Reply to "Prediction of epileptic seizures: are nonlinear methods relevant?"

Abstract

for tests of relevant null hypotheses 6,7 and their immediate relation to the de-tection method in the diagnosis of medical disorders. Ultimately, the op-erational use of proposed complicated statistics can be justified only by show-ing that they out-perform well-under-stood traditional statistics (such as variance) or provide complementary information. The fact that the signal it-self may be demonstrably nonlinear is simply not the relevant question when event detection is the aim. To establish the efficacy of any new detection approach to medical diagno-sis, we argue first for surrogate data tests against a null hypothesis relevant to some simple traditional statistic, and second for quantification of the false alarm rate. In the present case, the first point could be addressed using surrogates that preserve the temporal variation in the variance; the second point would require an experimental design including long records of seizure-free data. Competing interests statement The authors declare that they have no compet-ing financial interests. Martinerie et al. reply—Until 1998, neu-roscientists thought that epileptic seizures began abruptly, just a few sec-onds before clinical onset. It was dur-ing that year that two independent studies 4,8 showed that the non-linear time series analysis of EEG data could reveal dynamical changes several min-utes before seizure onset. The useful-ness of non-linear measures for the detection of pre-ictal changes has since been confirmed 9 . This new approach has opened a new field of seizure antic-ipation and defined a framework for better understanding of seizure genera-tion mechanisms. McSharry et al. have re-analyzed our 1998 database and have shown that the non-linear index is sensitive to am-plitude variance fluctuation. We have been aware of this limitation for some time now. We developed, in 1999, a new method 10 that did not involve the reconstruction of the dynamics from the amplitude of the signal, presenting a number of practical advantages over our previous method. The new method measures similarity to quantify the extent to which the EEG dynamics, re-constructed from the phase informa-tion, differ between periods taken at distant moments in time. The phase is defined as the time between two suc-cessive zero-crossing intervals. This relative measure reveals the spatial dis-tribution of pre-ictal dynamic changes (both linear and non-linear) that in-volve the epileptogenic area but do not seem to be confined to the restricted ictal onset region. Furthermore, it is very robust against noise and artifacts, and fast enough to be carried out in real time. The surrogate data that we had se-lected for the 1998 study to test the presence of deterministic structure in the time series 4 had been built for each block of data (20 s; this may not have been not clear in the paper) and were designed to reject a null hypothesis of a non-linear transformation of linearly filtered noise. Thus, the variances of the raw data and surrogate data were the same. We found a statistical differ-ence between the values of C(r 0) calcu-lated from the raw data and those calculated from the surrogate data, which led us to reject this null hypoth-esis. We know that one should be ex-tremely careful with the use of surrogate procedures (which can be very sensitive to the presence of spikes in the data and detect spurious non-linearity 11 , for example). It is advisable to obtain consistent results with more than one type of surrogate, to get an indication of non-linear deterministic structure. New strategies and algo-rithms are now available 12 . In conclusion, our recent results