Functional Principal Component Analysis Research Articles

Language-Specific Prosody in Statements of Palenquero/Spanish Bilinguals

This study explores the extent to which Palenquero/Spanish bilinguals, a population that is said to have a residual high tone of African origin, keep their two languages temporally and intonationally distinct across statements. While creole languages that emerged from the contact of African and European languages, such as Palenquero, may develop hybrid prosodic systems with tones from substrate languages, and stress from the majority language, language-specific prosody might be expected to converge or simplify over the course of time. As prosodic convergence seems to be inescapable under Palenquero’s circumstances, which factors could support language-specific prosody in this population, if there are any? Two-hundred and thirty-four five-syllable statements were elicited through a discourse completion task, with the participation of ten Palenquero/Spanish bilinguals, in two unilingual sessions. Both phrase-final lengthening and F0 contours were assessed using linear mixed-effects models testing their association with final stress, language, and generation. F0 contours were dimensionally reduced using functional principal component analysis. Despite the strong similarities between the two languages, results indicate that both groups keep their two languages intonationally distinct using plateau-shaped contours in Palenquero initial rises followed by steeper declinations in Spanish. However, elderly bilinguals implement penultimate lengthening language-specifically, being more pronounced in Palenquero. Adults, in contrast, do not show this distinction. In addition to this, elderly speakers show hyperarticulation in Spanish intonation, increasing the difference between their languages. This leads us to believe that adults exhibit a more simplified prosodic system between their languages, relative to elderly bilinguals. In spite of such differences, both generations seem to have the same underlying process (perhaps a substrate effect) driving plateau-shaped intonation in Palenquero, which enhances language differentiation.

Functional sufficient dimension reduction through information maximization with application to classification

Considering the case where the response variable is a categorical variable and the predictor is a random function, two novel functional sufficient dimensional reduction (FSDR) methods are proposed based on mutual information and square loss mutual information. Compared to the classical FSDR methods, such as functional sliced inverse regression and functional sliced average variance estimation, the proposed methods are appealing because they are capable of estimating multiple effective dimension reduction directions in the case of a relatively small number of categories, especially for the binary response. Moreover, the proposed methods do not require the restrictive linear conditional mean assumption and the constant covariance assumption. They avoid the inverse problem of the covariance operator which is often encountered in the functional sufficient dimension reduction. The functional principal component analysis with truncation be used as a regularization mechanism. Under some mild conditions, the statistical consistency of the proposed methods is established. Simulation studies and real data analyzes are used to evaluate the finite sample properties of our methods.

Impaired Neuromotor Control During Gait in Concussed Adolescents-A Frequency Analysis.

Disruptions in gait function are common after concussion in adolescents; however, the neuromotor control deficits driving these gait disruptions are not well known. Fifteen concussed (age mean [SD]): 17.4 [0.6], 13 females, days since injury: 26.3 [9.9]) and 17 uninjured (age: 18.0 [0.7], 10 females) adolescents completed 3 trials each of single-task gait and dual-task gait (DT). During DT, participants simultaneously walked while completing a serial subtraction task. Gait metrics and variability in instantaneous mean frequency in lower extremity muscles were captured by inertial sensors and surface electromyography, respectively. A 2-way analysis of covariance was used to compare gait metrics across groups and conditions. Functional principal components analysis was used to identify regions of variability in instantaneous mean frequency curves. Functional principal component scores were compared across groups using a Welch statistic. Both groups displayed worse performance on gait metrics during DT condition compared to single-task, with no differences between groups (P < .001). Concussed adolescents displayed significantly greater instantaneous mean frequency, indicated by functional principal component 1, in the tibialis anterior, biceps femoris, and semitendinosus (P < .05) during single-task and DT compared with uninjured adolescents. Our observations suggest that concussed adolescents display inefficient motor unit recruitment lasting longer than 2weeks following injury, regardless of the addition of a secondary task.

