Functional Data Analysis Applications in Medicine: A Systematic Review

Functional data analysis (FDA) is a contemporary area of statistics designed for analysis of functions or curves. FDA has grown in human movement applications over the last three decades, with it being applied across a range of sport applications including rowing, weightlifting, diving, race-walking, jumping and running. Functional principal components analysis (fPCA) has been the most commonly used technique in sports biomechanics, often being applied to better understand characteristics of variability present in curves from biomechanical variables sampled from sporting movements. Given that FDA is an area of statistics with specific techniques for processing and analysing data, it provides one valuable platform for biomechanists to understand and think about their data more holistically. Further, the visual interpretability that FDA techniques provide, there is great potential for FDA to be used beyond research contexts, as a suite of practical tools to assist practical sports biomechanists in making decisions in sport. This review aims to demonstrate some methods yet to be applied in sports biomechanics, with simple sports biomechanics data applications taken from rowing. This article aims to showcase the value that FDA may have in assisting practitioners as they make decisions with athletes regarding their movement characteristics.

Data with spatio-temporal structure can arise in many contexts, therefore a considerable interest in modelling these data has been generated, but the complexity of spatio-temporal models, together with the size of the dataset, results in a challenging task. The modelization is even more complex in presence of multivariate data. Since some modelling problems are more natural to think through in functional terms, even if only a finite number of observations is available, treating the data as functional can be useful (Berrendero et al. in Comput Stat Data Anal 55:2619–2634, 2011). Although in Ramsay and Silverman (Functional data analysis, 2nd edn. Springer, New York, 2005) the case of multivariate functional data is also contemplated, they do not cope with more than one dimension (only time is considered as covariate) in the domain of the considered functions. In estimating functional data through smoothing methods, a proper framework for incorporating space-time structures can be found in the generalized additive models (GAM), while classical dimension reduction techniques for functional data lead to functional principal component analysis (FPCA). In a previous work Ruggieri et al. (J Appl Stat 40(4):795–807, 2013) extended temporal FPCA, that is FPCA on data modelled as functions of the one-dimensional time, to multivariate (more than one variable, in our case pollutants) context. In this paper the computational aspects of FPCA are extended to more than one dimension: space (long, lat) and/or space-time; moreover, multidimensional (spatial, spatio-temporal) FPCA is extended to multivariate case. In order to provide a generalization of FPCA to multidimensional (spatio-temporal) and simultaneously multivariate data, we link GAM models together with the approach proposed by Ramsay and Silverman (2005). The paper describes all the computational details useful to implement this approach, while its effectiveness will be shown by a multivariate spatio-temporal environmental dataset, whose structure is actually very common in literature.

BackgroundA key problem in systems biology is estimating dynamical models of gene regulatory networks. Traditionally, this has been done using regression or other ad-hoc methods when the model is linear. More detailed, realistic modeling studies usually employ nonlinear dynamical models, which lead to computationally difficult parameter estimation problems. Functional data analysis methods, however, offer a means to simplify fitting by transforming the problem from one of matching modeled and observed dynamics to one of matching modeled and observed time derivatives–a regression problem, albeit a nonlinear one.ResultsWe formulate a functional data analysis approach for estimating the parameters of nonlinear dynamical models and evaluate this approach on data from two real systems, the gap gene system of Drosophila melanogaster and the synthetic IRMA network, which was created expressly as a test case for genetic network inference. We also evaluate the approach on simulated data sets generated by the GeneNetWeaver program, the basis for the annual DREAM reverse engineering challenge. We assess the accuracy with which the correct regulatory relationships within the networks are extracted, and consider alternative methods of regularization for the purpose of overfitting avoidance. We also show that the computational efficiency of the functional data analysis approach, and the decomposability of the resulting regression problem, allow us to explicitly enumerate and evaluate all possible regulator combinations for every gene. This gives deeper insight into the the relevance of different regulators or regulator combinations, and lets one check for alternative regulatory explanations.ConclusionsFunctional data analysis is a powerful approach for estimating detailed nonlinear models of gene expression dynamics, allowing efficient and accurate estimation of regulatory architecture.

The objective of this study is to develop a privacy-preserving framework for publishing longitudinal health data. Longitudinal health data contain valuable clinical information about patients collected over time and there is an increasing demand to use these data in medical and clinical research. However, since longitudinal health data contain personal information, improper release and usage of such data may violate privacy of patients. In this paper, we study the challenges of publishing longitudinal health data and propose a privacy notion, called (K,C) <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">P</sup> -privacy together with a hybrid anonymization algorithm. This work is the first attempt to anonymize multidimensional longitudinal data to prevent both identity disclosure and attribute disclosure. Experimental results on the synthetic data demonstrate the effectiveness of our approach.

