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

https://doi.org/10.1016/j.cmpb.2020.105314Get rights and content

Highlights

  • •

    A new tool for depending time series examination was developed.

  • •

    CAP can be estimated trough the analysis of dependent time series.

  • •

    The CAP scoring results are in the range of specialist agreement.

Abstract

Background

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.

Methods

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.

Results

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.

Conclusions

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.

Introduction

Time series analysis is based on the assumption that data points, which are taken over specific periods, can have an internal structure that can reveal important information of an event. The series is usually ordered in a sequence of values that are related to a variable, at equally spaced time intervals, and is used to determine characteristics of the data [1].

Multiple methods have been developed to study what happens within and between time series and, commonly, the series can be defined by a linear combination of previous values of the currently observed series that may also be contingent on lagged values of another series [1]. Regression can be used to address these cases, explaining the relationship between dependent and independent variables.

In the study of physiological signals, it is common to have a strong relationship between dependent and independent variables. Thus, the employment of regression can provide a model to analyze these variables based on lagged values. However, a compromise between the amount of information provided and the model complexity needs to be taken into consideration. Consequently, a model selection method should be used to avoid overfitting or underfitting the model.

The hypothesis tested in this work is that a matrix built with the measured energy of a fixed number of lags, named Matrix of Lags (MoL), can be a relevant tool for time series analysis of systems with dependent and independent variables. For this purpose, the electrical activity of the heart, measured by an electrocardiogram (ECG), was analyzed to perform an indirect detection of a sleep stability metric, the electroencephalography (EEG) Cyclic Alternating Pattern (CAP). It is a characteristic periodic activity from the sleep microstructure [2], [3], defined in the non-Rapid Eye Movement sleep (NREM), composed by an activation phase (A phase) that is followed by a quiescent phases (B phase), each lasting between 2 and 60 s [4].

CAP is an EEG marker of sleep instability [5] and is usually analyzed by performing a full-night polysomnography (PSG) that is considered the gold standard to study sleep. However, PSG is a slow and expensive process that requires specialized technicians and is unavailable to a large group of the world population. Multiple research has been recently developed to perform the sleep analysis with home monitoring devices that use fewer sensors and perform an automatic scoring of the recorded signals [6].

Despite this effort, EEG is a difficult sensor for self-assembly, limiting the possible applications of sleep quality metrics in this kind of devices. Thus, an indirect estimation of CAP, performed by analyzing the ECG signal, can be more suitable for home-monitoring devices, allowing to assess the sleep quality [7] and possibly help in the diagnosis of sleep quality deficits and sleep related disorders. The assumption of this work is that the concept of CAP could probably be extended to a broader multivariable context, as referred by Thomas et al. [8], considering the concept of a CAP epoch (a period where more than a defined percentage of its durations was scored as a CAP cycle).

The relationship between CAP and the ECG signals was first discovered by Thomas et al. [8] and Ibrahim et al. [9], examining the cardiopulmonary coupling between the heart rare variability and ECG derived respiration (EDR). They have verified that the energy in the high frequency band (0.1–0.4 Hz) was associated with deep sleep, physiologic respiratory sinus arrhythmia and absence of CAP periods while the energy in the very low and low frequency bands (respectively 0–0.01 Hz and 0.01–0.1 Hz) was related with wake or Rapid Eye Movement (REM) periods and the presence of CAP [8], [10]. Therefore, the main goal of this work was to develop the MoL as a tool for time series analysis. This tool was tested in the examination of data from a single-lead ECG to study the connection between the heart rate variability, through the normal-to-normal sinus interbeat intervals (N–N series), and the variability of the respiratory volume, measured by the EDR, to assess the occurrence of the CAP cycles. This connection was studied by feeding the information regarding the energy of the lags, which compose the MoL, to a machine learning classifier to perform the time window (minute by minute) classification.

The paper is organized as follows: the employed materials and methods are described in Section 2; the performance evaluation of the developed algorithms is presented in Section 3; Section 4 presents the discussion regarding the attained results; Section 5 concludes the article.

Section snippets

Materials and methods

The development of the MoL and application for the CAP cycle analysis is presented in this work. The single-lead ECG signals, from a public database (Section 2.1), were used to produce both the N–N series and EDR signal with a minute based CAP label (Section 2.2). Both N–N series and EDR signal were employed to create the MoL (Section 2.3). A classification was then performed (Section 2.5), either directly with the MoL or with the most relevant lags selected by a feature selection method (

Performance evaluation

To allow a fair comparison of the results, the parameters of the SVM were kept the same for all the simulations. Random sampling was employed on the data D creating two mutually exclusive sets used as 2 fold Cross Validation (CV), with subject independence, in each iteration: training M ∈ D and testing N ∈ D. The process was repeated 50 times, to achieve statistical significance, and the averaged value was considered for each performance metric.

The direct application of the MoL as features for

Discussion

Most of the methods proposed in the state of the art were developed for the estimation of the CAP A phases by examining specific features from the characteristic EEG bands [24]. These features were then fed to a classifier, typically developed using a machine learning approach such as Linear Discriminant Analysis (LDA), to create models which achieved a performance that ranged from 68% to 86% [25], [26]. A brief introduction to some of the details of the features employed by these models is

Conclusion

A method for time series analysis was developed and multiple tests were performed to further assess the performance for the CAP cycles estimation. This work has a special interest for home monitoring devices since the method is not computational demanding and, for the studied case, only data from a single-lead ECG is needed.

Three model selection criteria were tested and the indirect CAP cycle detection was performed by using the MoL as features. The most relevant lags were selected by SBS and

Declaration of Competing Interest

All authors declare no conflicts of interest in this paper.

Acknowledgments

Acknowledgment to the Portuguese Foundation for Science and Technology for their support through Projeto Estratégico LA 9 - UID/EEA/50009/2019.

Acknowledgment to ARDITI – Agência Regional para o Desenvolvimento da Investigação, Tecnologia e Inovação under the scope of the Project M1420-09-5369-FSE-000001 - PhD Studentship.

Acknowledgement to the Project MITIExcell co-financed by Regional Development European Funds, for the Operational Programme “Madeira 14-20” – EIXO PRIORITÁRIO 1, of Região

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