algorithm based on a response index, i.e., the percentage of channels in which the patient was classified as a responder. In other words, the patient is classified as a responder when this index is greater than 50 %; otherwise he is assigned to the non-responder category. The proposed classification scheme may seem arbitrary, but it is reminiscent of the nearest neighbor pattern classification introduced by Cover and Hart (1967). The existence of two classes (responders and non-responders) leads to the classification threshold equal to 50 %. Ideally, such an index should assume the value of 100 % for responders and 0 % for non-responders.