Applications of functional data analysis: A systematic review

Functional data geometric morphometrics with machine learning for craniodental shape classification in shrews

This work proposes a functional data analysis approach for morphometrics in classifying three shrew species (S. murinus, C. monticola, and C. malayana) from Peninsular Malaysia. Functional data geometric morphometrics (FDGM) for 2D landmark data is introduced and its performance is compared with classical geometric morphometrics (GM). The FDGM approach converts 2D landmark data into continuous curves, which are then represented as linear combinations of basis functions. The landmark data was obtained from 89 crania of shrew specimens based on three craniodental views (dorsal, jaw, and lateral). Principal component analysis and linear discriminant analysis were applied to both GM and FDGM methods to classify the three shrew species. This study also compared four machine learning approaches (naïve Bayes, support vector machine, random forest, and generalised linear model) using predicted PC scores obtained from both methods (a combination of all three craniodental views and individual views). The analyses favoured FDGM and the dorsal view was the best view for distinguishing the three species.

Functional data analysis-based yield modeling in year-round crop cultivation

Crop yield prediction is essential for effective agricultural management. We introduce a methodology for modeling the relationship between environmental parameters and crop yield in longitudinal crop cultivation, exemplified by strawberry and tomato production based on year-round cultivation. Employing functional data analysis (FDA), we developed a model to assess the impact of these factors on crop yield, particularly in the face of environmental fluctuation. Specifically, we demonstrated that a varying-coefficient functional regression model (VCFRM) is utilized to analyze time-series data, enabling to visualize seasonal shifts and the dynamic interplay between environmental conditions such as solar radiation and temperature and crop yield. The interpretability of our FDA-based model yields insights for optimizing growth parameters, thereby augmenting resource efficiency and sustainability. Our results demonstrate the feasibility of VCFRM-based yield modeling, offering strategies for stable, efficient crop production, pivotal in addressing the challenges of climate adaptability in plant factory-based horticulture.

Data-Fusion-Based Quality Enhancement for HR Measurements Collected by Wearable Sensors

The advancements of Internet of Things (IoT) technologies have enabled the implementation of smart and wearable sensors, which can be employed to provide older adults with affordable and accessible continuous biophysiological status monitoring. The quality of such monitoring data, however, is unsatisfactory due to excessive noise induced by various disturbances, such as motion artifacts. Existing methods take advantage of summary statistics, such as mean or median values, for denoising, without taking into account the biophysiological patterns embedded in data. In this research, a functional data analysis modeling method was proposed to enhance the data quality by learning individual subjects' diurnal heart rate (HR) patterns from historical data, which were further improved by fusing newly collected data. This proposed data-fusion approach was developed based on a Bayesian inference framework. Its effectiveness was demonstrated in an HR analysis from a prospective study involving older adults residing in assisted living or home settings. The results indicate that it is imperative to conduct personalized healthcare by estimating individualized HR patterns. Furthermore, the proposed calibration method provides a more accurate (smaller mean errors) and more precise (smaller error standard deviations) HR estimation than raw HR and conventional methods, such as the mean.

Predicting health outcomes with intensive longitudinal data collected by mobile health devices: a functional principal component regression approach

BACKGROUND

Intensive longitudinal data (ILD) collected in near real time by mobile health devices provide a new opportunity for monitoring chronic diseases, early disease risk prediction, and disease prevention in health research. Functional data analysis, specifically functional principal component analysis, has great potential to abstract trends in ILD but has not been used extensively in mobile health research.

OBJECTIVE

To introduce functional principal component analysis (fPCA) and demonstrate its potential applicability in estimating trends in ILD collected by mobile heath devices, assessing longitudinal association between ILD and health outcomes, and predicting health outcomes.

METHODS

fPCA and scalar-to-function regression models were reviewed. A case study was used to illustrate the process of abstracting trends in intensively self-measured blood glucose using functional principal component analysis and then predicting future HbA1c values in patients with type 2 diabetes using a scalar-to-function regression model.

RESULTS

Based on the scalar-to-function regression model results, there was a slightly increasing trend between daily blood glucose measures and HbA1c. 61% of variation in HbA1c could be predicted by the three preceding months' blood glucose values measured before breakfast (P < 0.0001, [Formula: see text]).

CONCLUSIONS

Functional data analysis, specifically fPCA, offers a unique tool to capture patterns in ILD collected by mobile health devices. It is particularly useful in assessing longitudinal dynamic association between repeated measures and outcomes, and can be easily integrated in prediction models to improve prediction precision.

Associations Between Patterns of Daily Stepping Behavior, Health-Related Quality of Life, and Pain Symptoms Among Older Adults with Chronic Pain: A Secondary Analysis of Two Randomized Controlled Trials

Purpose

One's amount, intensity, and distribution of physical activity may have implications for whether it has positive or negative effects on pain and quality of life for older adults living with chronic pain. Thus, we investigated baseline patterns of stepping related to pain symptoms and health-related quality of life at baseline and over a 12-week follow-up period.

Patients and Methods

Participants were low-active older adults (69.54±6.74 years) with obesity and chronic pain who enrolled in one of two randomized controlled trials. Participants completed measures of pain intensity, interference, and health-related quality of life and wore an accelerometer for 7 days at baseline and week 12. Functional principal components analysis identified patterns of within-day stepping behavior at baseline, and linear regressions were used to investigate how these component scores related to pain and health-related quality of life at baseline and over 12 weeks.

Results

Two patterns were extracted; one describing more vs less stepping and the second capturing movement later vs earlier in the day. More baseline stepping was associated with better physical functioning (B=0.148, p<0.001) and energy (B=0.073, p=0.033), while a later start in the day was associated with worse social functioning (B=-0.193, p=0.031). More stepping at baseline predicted positive changes in physical functioning (B=0.094, p=0.019), emotional role limitations (B=0.132, p=0.049), energy (B=0.112, p<0.001), social functioning (B=0.086, p=0.043), pain (B=0.086, p=0.009), general health (B=0.081, p=0.003) and pain intensity (B=-0.039, p=0.003). A later start to the day was associated with worsening physical functioning (B=-0.229, p<0.001), physical (B=-0.282, p=0.047) and emotional role limitations (B=-0.254, p=0.048), general health (B=-0.108, p=0.041), and pain interference (B=0.055, p=0.043).

