A new test for functional one-way ANOVA with applications to ischemic heart screening

Advancing statistical treatment of photolocomotor behavioral response study data

Fish photolocomotor behavioral response (PBR) studies have become increasingly prevalent in pharmacological and toxicological research to assess the environmental impact of various chemicals. There is a need for a standard, reliable statistical method to analyze PBR data. The most common method currently used, univariate analysis of variance (ANOVA), does not account for temporal dependence in observations and leads to incomplete or unreliable conclusions. Repeated measures ANOVA, another commonly used method, has drawbacks in its interpretability for PBR study data. Because each observation is collected continuously over time, we instead consider each observation to be a function and apply functional ANOVA (FANOVA) to PBR data. Using the functional approach not only accounts for temporal dependency but also retains the full structure of the data and allows for straightforward interpretation in any subregion of the domain. Unlike the traditional univariate and repeated measures ANOVA, the FANOVA that we propose is nonparametric, requiring minimal assumptions. We demonstrate the disadvantages of univariate and repeated measures ANOVA using simulated data and show how they are overcome by applying FANOVA. We then apply one-way FANOVA to zebrafish data from a PBR study and discuss how those results can be reproduced for future PBR studies.

A nonparametric test of group distributional differences for hierarchically clustered functional data

Biological sex and gender are critical variables in biomedical research, but are complicated by the presence of sex-specific natural hormone cycles, such as the estrous cycle in female rodents, typically divided into phases. A common feature of these cycles are fluctuating hormone levels that induce sex differences in many behaviors controlled by the electrophysiology of neurons, such as neuronal membrane potential in response to electrical stimulus, typically summarized using a priori defined metrics. In this paper, we propose a method to test for differences in the electrophysiological properties across estrous cycle phase without first defining a metric of interest. We do this by modeling membrane potential data in the frequency domain as realizations of a bivariate process, also depending on the electrical stimulus, by adopting existing methods for longitudinal functional data. We are then able to extract the main features of the bivariate signals through a set of basis function coefficients. We use these coefficients for testing, adapting methods for multivariate data to account for an induced hierarchical structure that is a product of the experimental design. We illustrate the performance of the proposed approach in simulations and then apply the method to experimental data.

Testing homogeneity: the trouble with sparse functional data

Testing the homogeneity between two samples of functional data is an important task. While this is feasible for intensely measured functional data, we explain why it is challenging for sparsely measured functional data and show what can be done for such data. In particular, we show that testing the marginal homogeneity based on point-wise distributions is feasible under some mild constraints and propose a new two-sample statistic that works well with both intensively and sparsely measured functional data. The proposed test statistic is formulated upon energy distance, and the convergence rate of the test statistic to its population version is derived along with the consistency of the associated permutation test. The aptness of our method is demonstrated on both synthetic and real data sets.

Functional ANOVA for Upper Extremity Fatigue Analysis during Dynamic Order Picking

OCCUPATIONAL APPLICATIONSMusculoskeletal disorders are prevalent among warehouse workers who engage in repetitive and dynamic tasks. To prevent such injuries, it is vital to identify the factors that influence fatigue in the upper extremities during these repetitive activities. Our study reveals that task factors, namely the bottle mass and picking rate, significantly influence upper extremity fatigue. In most cases, the fatigue indicator is a functional variable, meaning that the fatigue score or measurement is a curve captured over time, which could be modeled as a function. In this study, we demonstrate that functional data analysis tools, such as functional analysis of variance (FANOVA), prove more effective than traditional methods in specifying how task factors contribute to the development of fatigue in the upper extremities. Furthermore, since there are inherent differences among workers that could affect their fatigue development process, the data heterogeneity could be tackled by employing clustering methods.

Permutation-Based Inference for Function-on-Scalar Regression With an Application in PET Brain Imaging

The density of various proteins throughout the human brain can be studied through the use of positron emission tomography (PET) imaging. We report here on data from a study of serotonin transporter (5-HTT) binding. While PET imaging data analysis is most commonly performed on data that are aggregated into several discrete a priori regions of interest, in this study, primary interest is on measures of 5-HTT binding potential that are made at many locations along a continuous anatomically defined tract, one that was chosen to follow serotonergic axons. Our goal is to characterize the binding patterns along this tract and also to determine how such patterns differ between control subjects and depressed patients. Due to the nature of our data, we utilize function-on-scalar regression modeling to make optimal use of our data. Inference on both main effects (position along the tract; diagnostic group) and their interactions is made using permutation testing strategies that do not require distributional assumptions. Also, to investigate the question of homogeneity we implement a permutation testing strategy, which adapts a "block bootstrapping" approach from time series analysis to the functional data setting.

Functional ANOVA approaches for detecting changes in air pollution during the COVID-19 pandemic

Faced with novel coronavirus outbreak, the most hard-hit countries adopted a lockdown strategy to contrast the spread of virus. Many studies have already documented that the COVID-19 control actions have resulted in improved air quality locally and around the world. Following these lines of research, we focus on air quality changes in the urban territory of Chieti-Pescara (Central Italy), identified as an area of criticality in terms of air pollution. Concentrations of NO 2 , PM 10 , PM 2.5 and benzene are used to evaluate air pollution changes in this Region. Data were measured by several monitoring stations over two specific periods: from 1st February to 10 th March 2020 (before lockdown period) and from 11st March 2020 to 18 th April 2020 (during lockdown period). The impact of lockdown on air quality is assessed through functional data analysis. Our work makes an important contribution to the analysis of variance for functional data (FANOVA). Specifically, a novel approach based on multivariate functional principal component analysis is introduced to tackle the multivariate FANOVA problem for independent measures, which is reduced to test multivariate homogeneity on the vectors of the most explicative principal components scores. Results of the present study suggest that the level of each pollutant changed during the confinement. Additionally, the differences in the mean functions of all pollutants according to the location and type of monitoring stations (background vs traffic), are ascribable to the PM 10 and benzene concentrations for pre-lockdown and during-lockdown tenure, respectively. FANOVA has proven to be beneficial to monitoring the evolution of air quality in both periods of time. This can help environmental protection agencies in drawing a more holistic picture of air quality status in the area of interest.