Application of functional data analysis to explore movements: walking, running and jumping - A systematic review

BackgroundThe increasing development of artificial intelligence (AI) systems in medicine driven by researchers and entrepreneurs goes along with enormous expectations for medical care advancement. AI might change the clinical practice of physicians from almost all medical disciplines and in most areas of health care. While expectations for AI in medicine are high, practical implementations of AI for clinical practice are still scarce in Germany. Moreover, physicians’ requirements and expectations of AI in medicine and their opinion on the usage of anonymized patient data for clinical and biomedical research have not been investigated widely in German university hospitals.ObjectiveThis study aimed to evaluate physicians’ requirements and expectations of AI in medicine and their opinion on the secondary usage of patient data for (bio)medical research (eg, for the development of machine learning algorithms) in university hospitals in Germany.MethodsA web-based survey was conducted addressing physicians of all medical disciplines in 8 German university hospitals. Answers were given using Likert scales and general demographic responses. Physicians were asked to participate locally via email in the respective hospitals.ResultsThe online survey was completed by 303 physicians (female: 121/303, 39.9%; male: 173/303, 57.1%; no response: 9/303, 3.0%) from a wide range of medical disciplines and work experience levels. Most respondents either had a positive (130/303, 42.9%) or a very positive attitude (82/303, 27.1%) towards AI in medicine. There was a significant association between the personal rating of AI in medicine and the self-reported technical affinity level (H4=48.3, P<.001). A vast majority of physicians expected the future of medicine to be a mix of human and artificial intelligence (273/303, 90.1%) but also requested a scientific evaluation before the routine implementation of AI-based systems (276/303, 91.1%). Physicians were most optimistic that AI applications would identify drug interactions (280/303, 92.4%) to improve patient care substantially but were quite reserved regarding AI-supported diagnosis of psychiatric diseases (62/303, 20.5%). Of the respondents, 82.5% (250/303) agreed that there should be open access to anonymized patient databases for medical and biomedical research.ConclusionsPhysicians in stationary patient care in German university hospitals show a generally positive attitude towards using most AI applications in medicine. Along with this optimism comes several expectations and hopes that AI will assist physicians in clinical decision making. Especially in fields of medicine where huge amounts of data are processed (eg, imaging procedures in radiology and pathology) or data are collected continuously (eg, cardiology and intensive care medicine), physicians’ expectations of AI to substantially improve future patient care are high. In the study, the greatest potential was seen in the application of AI for the identification of drug interactions, assumedly due to the rising complexity of drug administration to polymorbid, polypharmacy patients. However, for the practical usage of AI in health care, regulatory and organizational challenges still have to be mastered.

Functional principal component analysis (FPCA) has been widely used to capture major modes of variation and reduce dimensions in functional data analysis. However, standard FPCA based on the sample covariance estimator does not work well if the data exhibits heavy-tailedness or outliers. To address this challenge, a new robust FPCA approach based on a functional pairwise spatial sign (PASS) operator, termed PASS FPCA, is introduced. We propose robust estimation procedures for eigenfunctions and eigenvalues. Theoretical properties of the PASS operator are established, showing that it adopts the same eigenfunctions as the standard covariance operator and also allows recovering ratios between eigenvalues. We also extend the proposed procedure to handle functional data measured with noise. Compared to existing robust FPCA approaches, the proposed PASS FPCA requires weaker distributional assumptions to conserve the eigenspace of the covariance function. Specifically, existing work are often built upon a class of functional elliptical distributions, which requires inherently symmetry. In contrast, we introduce a class of distributions called the weakly functional coordinate symmetry (weakly FCS), which allows for severe asymmetry and is much more flexible than the functional elliptical distribution family. The robustness of the PASS FPCA is demonstrated via extensive simulation studies, especially its advantages in scenarios with nonelliptical distributions. The proposed method was motivated by and applied to analysis of accelerometry data from the Objective Physical Activity and Cardiovascular Health Study, a large-scale epidemiological study to investigate the relationship between objectively measured physical activity and cardiovascular health among olderwomen.

For detecting anomalies or interventions in the field of forest monitoring we propose an approach based on the spatial and temporal forecast of satellite time series data. For each pixel of the satellite image three different types of forecasts are provided, namely spatial, temporal and combined spatio-temporal forecast. Spatial forecast means that a clustering algorithm is used to group the time series data based on the features normalised difference vegetation index (NDVI) and the short-wave infrared band (SWIR). For estimation of the typical temporal trajectory of the NDVI and SWIR during the vegetation period of each spatial cluster, we apply several methods of functional data analysis including functional principal component analysis, and a novel form of random regression forests with online learning (streaming) capability. The temporal forecast is carried out by means of functional time series analysis and an autoregressive integrated moving average model. The combination of the temporal forecasts, which is based on the past of the considered pixel, and spatial forecasts, which is based on highly correlated pixels within one cluster and their past, is performed by functional data analysis, and a variant of random regression forests adapted to online learning capabilities. For evaluation of the methods, the approaches are applied to a study area in Germany for monitoring forest damages caused by wind-storm, and to a study area in Spain for monitoring forest fires.