Evaluation and Selection of Multi-Spectral Indices to Classify Vegetation Using Multivariate Functional Principal Component Analysis

The identification, classification and mapping of different plant communities and habitats is of fundamental importance for defining biodiversity monitoring and conservation strategies. Today, the availability of high temporal, spatial and spectral data from remote sensing platforms provides dense time series over different spectral bands. In the case of supervised mapping, time series based on classical vegetation indices (e.g., NDVI, GNDVI, …) are usually input characteristics, but the selection of the best index or set of indices (which guarantees the best performance) is still based on human experience and is also influenced by the study area. In this work, several different time series, based on Sentinel-2 images, were created exploring new combinations of bands that extend the classic basic formulas as the normalized difference index. Multivariate Functional Principal Component Analysis (MFPCA) was used to contemporarily decompose the multiple time series. The principal multivariate seasonal spectral variations identified (MFPCA scores) were classified by using a Random Forest (RF) model. The MFPCA and RF classifications were nested into a forward selection strategy to identify the proper and minimum set of indices’ (dense) time series that produced the most accurate supervised classification of plant communities and habitat. The results we obtained can be summarized as follows: (i) the selection of the best set of time series is specific to the study area and the habitats involved; (ii) well-known and widely used indices such as the NDVI are not selected as the indices with the best performance; instead, time series based on original indices (in terms of formula or combination of bands) or underused indices (such as those derivable with the visible bands) are selected; (iii) MFPCA efficiently reduces the dimensionality of the data (multiple dense time series) providing ecologically interpretable results representing an important tool for habitat modelling outperforming conventional approaches that consider only discrete time series.

Multivariate Functional Clustering with Variable Selection and Application to Sensor Data from Engineering Systems

Multisensor data that track system operating behaviors are widely available nowadays from various engineering systems. Measurements from each sensor over time form a curve and can be viewed as functional data. Clustering of these multivariate functional curves is important for studying the operating patterns of systems. One complication in such applications is the possible presence of sensors whose data do not contain relevant information. Hence, it is desirable for the clustering method to equip with an automatic sensor selection procedure. Motivated by a real engineering application, we propose a functional data clustering method that simultaneously removes noninformative sensors and groups functional curves into clusters using informative sensors. Functional principal component analysis is used to transform multivariate functional data into a coefficient matrix for data reduction. We then model the transformed data by a Gaussian mixture distribution to perform model-based clustering with variable selection. Three types of penalties, the individual, variable, and group penalties, are considered to achieve automatic variable selection. Extensive simulations are conducted to assess the clustering and variable selection performance of the proposed methods. The application of the proposed methods to an engineering system with multiple sensors shows the promise of the methods and reveals interesting patterns in the sensor data. History: Kwok Tsui served as the senior editor for this article. Funding: The research by J. Min and Y. Hong was partially supported by the National Science Foundation [Grant CMMI-1904165] to Virginia Tech. The work by Y. Hong was partially supported by the Virginia Tech College of Science Research Equipment Fund. Data Ethics &amp; Reproducibility Note: The original dataset is proprietary and cannot be shared. The full code to replicate the results in this paper, based on summary statistics of the original data, is available at https://github.com/jiem3/MultiFuncClustering . The code applied to a simplified version is available at https://codeocean.com/capsule/4041000/tree/v1 , which covers the data analysis and part of the simulation scenarios with a single dataset under each scenario using a fixed set of hyperparameters, for reducing computation time, and at https://doi.org/10.1287/ijds.2022.0034 .

Joint analysis of multivariate longitudinal, imaging, and time-to-event data

Abstract Alzheimer’s (AD) is a progressive neurodegenerative disease frequently associated with memory deficits and cognitive decline. Despite its irreversible once onset, some discoveries revealed the existence of a certain percentage of people who are non-susceptible to AD. This study proposes a joint analysis of multivariate longitudinal data, survival data with a non-susceptible fraction, and ultrahigh-dimensional imaging data. The proposed model comprises three major components. The first component is a mixture proportional hazards cure model with images to examine the potential predictors of the non-susceptible probability and hazards of interest. The second component is a dynamic factor analysis model with images to characterize group-specific latent factors through multiple observed variables. The last component is a semiparametric trajectory model to reveal the change patterns of the dynamic latent factors in the ‘non-susceptible’ and ‘susceptible’ groups. A two-stage approach is developed for statistical inference. The first stage manages the imaging data through high-dimensional functional principal component analysis. The second stage develops a Bayesian approach coupled with penalized splines, data augmentation, and Markov chain Monte Carlo techniques to perform estimation. The application to the Alzheimer’s Disease Neuroimaging Initiative dataset sheds new insight into the pathology of AD.

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

BackgroundIntensive 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.ObjectiveTo 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.MethodsfPCA 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.ResultsBased 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, \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${R}_{adjusted}^{2}=0.61$$\\end{document}).ConclusionsFunctional 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.

