Bivariate Measures Research Articles

Factores asociados a anomalías congénitas en neonatos del Cauca

BackgroundCongenital anomalies are development defects associated with causes present before, during and after conception. Globally they affect 2-3% of all newborns, and are between second and fifth place as cause of infant mortality in Latin America. ObjectiveTo determine risk factors associated with birth defects in infants in three health institutions in Popayan, Cauca. MethodsA case-control study with incident cases was carried out. The study population was all infants of the three participating institutions during a 10 month period. The sample size was 87 cases (case:control ratio, 1:1). Sociodemographic variables, current and previous history of pregnancies, and environmental and infectious exposure were measured. Statistical analyses were based on description of frequencies and means, bivariate analysis and measures of association (disparity ratio and χ2). ResultsNinety-eight cases and 98 matched controls were included; 26.5% came from urban areas and 86.7% belonged to lower socioeconomic strata. The most frequent congenital anomalies were of multi-systemic type (18.4%), gastrointestinal (14.3%), and cardiovascular, musculoskeletal and craniofacial (11.2% each). Twenty-four cases died. The bivariate analysis showed associations between congenital anomalies and consumption of folic acid from first trimester (OR=0.8; 95% CI 0.67-0.94), exposure to electrical transformers (OR=1.7; 95% CI 1.1-2.8), consanguinity/origin of a same village (OR=1.4; 95% CI 1.0-1.9), and maternal age greater than or equal to 35 years (OR=1.4; 95% CI 1.0-1.9). ConclusionCongenital anomalies are a major cause of child morbidity and mortality, and are often associated with factors likely to be identified and even prevented.

A rule-based seizure prediction method for focal neocortical epilepsy

ObjectiveIn the present study, we have developed a novel patient-specific rule-based seizure prediction system for focal neocortical epilepsy. MethodsFive univariate measures including correlation dimension, correlation entropy, noise level, Lempel-Ziv complexity, and largest Lyapunov exponent as well as one bivariate measure, nonlinear interdependence, were extracted from non-overlapping 10-s segments of intracranial electroencephalogram (iEEG) data recorded using electrodes implanted deep in the brain and/or placed on the cortical surface. The spatio-temporal information was then integrated by using rules established based on patient-specific changes observed in the period prior to a seizure sample for each patient. The system was tested on 316h of iEEG data containing 49 seizures recorded in 11 patients with medically intractable focal neocortical epilepsy. ResultsFor seizure occurrence periods of 30 and 50min our method showed an average sensitivity of 79.9% and 90.2% with an average false prediction rate of 0.17 and 0.11/h, respectively. In terms of sensitivity and false prediction rate, the system showed superiority to random and periodical predictors. ConclusionsThe nonlinear analysis of iEEG in the period prior to seizures revealed patient-specific spatio-temporal changes that were significantly different from those observed within baselines in the majority of the seizures analyzed in this study. SignificanceThe present results suggest that the patient specific rule-based approach may become a potentially useful approach for predicting seizures prior to onset.

Inadequate Bivariate Measures of Health Inequality: The Impact of Income Distribution*

AbstractBivariate measures of health inequality are influenced by changes in two variables: health and a socioeconomic variable, such as income. For these measures, what is reported as an increase in health inequality might just as well be a reduction in income inequality. In particular, several papers have found that socioeconomic health inequalities in Nordic countries are no less than in other European countries. The correct interpretation could just be that income inequality is no higher in Nordic countries than in the rest of Europe. The problem is especially profound when the causality is running from health to income.

Estimating true brain connectivity from EEG/MEG data invariant to linear and static transformations in sensor space

The imaginary part of coherency is a measure to investigate the synchronization of brain sources on the EEG/MEG sensor level, robust to artifacts of volume conduction meaning that independent sources cannot generate a significant result. It does not mean, however, that volume conduction is irrelevant when true interactions are present. Here, we analyze in detail the possibilities to construct measures of true brain interactions which are strictly invariant to linear spatial transformations of the sensor data. Specifically, such measures can be constructed from maximization of imaginary coherency in virtual channels, bivariate measures as a corrected variate of imaginary coherence, and global measures indicating the total interaction contained within a space or between two spaces. A complete theoretic framework on this question is provided for second order statistical moments. Relations to existing linear and nonlinear approaches are presented. We applied the methods to resting state EEG data, showing clear interactions at all bands, and to a combined measurement of EEG and MEG during rest condition and a finger tapping task. We found that MEG was capable of observing brain interactions which were not observable in the EEG data.

