Matrix of Lags: A tool for analysis of multiple dependent time series applied for CAP scoring

Multiple methods have been developed to assess what happens between and within time series. In a particular type of these series, the previous values of the currently observed series are contingent on the lagged values of another series. These cases can commonly be addressed by regression. However, a model selection criteria should be employed to evaluate the compromise between the amount of information provided and the model complexity. This is the basis for the development of the Matrix of Lags (MoL), a tool to study dependent time series.

For each input, multiple regressions were applied to produce a model for each lag and a model selection criterion identifies the lags that will populate an auxiliary matrix. Afterwards, the energy of the lags (that are in the auxiliary matrix) was used to define a row of the MoL. Therefore, each input corresponds to a row of the MoL. To test the proposed tool, the heart rate variability and the electrocardiogram derived respiration were employed to perform the indirect estimation of the electroencephalography cyclic alternating pattern (CAP) cycles. Therefore, a support vector machine was fed with the MoL to perform the CAP cycle classification for each input signal. Multiple tests were carried out to further examine the proposed tool, including the effect of balancing the datasets, application of other regression methods and employment of two feature section models. The first was based on sequential backward selection while the second examined characteristics of a return map.

The best performance of the subject independent model was attained by feeding the lags, selected by sequential backward selection, to a support vector machine, achieving an average accuracy, sensitivity, specificity and area under the receiver operating characteristic curve of, respectively, 77%, 71%, 82% and 0.77.

The developed model allows to perform a measurement of a characteristic marker of sleep instability (the CAP cycle) and the results are in the upper bound of the specialist agreement range with visual analysis. Thus, the developed method could possibly be used for clinical diagnosis.