Conclusion

Findings suggest there is value in activity patterns as an indicator for additional behavioral intervention, as those who move little and/or delay daily movement are likely to experience subsequent decrements in quality of life and pain symptoms.

Oxytocin is not associated with postpartum hemorrhage in labor augmentation in a retrospective cohort study in the United States

BACKGROUND

Previous studies reported conflicting results on the relationship between oxytocin use for labor augmentation and the risk of postpartum hemorrhage, probably because it is rather challenging to disentangle oxytocin use from labor dystocia.

OBJECTIVE

This study aimed to investigate the independent association between oxytocin use for augmentation and the risk of postpartum hemorrhage by using advanced statistical modeling to control for labor patterns and other covariates.

STUDY DESIGN

We used data from 20,899 term, cephalic, singleton pregnancies of patients with spontaneous onset of labor and no previous cesarean delivery from Intermountain Healthcare in Utah in the Consortium on Safe Labor. Presence of postpartum hemorrhage was identified on the basis of a clinical diagnosis. Propensity scores were calculated using a generalized linear mixed model for oxytocin use for augmentation, and covariate balancing generalized propensity score was applied to obtain propensity scores for the duration and total dosage of oxytocin augmentation. A weighted generalized additive mixed model was used to depict dose-response curves between the duration and total dosage of oxytocin augmentation and the outcomes. The average treatment effects of oxytocin use for augmentation on postpartum hemorrhage and estimated blood loss (mL) were assessed by inverse probability weighting of propensity scores.

RESULTS

The odds of both postpartum hemorrhage and estimated blood loss increased modestly when the duration and/or total dosage of oxytocin used for augmentation increased. However, in comparison with women for whom oxytocin was not used, oxytocin augmentation was not clinically or statistically significantly associated with estimated blood loss (6.5 mL; 95% confidence interval, 2.5-10.3) or postpartum hemorrhage (adjusted odds ratio, 1.02; 95% confidence interval, 0.82-1.24) when rigorously controlling for labor pattern and potential confounders. The results remained consistent regardless of inclusion of women with an intrapartum cesarean delivery.

CONCLUSION

The odds of postpartum hemorrhage and estimated blood loss increased modestly with increasing duration and total dosage of oxytocin augmentation. However, in comparison with women for whom oxytocin was not used and after controlling for potential confounders, there was no clinically significant association between oxytocin use for augmentation and estimated blood loss or the risk of postpartum hemorrhage.

Understanding spatiotemporal patterns of COVID-19 incidence in Portugal: A functional data analysis from August 2020 to March 2022

During the SARS-CoV-2 pandemic, governments and public health authorities collected massive amounts of data on daily confirmed positive cases and incidence rates. These data sets provide relevant information to develop a scientific understanding of the pandemic's spatiotemporal dynamics. At the same time, there is a lack of comprehensive approaches to describe and classify patterns underlying the dynamics of COVID-19 incidence across regions over time. This seriously constrains the potential benefits for public health authorities to understand spatiotemporal patterns of disease incidence that would allow for better risk communication strategies and improved assessment of mitigation policies efficacy. Within this context, we propose an exploratory statistical tool that combines functional data analysis with unsupervised learning algorithms to extract meaningful information about the main spatiotemporal patterns underlying COVID-19 incidence on mainland Portugal. We focus on the timeframe spanning from August 2020 to March 2022, considering data at the municipality level. First, we describe the temporal evolution of confirmed daily COVID-19 cases by municipality as a function of time, and outline the main temporal patterns of variability using a functional principal component analysis. Then, municipalities are classified according to their spatiotemporal similarities through hierarchical clustering adapted to spatially correlated functional data. Our findings reveal disparities in disease dynamics between northern and coastal municipalities versus those in the southern and hinterland. We also distinguish effects occurring during the 2020-2021 period from those in the 2021-2022 autumn-winter seasons. The results provide proof-of-concept that the proposed approach can be used to detect the main spatiotemporal patterns of disease incidence. The novel approach expands and enhances existing exploratory tools for spatiotemporal analysis of public health data.

Relationship between neck kinematics and neck dissability index. An approach based on functional regression

Numerous studies use numerical variables of neck movement to predict the level of severity of a pathology. However, the correlation between these numerical variables and disability levels is low, less than 0.4 in the best cases, even less in subjects with nonspecific neck pain. This work aims to use Functional Data Analysis (FDA), in particular scalar-on-function regression, to predict the Neck Disability Index (NDI) of subjects with nonspecific neck pain using the complete movement as predictors. Several functional regression models have been implemented, doubling the multiple correlation coefficient obtained when only scalar predictors are used. The best predictive model considers the angular velocity curves as a predictor, obtaining a multiple correlation coefficient of 0.64. In addition, functional models facilitate the interpretation of the relationship between the kinematic curves and the NDI since they allow identifying which parts of the curves most influence the differences in the predicted variable. In this case, the movement's braking phases contribute to a greater or lesser NDI. So, it is concluded that functional regression models have greater predictive capacity than usual ones by considering practically all the information in the curve while allowing a physical interpretation of the results.

Human milk oligosaccharide composition and associations with growth: results from an observational study in the US

Background

Breast milk is the recommended source of nutrients for newborns and infants. Human milk oligosaccharides (HMO) are the third most abundant solid component in human milk and their composition varies during lactation.

Objectives

Our objective was to investigate longitudinal and cross-sectional changes in HMO composition and whether these changes were associated with infant growth up to 24 months of age. Associations with maternal characteristics were also investigated.

Methods

24 HMOs were quantified in samples taken at 2 weeks (n = 107), 6 weeks (n = 97) and 3 months (n = 76), using high performance liquid chromatography. Body length, weight, and head circumference were measured at 8 timepoints, until 24 months. Clusters of breast milk samples, reflecting different HMO profiles, were found through a data-driven approach. Longitudinal associations were investigated using functional principal component analysis (FPCA) and used to characterize patterns in the growth trajectories.