We present a load carriage analysis for Malaysian soldier using functional data analysis (FDA) technique. The objectives of the study are to test the significance of curve registration in the analysis process flow and to investigate the effect of 10% load increment from 0% BW up to 40% BW on ground reaction force (GRF) for normal walking. Preliminary experiment on GRF was done using Vicon 1.4 motion analysis system, Kirstle and AMTI force plates and markers. Functional data analysis method was applied to analyze the data. B-spline smoothing, time normalization, landmark registration and permutation tests were performed. The result confirms that FDA is one of the best techniques in analyzing gait data. Curves registration can well distinguish the load increment and should be included in analysis sequences. The results show that 10 % BW load increment has significant effect on GRF for a Malaysian military.

In health research discourse, there is the assumption that a controlled, planned clinical research naturally produces cleaner datasets, while real-world data suffers from quality deficiencies due to its spontaneous collection without anticipation of secondary research use. However, this binary view simplifies a complex reality. Both clinical research and real-world data exhibit quality issues, challenging the convention that data origin determines data integrity. What proves to be more vital is the way data quality (DQ) is being assessed—particularly when examining the exhibited relationships between data items that reflect the true complexity of healthcare information. Health data is inherently interconnected e.g., height relates to weight and age; medication dosages connect to patient characteristics and medical conditions. Yet most data quality assessment (DQA) studies limit their logical evaluations to only a handful of interdependent items, missing the broader web of relationships that could reveal critical quality issues. Contradictions within datasets serve as an important DQ indicator (measurable attribute of data) that extend far beyond simple data entry errors. When values contradict each other, they reveal misunderstandings of domain knowledge, failures in data capture infrastructure, and problems in data transformation processes. Given the complexity of the contradiction patterns, a comprehensive assessment becomes essential. Comprehensive DQA in health research requires evaluating data on multiple dimensions, such as completeness, conformance, and plausibility, to determine the suitability of data for intended use. These dimensions are used to group related measurable attributes of data referred to as indicators. While some DQ indicators are implemented as generic rules (e.g., completeness), contradiction, which denotes pair(s) of measurements or facts that cannot logically coexist, are multi-dimensional. Some contradictions require common knowledge for their evaluation—e.g., the disparity in age information at baseline and during follow-up visits. However, contradictions in the pre-analytic states of blood samples require knowledge of experts. Although various tools have been developed to assess contradictions in health data, the evolving nature of contradiction rules presents the following challenges for existing tools: 1) limited reusability across diverse health datasets due to incompatible predefined rules, 2) insufficient contextual information required for comprehensive contradiction assessment, and 3) lack of consistent representation of contradiction patterns to support transparent rule implementations and computational efficiency. To address these gaps in a systematic manner, the first step of this thesis was to adapt an existing tool developed based on an existing framework to assess broader contradiction rules introduced in the German Corona Consensus (GECCO) dataset. Building on the experience from the modification of Schmidt et al.'s tool, this thesis developed a new framework that generalizes the DQA tool to accept custom contradiction rules compatible with diverse health datasets. This is intended to empower domain experts in defining effective contradiction rules on an ad-hoc basis while maintaining alignment with established DQ indicators. Although the primary dependencies between health data items form the basis for contradiction rule definition, the required context for a comprehensive analysis is equally relevant. For example, diabetes mellitus (DM) and insulin medication (INS) are two interdependent items, however, it is the timestamps that indicate if the INS was administered before the DM diagnosis, which is a prelude for a conclusive contradiction finding. Through a qualitative grading scheme for analyzing metadata defined in a study database, this work created a mechanism to measure the availability of the contextual information required to support a context-aware contradiction analysis. However, having access to rich contextual information is only part of the solution—the way contradiction rules are structured and implemented is equally critical for effective DQA. While researchers have worked extensively on harmonizing DQ indicators, the challenge extends beyond categorization to implementation efficiency. Though the taxonomies for contradictions, such as logical and empirical contradictions, reflect the domain description, the rules implemented in the DQA systems do not rely on semantics. Extracting the structure of the varied contradiction patterns ensures transparency and consistency in rule implementation. This work evaluated the performance of different rule implementations and offered an optimization method that integrates the fastest and traceable units of the rules in one unified implementation. This is relevant because broadly defined DQA rules can cause performance degradation in large database infrastructures. With these several perspectives on contradictions as a DQ indicator, the contributions in this thesis enhance contradiction assessment by improving reusability across diverse health datasets, enabling context-aware assessments, and optimizing rule implementation for transparency and computational efficiency. This systematic approach supports high-quality health data assessment while maintaining traceability to support data cleansing efforts.