On the spectral formulation of Granger causality

Spectral measures of causality are used to explore the role of different rhythms in the causal connectivity between brain regions. We study several spectral measures related to Granger causality, comprising the bivariate and conditional Geweke measures, the directed transfer function, and the partial directed coherence. We derive the formulation of dependence and causality in the spectral domain from the more general formulation in the information-theory framework. We argue that the transfer entropy, the most general measure derived from the concept of Granger causality, lacks a spectral representation in terms of only the processes associated with the recorded signals. For all the spectral measures we show how they are related to mutual information rates when explicitly considering the parametric autoregressive representation of the processes. In this way we express the conditional Geweke spectral measure in terms of a multiple coherence involving innovation variables inherent to the autoregressive representation. We also link partial directed coherence with Sims' criterion of causality. Given our results, we discuss the causal interpretation of the spectral measures related to Granger causality and stress the necessity to explicitly consider their specific formulation based on modeling the signals as linear Gaussian stationary autoregressive processes.

Altered resting state complexity in schizophrenia

The complexity of the human brain's activity and connectivity varies over temporal scales and is altered in disease states such as schizophrenia. Using a multi-level analysis of spontaneous low-frequency fMRI data stretching from the activity of individual brain regions to the coordinated connectivity pattern of the whole brain, we investigate the role of brain signal complexity in schizophrenia. Specifically, we quantitatively characterize the univariate wavelet entropy of regional activity, the bivariate pairwise functional connectivity between regions, and the multivariate network organization of connectivity patterns. Our results indicate that univariate measures of complexity are less sensitive to disease state than higher level bivariate and multivariate measures. While wavelet entropy is unaffected by disease state, the magnitude of pairwise functional connectivity is significantly decreased in schizophrenia and the variance is increased. Furthermore, by considering the network structure as a function of correlation strength, we find that network organization specifically of weak connections is strongly correlated with attention, memory, and negative symptom scores and displays potential as a clinical biomarker, providing up to 75% classification accuracy and 85% sensitivity. We also develop a general statistical framework for the testing of group differences in network properties, which is broadly applicable to studies where changes in network organization are crucial to the understanding of brain function.

A Time-Frequency-Based Approach to Phase and Phase Synchrony Estimation

Time-varying phase synchrony is an important bivariate measure that quantifies the dynamics between nonstationary signals and has been widely used in many applications including chaotic oscillators in physics and multichannel electroencephalography recordings in neuroscience. Current state-of-the-art in time-varying phase estimation uses either the Hilbert transform or the complex wavelet transform of the signals. Both of these methods have some major drawbacks such as the assumption that the signals are narrowband for the Hilbert transform and the nonuniform time-frequency resolution inherent to the wavelet analysis. In this paper, a new phase estimation method based on the Rihaczek distribution and Reduced Interference Rihaczek distribution belonging to Cohen's class is proposed. These distributions offer phase estimates with uniformly high time-frequency resolution which can be used for defining time and frequency dependent phase synchrony. Properties of the phase estimator and the corresponding phase synchrony measure are evaluated both analytically and through simulations showing the effectiveness of the new measures compared to existing methods.

Review of the methods of determination of directed connectivity from multichannel data.

The methods applied for estimation of functional connectivity from multichannel data are described with special emphasis on the estimators of directedness such as directed transfer function (DTF) and partial directed coherence. These estimators based on multivariate autoregressive model are free of pitfalls connected with application of bivariate measures. The examples of applications illustrating the performance of the methods are given. Time-varying estimators of directedness: short-time DTF and adaptive methods are presented.

On a Possible Relationship between Linguistic Expertise and EEG Gamma Band Phase Synchrony.