Results

Four clusters of samples with similar HMO composition were derived. Two patterns of growth were identified for length, body weight and head circumference via the FPCA approach, explaining more than 90% of the variance. The first pattern measured general growth while the second corresponded to an initial reduced velocity followed by an increased velocity ("higher velocity"). Higher velocity for weight and height was significantly associated with negative Lewis status. Concentrations of 3'GL, 3FL, 6'GL, DSNLT, LNFP-II, LNFP-III, LNT, LSTb were negatively associated with higher velocity for length.

Conclusion

We introduced novel statistical approaches to establish longitudinal associations between HMOs evolution and growth. Based on our approach we propose that HMOs may act synergistically on children growth. A possible causal relationship should be further tested in pre-clinical and clinical setting.

Exploring the Effect of the Dynamics of Behavioral Phenotypes on Health Outcomes in an mHealth Intervention for Childhood Obesity: Longitudinal Observational Study

BACKGROUND

Advancements in mobile health technologies and machine learning approaches have expanded the framework of behavioral phenotypes in obesity treatment to explore the dynamics of temporal changes.

OBJECTIVE

This study aimed to investigate the dynamics of behavioral changes during obesity intervention and identify behavioral phenotypes associated with weight change using a hybrid machine learning approach.

METHODS

In total, 88 children and adolescents (ages 8-16 years; 62/88, 71% male) with age- and sex-specific BMI ≥85th percentile participated in the study. Behavioral phenotypes were identified using a hybrid 2-stage procedure based on the temporal dynamics of adherence to the 5 behavioral goals during the intervention. Functional principal component analysis was used to determine behavioral phenotypes by extracting principal component factors from the functional data of each participant. Elastic net regression was used to investigate the association between behavioral phenotypes and weight change.

RESULTS

Functional principal component analysis identified 2 distinctive behavioral phenotypes, which were named the high or low adherence level and late or early behavior change. The first phenotype explained 47% to 69% of each factor, whereas the second phenotype explained 11% to 17% of the total behavioral dynamics. High or low adherence level was associated with weight change for adherence to screen time (β=-.0766, 95% CI -.1245 to -.0312), fruit and vegetable intake (β=.1770, 95% CI .0642-.2561), exercise (β=-.0711, 95% CI -.0892 to -.0363), drinking water (β=-.0203, 95% CI -.0218 to -.0123), and sleep duration. Late or early behavioral changes were significantly associated with weight loss for changes in screen time (β=.0440, 95% CI .0186-.0550), fruit and vegetable intake (β=-.1177, 95% CI -.1441 to -.0680), and sleep duration (β=-.0991, 95% CI -.1254 to -.0597).

CONCLUSIONS

Overall level of adherence, or the high or low adherence level, and a gradual improvement or deterioration in health-related behaviors, or the late or early behavior change, were differently associated with weight loss for distinctive obesity-related lifestyle behaviors. A large proportion of health-related behaviors remained stable throughout the intervention, which indicates that health care professionals should closely monitor changes made during the early stages of the intervention.

TRIAL REGISTRATION

Clinical Research Information Science KCT0004137; https://tinyurl.com/ytxr83ay.

Predicting rainfall and irrigation requirements of corn in Ecuador

This work is a case study whose objective is prediction of irrigation needs of corn crops in different regions of Ecuador; being this a fundamental basic food for the country's economy, as in the remaining countries of the Andean area. The proposed methodology seeks to help improving the quality of corn crop. Specifically, we propose the application of regression models, within the framework of Functional Data Analysis (FDA), to predict the amount of rainfall (scalar response variable) in the places with the highest production of corn in Ecuador, as a function of functional covariates such as temperature and wind speed. From the estimation of the amount of rainfall, effective precipitation is calculated. This is the fraction of water used by the crops, from which the value of real evapotranspiration or ETc is obtained and, more importantly, the irrigation requirements at each stage of the corn crop, for its adequate physiological development. Application of regression models based on functional basis, Functional Principal Components (FPC) or Functional Partial Least Squares (FPLS) for scalar response variable, allows us to use the information of variables such as wind speed and temperature (of functional nature) in a better way than using multivariate models, for predicting the amount of rainfall, obtaining, as a result, very explicative models, defined by a high goodness of fit (R 2 = 0.97 , with 6 significant parameters and an error of 0.14) and practical utility. The model has been also applied to North Peru regions, obtaining rainfall prediction errors between 9% and 22%. Thus, the geographical limitations of the model could be the Andean regions with similar climate. In addition, this study proposes the application of FDA exploratory analysis and FDA outlier detection techniques as a common and useful practice in the specific domain of rainfall prediction studies, prior to applying the regression models.

Geo-epidemiology of malaria incidence in the Vhembe District to guide targeted elimination strategies, South-Africa, 2015-2018: a local resurgence

In South Africa, the population at risk of malaria is 10% (around six million inhabitants) and concern only three provinces of which Limpopo Province is the most affected, particularly in Vhembe District. As the elimination approaches, a finer scale analysis is needed to accelerate the results. Therefore, in the process of refining local malaria control and elimination strategies, the aim of this study was to identify and describe malaria incidence patterns at the locality scale in the Vhembe District, Limpopo Province, South Africa. The study area comprised 474 localities in Vhembe District for which smoothed malaria incidence curve were fitted with functional data method based on their weekly observed malaria incidence from July 2015 to June 2018. Then, hierarchical clustering algorithm was carried out considering different distances to classify the 474 smoothed malaria incidence curves. Thereafter, validity indices were used to determine the number of malaria incidence patterns. The cumulative malaria incidence of the study area was 4.1 cases/1000 person-years. Four distinct patterns of malaria incidence were identified: high, intermediate, low and very low with varying characteristics. Malaria incidence increased across transmission seasons and patterns. The localities in the two highest incidence patterns were mainly located around farms, and along the rivers. Some unusual malaria phenomena in Vhembe District were also highlighted as resurgence. Four distinct malaria incidence patterns were found in Vhembe District with varying characteristics. Findings show also unusual malaria phenomena in Vhembe District that hinder malaria elimination in South Africa. Assessing the factors associated with these unusual malaria phenome would be helpful on building innovative strategies that lead South Africa on malaria elimination.

