EMD-regression for modelling multi-scale relationships, and application to weather-related cardiovascular mortality

Empirical mode decomposition of local field potential data from optogenetic experiments

Introduction

This study investigated the effects of cocaine administration and parvalbumin-type interneuron stimulation on local field potentials (LFPs) recorded in vivo from the medial prefrontal cortex (mPFC) of six mice using optogenetic tools.

Methods

The local network was subject to a brief 10 ms laser pulse, and the response was recorded for 2 s over 100 trials for each of the six subjects who showed stable coupling between the mPFC and the optrode. Due to the strong non-stationary and nonlinearity of the LFP, we used the adaptive, data-driven, Empirical Mode Decomposition (EMD) method to decompose the signal into orthogonal Intrinsic Mode Functions (IMFs).

Results

Through trial and error, we found that seven is the optimum number of orthogonal IMFs that overlaps with known frequency bands of brain activity. We found that the Index of Orthogonality (IO) of IMF amplitudes was close to zero. The Index of Energy Conservation (IEC) for each decomposition was close to unity, as expected for orthogonal decompositions. We found that the power density distribution vs. frequency follows a power law with an average scaling exponent of ~1.4 over the entire range of IMF frequencies 2-2,000 Hz.

Discussion

The scaling exponent is slightly smaller for cocaine than the control, suggesting that neural activity avalanches under cocaine have longer life spans and sizes.

Data-Enhancement Strategies in Weather-Related Health Studies

Although the relationship between weather and health is widely studied, there are still gaps in this knowledge. The present paper proposes data transformation as a way to address these gaps and discusses four different strategies designed to study particular aspects of a weather–health relationship, including (i) temporally aggregating the series, (ii) decomposing the different time scales of the data by empirical model decomposition, (iii) disaggregating the exposure series by considering the whole daily temperature curve as a single function, and (iv) considering the whole year of data as a single, continuous function. These four strategies allow studying non-conventional aspects of the mortality-temperature relationship by retrieving non-dominant time scale from data and allow to study the impact of the time of occurrence of particular event. A real-world case study of temperature-related cardiovascular mortality in the city of Montreal, Canada illustrates that these strategies can shed new lights on the relationship and outlines their strengths and weaknesses. A cross-validation comparison shows that the flexibility of functional regression used in strategies (iii) and (iv) allows a good fit of temperature-related mortality. These strategies can help understanding more accurately climate-related health.

Cardiovascular Health Peaks and Meteorological Conditions: A Quantile Regression Approach

Cardiovascular morbidity and mortality are influenced by meteorological conditions, such as temperature or snowfall. Relationships between cardiovascular health and meteorological conditions are usually studied based on specific meteorological events or means. However, those studies bring little to no insight into health peaks and unusual events far from the mean, such as a day with an unusually high number of hospitalizations. Health peaks represent a heavy burden for the public health system; they are, however, usually studied specifically when they occur (e.g., the European 2003 heatwave). Specific analyses are needed, using appropriate statistical tools. Quantile regression can provide such analysis by focusing not only on the conditional median, but on different conditional quantiles of the dependent variable. In particular, high quantiles of a health issue can be treated as health peaks. In this study, quantile regression is used to model the relationships between conditional quantiles of cardiovascular variables and meteorological variables in Montreal (Canada), focusing on health peaks. Results show that meteorological impacts are not constant throughout the conditional quantiles. They are stronger in health peaks compared to quantiles around the median. Results also show that temperature is the main significant variable. This study highlights the fact that classical statistical methods are not appropriate when health peaks are of interest. Quantile regression allows for more precise estimations for health peaks, which could lead to refined public health warnings.

The multi-timescale temporal patterns and dynamics of land surface temperature using Ensemble Empirical Mode Decomposition

Temporal variation patterns of Land Surface Temperature (LST) under different time scales are crucial in understanding the response of urban thermal environment to different forcings. However, there is no integrated toolset to extract such patterns from satellite remotely sensed time series LST (TSLST) data. This paper presents a workflow to extract the multi-timescale temporal patterns and dynamics from nonlinear and non-stationary TSLST data by taking Wuhan, China as case study. The 8-day MODerate-resolution Imaging Spectroradiometer (MODIS) satellite image products spanning the 2003-2017 period are used to generate a TSLST dataset with continuous and smooth surfaces on the monthly basis through the non-parametric Multi-Task Gaussian Process Modeling (MTGP). The study area is segmented into multiple time series clusters by k-means to bridge with urban planning in terms of research and implementation scale. Then, temporal patterns including annual, interannual components, and overall trends are reconstructed based on the components with characteristic time scales decomposed by the adaptive Ensemble Empirical Mode Decomposition (EEMD) method. The generated patterns of the 17 time series clusters are interpreted from the perspective of earth revolution, meteorological cycles and urbanization. Specifically, the annual components which are mainly generated by earth revolution reveal consistent rhythmic patterns among the time series. The interannual components preserve similar shapes although they differ in amplitudes. The overall shape is basically consistent with that of air temperature of Central China, which may be mainly induced by the El Niño-Southern Oscillation (ENSO) phenomenon. The overall trends which exert considerable differences are grouped into three types by shape. Such differences may be potentially caused by the inconsistent levels of localized urbanization, afforestation or circular economy development. This study facilitates the understanding of TSLST patterns and human-environment interactions. The proposed workflow can be utilized for other cities and potentially used for comparison among different cities.

A new look at weather-related health impacts through functional regression

A major challenge of climate change adaptation is to assess the effect of changing weather on human health. In spite of an increasing literature on the weather-related health subject, many aspect of the relationship are not known, limiting the predictive power of epidemiologic models. The present paper proposes new models to improve the performances of the currently used ones. The proposed models are based on functional data analysis (FDA), a statistical framework dealing with continuous curves instead of scalar time series. The models are applied to the temperature-related cardiovascular mortality issue in Montreal. By making use of the whole information available, the proposed models improve the prediction of cardiovascular mortality according to temperature. In addition, results shed new lights on the relationship by quantifying physiological adaptation effects. These results, not found with classical model, illustrate the potential of FDA approaches.

Aggregating the response in time series regression models, applied to weather-related cardiovascular mortality

In environmental epidemiology studies, health response data (e.g. hospitalization or mortality) are often noisy because of hospital organization and other social factors. The noise in the data can hide the true signal related to the exposure. The signal can be unveiled by performing a temporal aggregation on health data and then using it as the response in regression analysis. From aggregated series, a general methodology is introduced to account for the particularities of an aggregated response in a regression setting. This methodology can be used with usually applied regression models in weather-related health studies, such as generalized additive models (GAM) and distributed lag nonlinear models (DLNM). In particular, the residuals are modelled using an autoregressive-moving average (ARMA) model to account for the temporal dependence. The proposed methodology is illustrated by modelling the influence of temperature on cardiovascular mortality in Canada. A comparison with classical DLNMs is provided and several aggregation methods are compared. Results show that there is an increase in the fit quality when the response is aggregated, and that the estimated relationship focuses more on the outcome over several days than the classical DLNM. More precisely, among various investigated aggregation schemes, it was found that an aggregation with an asymmetric Epanechnikov kernel is more suited for studying the temperature-mortality relationship.