Recent research has shown that extensive training in and exposure to a second language can modify the language organization in the brain by causing both structural and functional changes. However it is not yet known how these changes are manifested by the dynamic brain oscillations and synchronization patterns subserving the language networks. In search for synchronization correlates of proficiency and expertise in second language acquisition, multivariate EEG signals were recorded from 44 high and low proficiency bilinguals during processing of natural language in their first and second languages. Gamma band (30–45 Hz) phase synchronization (PS) was calculated mainly by two recently developed methods: coarse-graining of Markov chains (estimating global phase synchrony, measuring the degree of PS between one electrode and all other electrodes), and phase lag index (PLI; estimating bivariate phase synchrony, measuring the degree of PS between a pair of electrodes). On comparing second versus first language processing, global PS by coarse-graining Markov chains indicated that processing of the second language needs significantly higher synchronization strength than first language. On comparing the proficiency groups, bivariate PS measure (i.e., PLI) revealed that during second language processing the low proficiency group showed stronger and broader network patterns than the high proficiency group, with interconnectivities between a left fronto-parietal network. Mean phase coherence analysis also indicated that the network activity was globally stronger in the low proficiency group during second language processing.

Identification of Preseizure States in Epilepsy: A Data-Driven Approach for Multichannel EEG Recordings

The retrospective identification of preseizure states usually bases on a time-resolved characterization of dynamical aspects of multichannel neurophysiologic recordings that can be assessed with measures from linear or non-linear time series analysis. This approach renders time profiles of a characterizing measure – so-called measure profiles – for different recording sites or combinations thereof. Various downstream evaluation techniques have been proposed to single out measure profiles that carry potential information about preseizure states. These techniques, however, rely on assumptions about seizure precursor dynamics that might not be generally valid or face the statistical problem of multiple testing. Addressing these issues, we have developed a method to preselect measure profiles that carry potential information about preseizure states, and to identify brain regions associated with seizure precursor dynamics. Our data-driven method is based on the ratio S of the global to local temporal variance of measure profiles. We evaluated its suitability by retrospectively analyzing long-lasting multichannel intracranial EEG recordings from 18 patients that included 133 focal onset seizures, using a bivariate measure for the strength of interactions. In 17/18 patients, we observed S to be significantly correlated with the predictive performance of measure profiles assessed retrospectively by means of receiver-operating-characteristic statistics. Predictive performance was higher for measure profiles preselected with S than for a manual selection using information about onset and spread of seizures. Across patients, highest predictive performance was not restricted to recordings from focal areas, thus supporting the notion of an extended epileptic network in which even distant brain regions contribute to seizure generation. We expect our method to provide further insight into the complex spatial and temporal aspects of the seizure generating process.

Multivariate Empirical Mode Decomposition for Quantifying Multivariate Phase Synchronization

Quantifying the phase synchrony between signals is important in many different applications, including the study of the chaotic oscillators in physics and the modeling of the joint dynamics between channels of brain activity recorded by electroencephalogram (EEG). Current measures of phase synchrony rely on either the wavelet transform or the Hilbert transform of the signals and suffer from constraints such as the limit on time-frequency resolution in the wavelet analysis and the prefiltering requirement in Hilbert transform. Furthermore, the current phase synchrony measures are limited to quantifying bivariate relationships and do not reveal any information about multivariate synchronization patterns, which are important for understanding the underlying oscillatory networks. In this paper, we address these two issues by employing the recently introduced multivariate empirical mode decomposition (MEMD) for quantifying multivariate phase synchrony. First, an MEMD-based bivariate phase synchrony measure is defined for a more robust description of time-varying phase synchrony across frequencies. Second, the proposed bivariate phase synchronization index is used to quantify multivariate synchronization within a network of oscillators using measures of multiple correlation and complexity. Finally, the proposed measures are applied to both simulated networks of chaotic oscillators and real EEG data.

Slope Estimation for Bivariate Longitudinal Outcomes Adjusting for Informative Right Censoring by Using a Discrete Survival Model: Application to the Renal Transplant Cohort

SummaryPatients undergoing renal transplantation are prone to graft failure which causes loss of follow-up measures on their levels of blood urea nitrogen and serum creatinine. These two outcomes are measured repeatedly over time to assess renal function following transplantation. Loss of follow-up on these bivariate measures results in informative right censoring, which is a common problem in longitudinal data that should be adjusted for so that valid estimates are obtained. In this study, we propose a bivariate model that jointly models these two longitudinal correlated outcomes and generates population and individual slopes adjusting for informative right censoring by using a discrete survival approach. The approach proposed is applied to a clinical data set of patients who had undergone renal transplantation. A simulation study validates the effectiveness of the approach.