Spectral features of resting-state EEG in Parkinson's Disease: A multicenter study using functional data analysis

OBJECTIVE

This study aims 1) To analyse differences in resting-state electroencephalogram (rs-EEG) spectral features of Parkinson's Disease (PD) and healthy subjects (non-PD) using Functional Data Analysis (FDA) and 2) To explore, in four independent cohorts, the external validity and reproducibility of the findings using both epoch-to-epoch FDA and averaged-epochs approach.

METHODS

We included 169 subjects (85 non-PD; 84 PD) from four centres. Rs-EEG signals were preprocessed with a combination of automated pipelines. Sensor-level relative power spectral density (PSD), dominant frequency (DF), and DF variability (DFV) features were extracted. Differences in each feature were compared between PD and non-PD on averaged epochs and using FDA to model the epoch-to-epoch change of each feature.

RESULTS

For averaged epochs, significantly higher theta relative PSD in PD was found across all datasets. Also, higher pre-alpha relative PSD was observed in three of four datasets in PD patients. For FDA, similar findings were achieved in theta, but all datasets showed consistently significant posterior pre-alpha differences across multiple epochs.

CONCLUSIONS

Increased generalised theta, with posterior pre-alpha relative PSD, was the most reproducible finding in PD.

SIGNIFICANCE

Rs-EEG theta and pre-alpha findings are generalisable in PD. FDA constitutes a reliable and powerful tool to analyse epoch-to-epoch the rs-EEG.

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.

Feasibility Study on Virtual Reality Based Basketball Tactic Training

In this article, a VR-based basketball training system comprising a standalone VR device and a tablet is proposed. The system is intended to improve the ability of players to understand offensive tactics and practice these tactics correctly. We compare the training effectiveness of various degrees of immersion, including a conventional basketball tactic board, a 2D monitor, and virtual reality. A multi-camera-based human tracking system was designed and built around a real-world basketball court to record and analyze the running trajectory of each player during tactical execution. The accuracy of the running path and hesitation time at each tactical step were evaluated for each participant. Furthermore, we assessed several subjective measurements, including simulator sickness, presence, and sport imagery ability, to conduct a more comprehensive exploration of the feasibility of the proposed VR framework for basketball tactics training. The results indicate that the proposed system is useful for learning complex tactics. Furthermore, high VR immersion training improves athletes' abilities with regards to strategic imagery.

Representation Theorem and Functional CLT for RKHS-Based Function-on-Function Regressions

We investigate a nonparametric, varying coefficient regression approach for modeling and estimating the regression effects caused by two functionally correlated datasets. Due to modern biomedical technology to measure multiple patient features during a time interval or intermittently at several discrete time points to review underlying biological mechanisms, statistical models that do not properly incorporate interventions and their dynamic responses may lead to biased estimates of the intervention effects. We propose a shared parameter change point function-on-function regression model to evaluate the pre- and post-intervention time trends and develop a likelihood-based method for estimating the intervention effects and other parameters. We also propose new methods for estimating and hypothesis testing regression parameters for functional data via reproducing kernel Hilbert space. The estimators of regression parameters are closed-form without computation of the inverse of a large matrix, and hence are less computationally demanding and more applicable. By establishing a representation theorem and a functional central limit theorem, the asymptotic properties of the proposed estimators are obtained, and the corresponding hypothesis tests are proposed. Application and the statistical properties of our method are demonstrated through an immunotherapy clinical trial of advanced myeloma and simulation studies.

Functional Kriging for Spatiotemporal Modeling of Nitrogen Dioxide in a Middle Eastern Megacity

Long-term hour-specific air pollution exposure estimates have rarely been of interest in epidemiological research. However, this can be relevant for studies that aim to estimate the residential exposure for the hours that subjects mostly spend time there, or for those hours that they may work in another location. Here, we developed a model by spatially predicting the long-term diurnal curves of nitrogen dioxide (NO2) in Tehran, Iran, one of the most polluted and populated megacities in the Middle East. We used the statistical framework of functional data analysis (FDA) including ordinary kriging for functional data (OKFD) and functional analysis of variance (fANOVA) for modeling. The long-term NO2 diurnal curves had two distinct maxima and minima. The absolute minimum value of the city average was 40.6 ppb (around 4:00 p.m.) and the absolute maximum value was 52.0 ppb (around 10:00 p.m.). The OKFD showed the concentrations, the diurnal maximum/minimum values, and their corresponding occurring times varied across the city. The fANOVA highlighted that the effect of population density on the NO2 concentrations is not constant and depends on time within the diurnal period. The provided estimation of long-term hour-specific maps can inform future epidemiological studies to use the long-term mean for specific hour(s) of the day. Moreover, the demonstrated FDA framework can be used as a set of flexible statistical methods.

The dynamics of ideology drift among U.S. Supreme Court justices: A functional data analysis

We study the U.S. Supreme Court dynamics by analyzing the temporal evolution of the underlying policy positions of the Supreme Court Justices as reflected by their actual voting data, using functional data analysis methods. The proposed fully flexible nonparametric method makes it possible to dissect the time-dynamics of policy positions at the level of individual Justices, as well as providing a comprehensive view of the ideology evolution over the history of Supreme Court since its establishment. In addition to quantifying individual Justice’s policy positions, we uncover average changes over time and also the major patterns of change over time. Additionally, our approach allows for representing highly complex dynamic trajectories by a few principal components which complements other models of analyzing and predicting court behavior.