The differentiation between age classes of Scots pine ( Pinus sylvestris L.) was analyzed with regard to the five-year increment of seven traits: height growth (zh5), diameter growth at breast height (zd5), cross-sectional area growth at breast height (zg5), volume growth (zv5), volume growth intensity coefficient (i5), and slenderness (s). Measurements were made in five periods for 24-year-old trees and six periods for 33-year-old trees, all growing in fresh mixed coniferous forest sites. Repeated measures data analysis was conducted separately for all traits. Multivariable functional data analysis (FDA) was proposed to compare age classes of trees. The functional variables which resulted from this analysis can be used, as data, in many analyses (designate functions representing each of trees, FPCA – functional principal component analysis, FLDC – discriminant analysis, permutation analysis of variance). The results of the above analyses revealed significant differences between age groups. Furthermore the functions and FPCA were used to detect outliers. This procedure had not previously been used for such a purpose. FPCA explained 55% of the total variance, with the first two components clearly separating the groups. The study showed that 33-year-old trees exhibit stable growth, while 24-year-old trees show greater variability, highlighting the impact of age on growth dynamics. Permutation analysis of variance confirmed significant growth differences between the groups. The findings highlight the importance of age as a factor influencing tree growth and demonstrate the effectiveness of the multivariable FDA approach for analyzing such data.

The knowledge of the urban air quality represents the first step to face air pollution issues. For the last decades many cities can rely on a network of monitoring stations recording concentration values for the main pollutants. This paper focuses on functional principal component analysis (FPCA) to investigate multiple pollutant datasets measured over time at multiple sites within a given urban area. Our purpose is to extend what has been proposed in the literature to data that are multisite and multivariate at the same time. The approach results to be effective to highlight some relevant statistical features of the time series, giving the opportunity to identify significant pollutants and to know the evolution of their variability along time. The paper also deals with missing value issue. As it is known, very long gap sequences can often occur in air quality datasets, due to long time failures not easily solvable or to data coming from a mobile monitoring station. In the considered dataset, large and continuous gaps are imputed by empirical orthogonal function procedure, after denoising raw data by functional data analysis and before performing FPCA, in order to further improve the reconstruction.

Improvements in next-generation sequencing (NGS) technology and computer systems have enabled personalized therapies based on genomic information. Recently, health management strategies using genomics and big data have been developed for application in medicine and public health science. In this review, I first discuss the development of a genomic information management system (GIMS) to maintain a highly detailed health record and detect diseases by collecting the genomic information of one individual over time. Maintaining a health record and detecting abnormal genomic states are important; thus, the development of a GIMS is necessary. Based on the current research status, open public data, and databases, I discuss the possibility of a GIMS for clinical use. I also discuss how the analysis of genomic information as big data can be applied for clinical and research purposes. Tremendous volumes of genomic information are being generated, and the development of methods for the collection, cleansing, storing, indexing, and serving must progress under legal regulation. Genetic information is a type of personal information and is covered under privacy protection; here, I examine the regulations on the use of genetic information in different countries. This review provides useful insights for scientists and clinicians who wish to use genomic information for healthy aging and personalized medicine.

We consider modeling and analysis of functional data arising in method comparison studies. The observed data consist of repeated measurements of a continuous variable obtained using multiple methods of measurement on a sample of subjects. The data are treated as multivariate functional data that are observed with noise at a common set of discrete time points which may vary from subject to subject. The proposed methodology uses functional principal components analysis within the framework of a mixed-effects model to represent the observations in terms of a small number of method-specific principal components. Two approaches for estimating the unknowns in the model, both adaptations of general techniques developed for multivariate functional principal components analysis, are presented. Bootstrapping is employed to get estimates of bias and covariance matrix of model parameter estimates. These in turn are used to compute confidence intervals for parameters and functions thereof, such as the measures of similarity and agreement between the measurement methods, that are necessary for data analysis. The estimation approaches are evaluated using simulation. The methodology is illustrated by analyzing two datasets.

To the Editor Drs Newgard and Lewis1 provided an overview of many important issues to consider when dealing with missing data in clinical research. In particular, they summarized the following limitations of traditional imputation methods: failure to account for uncertainty in imputed values, failure to make full use of observed values, possibilities for bias, and artificially low variance.