Time-frequency characterization of electrocorticographic recordings of epileptic patients using frequency-entropy similarity: A comparison to other bi-variate measures

Expert evaluation of electrocorticographic (ECoG) recordings forms the linchpin of seizure onset zone localization in the evaluation of epileptic patients for surgical resection. Numerous methods have been developed to analyze these complex recordings, including uni-variate (characterizing single channels), bi-variate (comparing channel pairs) and multivariate measures. Developing reliable algorithms may be helpful in clinical tasks such as localization of epileptogenic zones and seizure anticipation, as well as enabling better understanding of neuronal function and dynamics. Recently we have developed the frequency-entropy (F-E) similarity measure, and have tested its capability in mapping the epileptogenic zones. The F-E similarity measure compares time-frequency characterizations of two recordings. In this study, we examine the method's principles and utility and compare it to previously described bi-variate correspondence measures such as correlation, coherence, mean phase coherence and spectral comparison methods. Specially designed synthetic signals were used for illuminating theoretical differences between the measures. Intracranial recordings of four epileptic patients were then used for the measures’ comparative analysis by creating a mean inter-electrode matrix for each of the correspondence measures and comparing the structure of these matrices during the inter-ictal and ictal periods. We found that the F-E similarity measure is able to discover spectral and temporal features in data which are hidden for the other measures and are important for foci localization.

Statistic Complexity: Combining Kolmogorov Complexity with an Ensemble Approach

BackgroundThe evaluation of the complexity of an observed object is an old but outstanding problem. In this paper we are tying on this problem introducing a measure called statistic complexity.Methodology/Principal FindingsThis complexity measure is different to all other measures in the following senses. First, it is a bivariate measure that compares two objects, corresponding to pattern generating processes, on the basis of the normalized compression distance with each other. Second, it provides the quantification of an error that could have been encountered by comparing samples of finite size from the underlying processes. Hence, the statistic complexity provides a statistical quantification of the statement ‘ is similarly complex as ’.ConclusionsThe presented approach, ultimately, transforms the classic problem of assessing the complexity of an object into the realm of statistics. This may open a wider applicability of this complexity measure to diverse application areas.

A multivariate version of Hoeffding’s Phi-Square

A multivariate measure of association is proposed, which extends the bivariate copula-based measure Phi-Square introduced by Hoeffding [22]. We discuss its analytical properties and calculate its explicit value for some copulas of simple form; a simulation procedure to approximate its value is provided otherwise. A nonparametric estimator for multivariate Phi-Square is derived and its asymptotic behavior is established based on the weak convergence of the empirical copula process both in the case of independent observations and dependent observations from strictly stationary strong mixing sequences. The asymptotic variance of the estimator can be estimated by means of nonparametric bootstrap methods. For illustration, the theoretical results are applied to financial asset return data.

Test and asymptotic normality for mixed bivariate measure

Consider a pair of random variables whose joint probability measure is the sum of an absolutely continuous measure, a discrete measure and a finite number of absolutely continuous measures on some lines called jum lines. The central limit theorem of the densities estimates is studied and its rate of convergence is given. A statistical test is developed to locate the jump points. An application on real data was conducted.

Inferring spatiotemporal network patterns from intracranial EEG data

The characterization of spatial network dynamics is desirable for a better understanding of seizure physiology. The goal of this work is to develop a computational method for identifying transient spatial patterns from intracranial electroencephalographic (iEEG) data. Starting with bivariate synchrony measures, such as phase correlation, a two-step clustering procedure is used to identify statistically significant spatial network patterns, whose temporal evolution can be inferred. We refer to this as the composite synchrony profile (CSP) method. The CSP method was verified with simulated data and evaluated using ictal and interictal recordings from three patients with intractable epilepsy. Application of the CSP method to these clinical iEEG datasets revealed a set of distinct CSPs with topographies consistent with medial temporal/limbic and superior parietal/medial frontal networks thought to be involved in the seizure generation process. By combining relatively straightforward multivariate signal processing techniques, such as phase synchrony, with clustering and statistical hypothesis testing, the methods we describe may prove useful for network definition and identification. The network patterns we observe using the CSP method cannot be inferred from direct visual inspection of the raw time series data, nor are they apparent in voltage-based topographic map sequences.