Modelling time-varying covariates effect on survival via functional data analysis: application to the MRC BO06 trial in osteosarcoma

Time-varying covariates are of great interest in clinical research since they represent dynamic patterns which reflect disease progression. In cancer studies biomarkers values change as functions of time and chemotherapy treatment is modified by delaying a course or reducing the dose intensity, according to patient’s toxicity levels. In this work, a Functional covariate Cox Model (FunCM) to study the association between time-varying processes and a time-to-event outcome is proposed. FunCM first exploits functional data analysis techniques to represent time-varying processes in terms of functional data. Then, information related to the evolution of the functions over time is incorporated into functional regression models for survival data through functional principal component analysis. FunCM is compared to a standard time-varying covariate Cox model, commonly used despite its limiting assumptions that covariate values are constant in time and measured without errors. Data from MRC BO06/EORTC 80931 randomised controlled trial for treatment of osteosarcoma are analysed. Time-varying covariates related to alkaline phosphatase levels, white blood cell counts and chemotherapy dose during treatment are investigated. The proposed method allows to detect differences between patients with different biomarkers and treatment evolutions, and to include this information in the survival model. These aspects are seldom addressed in the literature and could provide new insights into the clinical research.

Spatiotemporal analysis of urban road congestion during and post COVID-19 pandemic in Shanghai, China

Coronavirus Disease 2019 (COVID-19) has become one of the most serious global health crises in decades and tremendously influence the human mobility. Many residents changed their travel behavior during and after the pandemic, especially for a certain percentage of public transport users who chose to drive their owned vehicles. Thus, urban roadway congestion has been getting worse, and the spatiotemporal congestion patterns has changed significantly. Understanding spatiotemporal heterogeneity of urban roadway congestion during and post the pandemic is essential for mobility management. In this study, an analytical framework was proposed to investigate the spatiotemporal heterogeneity of urban roadway congestion in Shanghai, China. First, the matrix of average speed in each traffic analysis zones (TAZs) was calculated to extract spatiotemporal heterogeneity variation features. Second, the heterogenous component of each TAZ was extracted from the overall traffic characteristics using robust principal component analysis (RPCA). Third, clustering analysis was employed to explain the spatiotemporal distribution of heterogeneous traffic characteristics. Finally, fluctuation features of these characteristics were analyzed by iterated cumulative sums of squares (ICSS). The case study results suggested that the urban road traffic state evolution was complicated and varied significantly in different zones and periods during the long-term pandemic. Compared with suburban areas, traffic conditions in city central areas are more susceptible to the pandemic and other events. In some areas, the heterogeneous component shows opposite characteristics on working days and holidays with others. The key time nodes of state change for different areas have commonness and individuality. The proposed analytical framework and empirical results contribute to the policy decision-making of urban road transportation system during and post the COVID-19 pandemic.

Maternal blood pressure trajectories and associations with gestational age at birth: a functional data analytic approach

BACKGROUND

Research has revealed group-level differences in maternal blood pressure trajectories across pregnancy. These trajectories are typically constructed using clinical blood pressure data and multivariate statistical methods that are prone to bias and ignore the functional, dynamic process underlying a single blood pressure observation. The aim of this study was to use functional data analysis to explore blood pressure variation across pregnancy, and multivariate methods to examine whether trajectories are related to gestational age at birth.

METHODS

Clinical blood pressure observations were available from 370 women who participated in a longitudinal pregnancy cohort study conducted in Montreal, Quebec, Canada. Functional data analysis was used to smooth blood pressure data and then to conduct a functional principal component analysis to examine predominant modes of variation.

RESULTS

Three eigenfunctions explained greater than 95% of the total variance in blood pressure. The first accounted for approximately 80% of the variance and was characterized by a prolonged-decrease trajectory in blood pressure; the second explained 10% of the variance and captured a late-increase trajectory; and the third accounted for approximately 7% of the variance and captured a mid-decrease trajectory. The prolonged-decrease trajectory of blood pressure was associated with older, and late-increase with younger gestational age at birth.

CONCLUSION

Functional data analysis is a useful method to model repeated maternal blood pressure observations and many other time-related cardiovascular processes. Results add to previous research investigating blood pressure trajectories across pregnancy through identification of additional, potentially clinically important modes of variation that are associated with gestational age at birth.

Detection of Multidecadal Changes in Vegetation Dynamics and Association with Intra-Annual Climate Variability in the Columbia River Basin

Remotely-sensed Leaf Area Index (LAI) is a useful metric for assessing changes in vegetation cover and greeness over time and space. Satellite-derived LAI measurements can be used to assess these intra- and inter-annual vegetation dynamics and how they correlate with changing regional and local climate conditions. The detection of such changes at local and regional levels is challenged by the underlying continuity and extensive missing values of high-resolution spatio-temporal vegetation data. Here, the feasibility of functional data analysis methods was evaluated to improve the exploration of such data. In this paper, an investigation of multidecadal variation in LAI is conducted in the Columbia River Watershed, as detected by NOAA Advanced Very High-Resolution Radiometer (AVHRR) satellite imaging. The inter- and intra-annual correlation of LAI with temperature and precipitation were then investigated using data from the European Centre for Medium-Range Weather Forecasts global atmospheric re-analysis (ERA-Interim) in the period 1996–2017. A functional cluster analysis model was implemented to identify regions in the Columbia River Watershed that exhibit similar long-term greening trends. Across this region, a multidecadal trend toward earlier and higher annual LAI peaks was detected, and strong correlations were found between earlier and higher LAI peaks and warmer temperatures in late winter and early spring. Although strongly correlated to LAI, maximum temperature and precipitation do not demonstrate a similar strong multidecadal trend over the studied time period. The modeling approach is proficient for analyzing tens or hundreds of thousands of sampled sites without parallel processing or high-performance computing (HPC).