Functional modeling of pedaling kinematics for the Stroke patients

Understanding deficits in motor control through the analysis of pedaling biomechanics plays a key role in the treatment of stroke patients. A thorough study of the impact of different exercise patterns and workloads on the change between pre- and post-treatment movement patterns in the patients is therefore of utmost importance to the clinicians. The objective of this study was to analyze the difference between pre- and post-treatment pedaling torques when the patients are subject to different exercise groups with varying workloads. The effects of affected vs unaffected side along with the covariates age and BMI have also been accounted for in this work. Two different three-way ANOVA-based approaches have been implemented here. In the first approach, a random projection-based ANOVA technique has been performed treating the pedaling torques as functional response, whereas the second approach utilizes distance measures to summarize the difference between pre- and post-treatment torques and perform nonparametric tests on it. Bayesian bootstrap has been used here to perform tests on the median distance. A group of stroke patients have been studied in the Cleveland Clinic categorizing them into different exercise groups and workload patterns. The data obtained have been analyzed with the aforementioned techniques, and the results have been reported here. These techniques turn out to be promising and will help clinicians recommend personalized treatment to stroke patients for optimal results.

The left cerebral hemisphere may be dominant for the control of bimanual symmetric reach-to-grasp movements

Previous research has established that the left cerebral hemisphere is dominant for the control of continuous bimanual movements. The lateralisation of motor control for discrete bimanual movements, in contrast, is underexplored. The purpose of the current study was to investigate which (if either) hemisphere is dominant for discrete bimanual movements. Twenty-one participants made bimanual reach-to-grasp movements towards pieces of candy. Participants grasped the candy to either place it in their mouths (grasp-to-eat) or in a receptacle near their mouths (grasp-to-place). Research has shown smaller maximum grip apertures (MGAs) for unimanual grasp-to-eat movements than unimanual grasp-to-place movements when controlled by the left hemisphere. In Experiment 1, participants made bimanual symmetric movements where both hands made grasp-to-eat or grasp-to-place movements. We hypothesised that a left hemisphere dominance for bimanual movements would cause smaller MGAs in both hands during bimanual grasp-to-eat movements compared to those in bimanual grasp-to-place movements. The results revealed that MGAs were indeed smaller for bimanual grasp-to-eat movements than grasp-to-place movements. This supports that the left hemisphere may be dominant for the control of bimanual symmetric movements, which agrees with studies on continuous bimanual movements. In Experiment 2, participants made bimanual asymmetric movements where one hand made a grasp-to-eat movement while the other hand made a grasp-to-place movement. The results failed to support the potential predictions of left hemisphere dominance, right hemisphere dominance, or contralateral control.

A Statistical Method to Enhance the Analysis of the Differences Among High-Resolution Melting (HRM) Curves of PCR-Amplified DNA Fragments

Consistent differences among melting curves of PCR-amplified DNA fragments are treated by normalizing the relative fluorescence units (RFU) and performing a clustering analysis, but statistically significant differences among curves are not usually determined. In the present study, an analysis based on functional data analysis (FDA) was implemented to evaluate the existence of statistically significant differences between normalized RFU curves obtained from PCR-HRM (high-resolution melting) analysis by using ANOVA for functional data. The effectiveness of the FDA method was analyzed with data from a set of samples of eight animal species of interest in food analysis, as well as mixtures of DNA from these species, analyzed by PCR-HRM to differentiate them. The statistical method described in this study has been demonstrated to be a robust and precise tool to discriminate among melting curves derived from HRM analysis. This method has advantages over the current comparison methods. PRACTICAL APPLICATION: As long as food fraud and mislabeling exist, new techniques for species identification are needed. High-resolution melting (HRM) has been shown to be a rapid, reliable and inexpensive species identification method. In the present study, functional data analysis (FDA) was applied to HRM curves of DNA from eight animal species used for food, as well as to mixtures of these species in different proportions. FDA has advantages over the usual methods, providing a deeper statistical analysis and facilitating the data interpretation as shown by the HRM analysis for a clearer comparison among individual species and mixtures of species.

A functional generalized F-test for signal detection with applications to event-related potentials significance analysis

Motivated by the analysis of complex dependent functional data such as event-related brain potentials (ERP), this paper considers a time-varying coefficient multivariate regression model with fixed-time covariates for testing global hypotheses about population mean curves. Based on a reduced-rank modeling of the time correlation of the stochastic process of pointwise test statistics, a functional generalized F-test is proposed and its asymptotic null distribution is derived. Our analytical results show that the proposed test is more powerful than functional analysis of variance testing methods and competing signal detection procedures for dependent data. Simulation studies confirm such power gain for data with patterns of dependence similar to those observed in ERPs. The new testing procedure is illustrated with an analysis of the ERP data from a study of neural correlates of impulse control.