Coherence Spectrum Estimation From Nonuniformly Sampled Sequences

Magnitude squared coherence (MSC) is a useful bivariate spectral measure that finds application in a wide variety of fields. In this paper, we develop a nonparametric Capon-based MSC estimator that utilizes a segmented reformulation of the recently introduced iterative adaptive approach (IAA) to provide high resolution MSC spectrum estimates. The proposed estimator, termed segmented-IAA-MSC (or SIAA-MSC, for short), allows for unevenly sampled data as well as for sequences with arbitrarily missing samples. The estimator first uses segmented-IAA to find accurate estimates of the auto- and cross-covariance matrices of the given sequences. These estimates are then used in a Capon-based MSC estimator reformulated to allow for nonuniformly sampled sequences. To achieve higher statistical accuracy, the estimation problem is formulated so as to allow for overlapped segmentation of the available data. The proposed SIAA-MSC estimator is found to yield improved estimates as compared to the more commonly used least squares Fourier transform (LSFT) based MSC estimator.

Prediction of the Madden–Julian oscillation with the POAMA dynamical prediction system

Predictions of the Madden–Julian oscillation (MJO) are assessed using a 10-member ensemble of hindcasts from POAMA, the Australian Bureau of Meteorology coupled ocean–atmosphere seasonal prediction system. The ensemble of hindcasts was initialised from observed atmosphere and ocean initial conditions on the first of each month during 1980–2006. The MJO is diagnosed using the Wheeler-Hendon Real-time Multivariate MJO (RMM) index, which involves projection of daily data onto the leading pair of eigenmodes from an analysis of zonal winds at 200 and 850 hPa and outgoing longwave radiation (OLR) averaged about the equator. Forecasts of the two component (RMM1 and RMM2) index are quantitatively compared with observed behaviour derived from NCEP reanalyses and satellite OLR using the bivariate correlation skill, root-mean-square error (RMSE), and measures of the MJO amplitude and phase error. Comparison is also made with a simple vector autoregressive (VAR) prediction model of RMM as a benchmark. Using the full hindcast set, we find that the MJO can be predicted with the POAMA ensemble out to about 21 days as measured by the bivariate correlation exceeding 0.5 and the bivariate RMSE remaining below ~1.4 (which is the value for a climatological forecast). The VAR model, by comparison, drops to a correlation of 0.5 by about 12 days. The prediction limit from POAMA increases by less than 2 days for times when the MJO has large initial amplitude, and has little sensitivity to the initial phase of the MJO. The VAR model, on the other hand, shows a somewhat larger increase in skill for times of strong MJO variability and has greater sensitivity to initial phase, with lower skill for times when MJO convection is developing in the Indian Ocean. The sensitivity to season is, however, greater for POAMA, with maximum skill occurring in the December–January–February season and minimum skill in June–July–August. Examination of the MJO amplitudes shows that individual POAMA members have slightly above observed amplitude after a spin-up of about 10 days, whereas examination of the MJO phase error reveals that the model has a consistent tendency to propagate the MJO slightly slower than observed. Finally, an estimate of potential predictability of the MJO in POAMA hindcasts suggests that actual MJO prediction skill may be further improved through continued development of the dynamical prediction system.

Classification of bivariate measures of linear association

Given an n × 2 matrix, its rows can be geometrically interpreted as a cloud of points in the plane. Such a cloud of points could show clustering around a straight line. In statistics Pearson’s (empiric) correlation coefficient is often used to capture the degree to which this phenomenon occurs in a number. This seems a peculiar usage, for Pearson’s correlation coefficient changes when the cloud of points is rotated. Hence, whereas the shape of the cloud of points is completely preserved, the very number that is supposed to characterize clustering around a line changes its values (see also [4], [5], [6]). Other measures of linear association that do better in this respect can easily be created. Such measures, however, fail as a rule to be invariant under the action of rescaling the data. It will be explained that this is no coincidence.