Model-based joint curve registration and classification

In this paper, we consider the problem of classification of misaligned multivariate functional data. We propose to use a model-based approach for the joint registration and classification of such data. The observed functional inputs are modeled as a functional nonlinear mixed effects model containing a nonlinear functional fixed effect constructed upon warping functions to account for curve alignment, and a nonlinear functional random effects component to address the variability among subjects. The warping functions are also modeled to accommodate common effect within groups and the variability between subjects. Then, a functional logistic regression model defined upon the representation of the aligned curves and scalar inputs is used to account for curve classification. EM-based algorithms are developed to perform maximum likelihood inference of the proposed models. The identifiability of the registration model and the asymptotical properties of the proposed method are established. The performance of the proposed procedure is illustrated via simulation studies and an analysis of a hyoid bone movement data application. The statistical developments proposed in this paper were motivated by the hyoid bone movement study, the methodology is designed and presented generality and can be applied to numerous areas of scientific research.

Machine Learning for Automated Industrial IoT Attack Detection: An Efficiency-Complexity Trade-off

Critical city infrastructures that depend on smart Industrial Internet of Things (IoT) devices have been increasingly becoming a target of cyberterrorist or hacker attacks. Although this has led to multiple studies in the recent past, there exists a paucity of literature concerning real-time Industrial IoT attack detection. The goal of this article is to build a machine-learning approach using Industrial IoT sensor readings for accurately tracking down Industrial IoT attacks in real time. We analyze IoT system behavior under a lab-controlled series of attacks on a Secure Water Treatment (SWaT) system. The system is analytically challenging in that it results in sensor readings that resemble waveforms. To that end, we develop a novel early detection method using functional shape analysis (FSA) to extract features from the data that can capture the profile of the waveform. Our results show an efficiency-complexity trade-off between functional and non-functional methods in predicting IoT attacks.

Smoothing splines of apex predator movement: Functional modeling strategies for exploring animal behavior and social interactions

The collection of animal position data via GPS tracking devices has increased in quality and usage in recent years. Animal position and movement, although measured discretely, follows the same principles of kinematic motion, and as such, the process is inherently continuous and differentiable. I demonstrate the functionality and visual elegance of smoothing spline models. I discuss the challenges and benefits of implementing such an approach, and I provide an analysis of movement and social interaction of seven jaguars inhabiting the Taiamã Ecological Station, Pantanal, Brazil, a region with the highest known density of jaguars. In the analysis, I derive measures for pairwise distance, cooccurrence, and spatiotemporal association between jaguars, borrowing ideas from density estimation and information theory. These measures are feasible as a result of spline model estimation, and they provide a critical tool for a deeper investigation of cooccurrence duration, frequency, and localized spatio-temporal relationships between animals. In this work, I characterize a variety of interactive relationships between pairs of jaguars, and I particularly emphasize the relationships in movement of two male-female and two male-male jaguar pairs exhibiting highly associative relationships.

Statistical kinematic modelling: concepts and model validity

Data reduction techniques are applied to reduce the volume of data while maintaining its integrity. For cyclic motion data, a reliable overview comparing these methods is lacking. Therefore, this study aims to evaluate the features of the different data reduction techniques by applying them to large public data sets. The periodicity of cyclic motion can be exploited by either analysing a single cycle or studying a series of cycles. Analysing single cycles requires a pre-processing step to isolate the amplitude variability. Three different alignment techniques were evaluated, namely Linear length normalisation (LLN), piecewise LLN (PLLN) and continuous registration (CR). CR showed to remove the most phase variation. For the data reduction, three techniques were assessed (i.e., principal component analysis (PCA), principal polynomial analysis (PPA) and multivariate functional PCA (MFPCA)) based on the in- and out-of-sample error, the compactness and the computation time. The differences were found to be minimal. From our results, PPA appeared to be most useful for data compression. Further, we recommend PCA and MFPCA for classification and feature extraction purposes. We suggest the use of PCA when computation time is key and we advise the use of MFPCA when the inclusion of different data sources is desired. In contrast, the analysis of a series of cycles requires a pre-processing step to decompose the series. Further, a regression model was used to compensate for the difference in fundamental frequency. PCA on FC and MFPCA with splines were applied on the frequency compensated curves. Both methods performed as good.

Cross-Validation, Information Theory, or Maximum Likelihood? A Comparison of Tuning Methods for Penalized Splines

Functional data analysis techniques, such as penalized splines, have become common tools used in a variety of applied research settings. Penalized spline estimators are frequently used in applied research to estimate unknown functions from noisy data. The success of these estimators depends on choosing a tuning parameter that provides the correct balance between fitting and smoothing the data. Several different smoothing parameter selection methods have been proposed for choosing a reasonable tuning parameter. The proposed methods generally fall into one of three categories: cross-validation methods, information theoretic methods, or maximum likelihood methods. Despite the well-known importance of selecting an ideal smoothing parameter, there is little agreement in the literature regarding which method(s) should be considered when analyzing real data. In this paper, we address this issue by exploring the practical performance of six popular tuning methods under a variety of simulated and real data situations. Our results reveal that maximum likelihood methods outperform the popular cross-validation methods in most situations—especially in the presence of correlated errors. Furthermore, our results reveal that the maximum likelihood methods perform well even when the errors are non-Gaussian and/or heteroscedastic. For real data applications, we recommend comparing results using cross-validation and maximum likelihood tuning methods, given that these methods tend to perform similarly (differently) when the model is correctly (incorrectly) specified.

Functional data analysis characterizes the shapes of the first COVID-19 epidemic wave in Italy

We investigate patterns of COVID-19 mortality across 20 Italian regions and their association with mobility, positivity, and socio-demographic, infrastructural and environmental covariates. Notwithstanding limitations in accuracy and resolution of the data available from public sources, we pinpoint significant trends exploiting information in curves and shapes with Functional Data Analysis techniques. These depict two starkly different epidemics; an "exponential" one unfolding in Lombardia and the worst hit areas of the north, and a milder, "flat(tened)" one in the rest of the country-including Veneto, where cases appeared concurrently with Lombardia but aggressive testing was implemented early on. We find that mobility and positivity can predict COVID-19 mortality, also when controlling for relevant covariates. Among the latter, primary care appears to mitigate mortality, and contacts in hospitals, schools and workplaces to aggravate it. The techniques we describe could capture additional and potentially sharper signals if applied to richer data.

Regional and temporal patterns of influenza: Application of functional data analysis

BACKGROUND

The accurate estimation of temporal patterns of influenza may help in utilizing hospital resources and guiding influenza surveillance. This paper proposes functional data analysis (FDA) to improve the prediction of temporal patterns of influenza.

METHODS

We illustrate FDA methods using the weekly Influenza-like Illness (ILI) activity level data from the U.S. We propose to use the Fourier basis function for transforming discrete weekly data to the smoothed functional ILI activities. Functional analysis of variance (FANOVA) is used to examine the regional differences in temporal patterns and the impact of state's political orientation.

RESULTS

The ILI activity has a very distinct peak at the beginning and end of the year. There are significant differences in average level of ILI activities among geographic regions. However, the temporal patterns in terms of the peak and flat time are quite consistent across regions. The geographic and temporal patterns of ILI activities also depend on the political make-up of states. The states affiliated with Republicans had higher ILI activities than those affiliated with Democrats across the whole year. The influence of political party affiliation on temporal pattern is quite different among geographic regions.

CONCLUSIONS

Functional data analysis can help us to reveal the temporal variability in average ILI levels, rate of change in ILI levels, and the effect of geographical regions. Consideration should be given to wider application of FDA to generate more accurate estimates in public health and biomedical research.

Functional Data Visualization and Outlier Detection on the Anomaly of El Niño Southern Oscillation

The El Niño Southern Oscillation (ENSO) is a well-known cause of year-to-year climatic variations on Earth. Floods, droughts, and other natural disasters have been linked to the ENSO in various parts of the world. Hence, modeling the ENSO’s effects and the anomaly of the ENSO phenomenon has become a main research interest. Statistical methods, including linear and nonlinear models, have intensively been used in modeling the ENSO index. However, these models are unable to capture sufficient information on ENSO index variability, particularly on its temporal aspects. Hence, this study adopted functional data analysis theory by representing a multivariate ENSO index (MEI) as functional data in climate applications. This study included the functional principal component, which is purposefully designed to find new functions that reveal the most important type of variation in the MEI curve. Simultaneously, graphical methods were also used to visualize functional data and capture outliers that may not have been apparent from the original data plot. The findings suggest that the outliers obtained from the functional plot are then related to the El Niño and La Niña phenomena. In conclusion, the functional framework was found to be more flexible in representing the climate phenomenon as a whole.

Urban road congestion patterns under the COVID-19 pandemic: A case study in Shanghai

The novel coronavirus (COVID-19) pandemic has had a significant impact on human mobility around the world. Many cities issued “stay-at-home” orders during the outbreak of COVID-19, and many commuters have also changed their travel modes in the post pandemic period; e.g., transit/bus passengers have switched to driving or car-sharing. Urban road traffic congestion patterns are significantly different than they were pre-pandemic, and understanding such changes can be an opportunity to improve future emergency traffic management and control. Previous studies on this topic have focused on natural disasters or major accidents/incidents. However, very few studies have analyzed the empirical traffic congestion patterns that have occurred during a pandemic. This study takes Shanghai as an example, and conducts a retrospective analysis of empirical spatio-temporal road traffic congestion during the COVID-19 pandemic. The three-month road traffic speed data in the 446 Traffic Analysis Zones (TAZs) collected from Baidu Maps was used in this study. The algorithm of Singular Value Decomposition (SVD) was employed to investigate the inherent composition of the spatio-temporal variation simultaneously influenced by several factors. Three principal components were identified from the spatio-temporal variation, including the stable, main part of variation; the part of the variation that is affected by commuting; and the part of the variation that is affected by migrant populations and the pandemic. The results may suggest ways to improve the emergency management and control of urban roadways in other metropolitan areas worldwide during and after the COVID-19 pandemic period.

Advanced Statistical Analysis of 3D Kinect Data: A Comparison of the Classification Methods

This paper focuses on the statistical analysis of mimetic muscle rehabilitation after head and neck surgery causing facial paresis in patients after head and neck surgery. Our work deals with an evaluation problem of mimetic muscle rehabilitation that is observed by a Kinect stereo-vision camera. After a specific brain surgery, patients are often affected by face palsy, and rehabilitation to renew mimetic muscle innervation takes several months. It is important to be able to observe the rehabilitation process in an objective way. The most commonly used House–Brackmann (HB) scale is based on the clinician’s subjective opinion. This paper compares different methods of supervised learning classification that should be independent of the clinician’s opinion. We compare a parametric model (based on logistic regression), non-parametric model (based on random forests), and neural networks. The classification problem that we have studied combines a limited dataset (it contains only 122 measurements of 93 patients) of complex observations (each measurement consists of a collection of time curves) with an ordinal response variable. To balance the frequencies of the considered classes in our data set, we reclassified the samples from HB4 to HB3 and HB5 to HB6—it means that only four HB grades are used for classification algorithm. The parametric statistical model was found to be the most suitable thanks to its stability, tractability, and reasonable performance in terms of both accuracy and precision.

Comparison of functional and discrete data analysis regimes for Raman spectra

Raman spectral data are best described by mathematical functions; however, due to the spectroscopic measurement setup, only discrete points of these functions are measured. Therefore, we investigated the Raman spectral data for the first time in the functional framework. First, we approximated the Raman spectra by using B-spline basis functions. Afterwards, we applied the functional principal component analysis followed by the linear discriminant analysis (FPCA-LDA) and compared the results with those of the classical principal component analysis followed by the linear discriminant analysis (PCA-LDA). In this context, simulation and experimental Raman spectra were used. In the simulated Raman spectra, normal and abnormal spectra were used for a classification model, where the abnormal spectra were built by shifting one peak position. We showed that the mean sensitivities of the FPCA-LDA method were higher than the mean sensitivities of the PCA-LDA method, especially when the signal-to-noise ratio is low and the shift of the peak position is small. However, for a higher signal-to-noise ratio, both methods performed equally. Additionally, a slight improvement of the mean sensitivity could be shown if the FPCA-LDA method was applied to experimental Raman data.

Prescreening and treatment of aortic dissection through an analysis of infinite-dimension data

BACKGROUND

Aortic dissection (AD) is one of the most catastrophic aortic diseases associated with a high mortality rate. In contrast to the advances in most cardiovascular diseases, both the incidence and in-hospital mortality rate of AD have experienced deviant increases over the past 20 years, highlighting the need for fresh prospects on the prescreening and in-hospital treatment strategies.

METHODS

Through two cross-sectional studies, we adopt image recognition techniques to identify pre-disease aortic morphology for prior diagnoses; assuming that AD has occurred, we employ functional data analysis to determine the optimal timing for BP and HR interventions to offer the highest possible survival rate.

RESULTS

Compared with the healthy control group, the aortic centerline is significantly more slumped for the AD group. Further, controlling patients' blood pressure and heart rate according to the likelihood of adverse events can offer the highest possible survival probability.

CONCLUSIONS

The degree of slumpness is introduced to depict aortic morphological changes comprehensively. The morphology-based prediction model is associated with an improvement in the predictive accuracy of the prescreening of AD. The dynamic model reveals that blood pressure and heart rate variations have a strong predictive power for adverse events, confirming this model's ability to improve AD management.

Principal Component Analysis of the Running Ground Reaction Forces With Different Speeds

Ground reaction force (GRF) is a key metric in biomechanical research, including parameters of loading rate (LR), first impact peak, second impact peak, and transient between first and second impact peaks in heel strike runners. The GRFs vary over time during stance. This study was aimed to investigate the variances of GRFs in rearfoot striking runners across incremental speeds. Thirty female and male runners joined the running tests on the instrumented treadmill with speeds of 2.7, 3.0, 3.3, and 3.7 m/s. The discrete parameters of vertical average loading rate in the current study are consistent with the literature findings. The principal component analysis was modeled to investigate the main variances (95%) in the GRFs over stance. The females varied in the magnitude of braking and propulsive forces (PC1, 84.93%), whereas the male runners varied in the timing of propulsion (PC1, 53.38%). The female runners dominantly varied in the transient between the first and second peaks of vertical GRF (PC1, 36.52%) and LR (PC2, 33.76%), whereas the males variated in the LR and second peak of vertical GRF (PC1, 78.69%). Knowledge reported in the current study suggested the difference of the magnitude and patterns of GRF between male and female runners across different speeds. These findings may have implications for the prevention of sex-specific running-related injuries and could be integrated with wearable signals for the in-field prediction and estimation of impact loadings and GRFs.

Hyoid kinematic features for poor swallowing prognosis in patients with post-stroke dysphagia

Identification of prognostic factors for swallowing recovery in patients with post-stroke dysphagia is crucial for determining therapeutic strategies. We aimed at exploring hyoid kinematic features of poor swallowing prognosis in patients with post-stroke dysphagia. Of 122 patients who experienced dysphagia following ischemic stroke, 18 with poor prognosis, and 18 age- and sex-matched patients with good prognosis were selected and retrospectively reviewed. Positional data of the hyoid bone during swallowing were obtained from the initial videofluoroscopic swallowing study after stroke onset. Normalized hyoid profiles of displacement/velocity and direction angle were analyzed using functional regression analysis, and maximal or mean values were compared between the good and poor prognosis patient groups. Kinematic analysis showed that maximal horizontal displacement (P = 0.031) and velocity (P = 0.034) in forward hyoid motions were significantly reduced in patients with poor prognosis compared to those with good prognosis. Mean direction angle for the initial swallowing phase was significantly lower in patients with poor prognosis than in those with good prognosis (P = 0.0498). Our study revealed that reduced horizontal forward and altered initial backward motions of the hyoid bone during swallowing can be novel kinematic features indicating poor swallowing prognosis in patients with post-stroke dysphagia.

Advanced Statistical Analysis of 3D Kinect Data: Mimetic Muscle Rehabilitation Following Head and Neck Surgeries Causing Facial Paresis

An advanced statistical analysis of patients’ faces after specific surgical procedures that temporarily negatively affect the patient’s mimetic muscles is presented. For effective planning of rehabilitation, which typically lasts several months, it is crucial to correctly evaluate the improvement of the mimetic muscle function. The current way of describing the development of rehabilitation depends on the subjective opinion and expertise of the clinician and is not very precise concerning when the most common classification (House–Brackmann scale) is used. Our system is based on a stereovision Kinect camera and an advanced mathematical approach that objectively quantifies the mimetic muscle function independently of the clinician’s opinion. To effectively deal with the complexity of the 3D camera input data and uncertainty of the evaluation process, we designed a three-stage data-analytic procedure combining the calculation of indicators determined by clinicians with advanced statistical methods including functional data analysis and ordinal (multiple) logistic regression. We worked with a dataset of 93 distinct patients and 122 sets of measurements. In comparison to the classification with the House–Brackmann scale the developed system is able to automatically monitor reinnervation of mimetic muscles giving us opportunity to discriminate even small improvements during the course of rehabilitation.

Identifying subpopulations of septic patients: A temporal data-driven approach

Sepsis is one of the deadliest diseases in North America and in spite of the vast amount of research on this topic there is still uncertainty in the outcome of sepsis treatments. This study aimed at investigating the informativeness of temporal electronic health records (EHR) in stratifying septic patients and identifying subpopulations of septic patients with similar trajectories and clinical needs. We performed hierarchical clustering and Density-Based Spatial Clustering of Applications with Noise (DBSCAN) analyses using data from septic patients in the MIMIC III intensive care unit database. The t-Distributed Stochastic Neighbor Embedding (t-SNE) method was utilized to map patients to a two-dimensional space. We utilized silhouette index and cluster-wise stability assessment by resampling to investigate the validity of the clusters. The hierarchical clustering with Euclidean metric identified twelve clinically recognizable subgroups that demonstrated different characteristics in spite of sharing common conditions. Our results demonstrated that data-driven approaches can help in customizing care platforms for septic patients by identifying similar clinically relevant groups.