Functional principal component analysis for incomplete space–time data

AbstractEnvironmental signals, acquired, e.g., by remote sensing, often present large gaps of missing observations in space and time. In this work, we present an innovative approach to identify the main variability patterns, in space–time data, when data may be affected by complex missing data structures. We formalize the problem in the framework of functional data analysis, proposing an innovative method of functional principal component analysis (fPCA) for incomplete space–time data. The functional nature of the proposed method permits to borrow information from measurements observed at nearby spatio-temporal locations. The resulting functional principal components are smooth fields over the considered spatio-temporal domain, and can lead to interesting insights in the spatio-temporal dynamic of the phenomenon under study. Moreover, they can be used to provide a reconstruction of the missing entries, also under severe missing data patterns. The proposed model combines a weighted rank-one approximation of the data matrix with a roughness penalty. We show that the estimation problem can be solved using a majorize–minimization approach, and provide a numerically efficient algorithm for its solution. Thanks to a discretization based on finite elements in space and B-splines in time, the proposed method can handle multidimensional spatial domains with complex shapes, such as water bodies with complicated shorelines, or curved spatial regions with complex orography. As shown by simulation studies, the proposed space–time fPCA is superior to alternative techniques for Principal Component Analysis with missing data. We further highlight the potentiality of the proposed method for environmental problems, by applying space–time fPCA to the study of the lake water surface temperature (LWST) of Lake Victoria, in Central Africa, starting from satellite measurements with large gaps. LWST is considered one of the fundamental indicators of how climate change is affecting the environment, and is recognized as an essential climate variable.

Functional support vector machine.

Linear and generalized linear scalar-on-function modeling have been commonly used to understand the relationship between a scalar response variable (e.g. continuous, binary outcomes) and functional predictors. Such techniques are sensitive to model misspecification when the relationship between the response variable and the functional predictors is complex. On the other hand, support vector machines (SVMs) are among the most robust prediction models but do not take account of the high correlations between repeated measurements and cannot be used for irregular data. In this work, we propose a novel method to integrate functional principal component analysis with SVM techniques for classification and regression to account for the continuous nature of functional data and the nonlinear relationship between the scalar response variable and the functional predictors. We demonstrate the performance of our method through extensive simulation experiments and two real data applications: the classification of alcoholics using electroencephalography signals and the prediction of glucobrassicin concentration using near-infrared reflectance spectroscopy. Our methods especially have more advantages when the measurement errors in functional predictors are relatively large.

Demonstrating the relevance of spatial-functional statistical analysis in marine ecological studies: The case of environmental variations in micronektonic layers

In this study, we conducted an analysis of a multifrequency acoustics dataset acquired from scientific echosounders in the West African water. Our objective was to explore the spatial arrangement of marine organism aggregations. We investigated various attributes of these intricate biological entities, such as thickness, relative density, and depth, in relation to their surroundings. These environmental conditions were represented at a fine scale using a towed multiparameter system. This study is closely intertwined with two key domains: Fisheries acoustics techniques and functional data analysis. Fisheries acoustics techniques facilitate the collection of high-resolution spatial and temporal data concerning marine organisms at various depths and spatial scales, all without causing any disturbance. On the other hand, spatial-functional data analysis is a statistical approach for examining data characterised by functional attributes distributed across a spatial domain. This analysis encompasses dimension reduction techniques, as well as supervised and unsupervised methods, which take into consideration spatial dependencies within extensive datasets.We began by applying multivariate statistical techniques and subsequently employed Functional Data Analysis (FDA). In the modeling section, we introduced the spatial dimension with the spatial coordinates as covariates in the General Additive Model (GAM) and Functional Generalized Spectral Additive Model (FGSAM) models, aiming to underscore its relevance in those contexts. In an exploratory phase, Multivariate Functional Principal Component Analysis provided detailed insights into the variations of parameters at different depths, a capability not offered by traditional Principal Component Analysis. When it came to regression tasks, we explored the interactions between descriptors of Sound Scattering Layers and key environmental variables, both with and without considering spatial dimensions. Our findings revealed significant distinctions between northern and southern Sound Scattering Layers, as well as between coastal and high-sea regions. The use of the spatial locations enhanced the performance of GAM and FGSAM, particularly in the case of salinity, reflecting the influence of water mixing and seawater temperature. The multifaceted effects of environmental variations on Sound Scattering Layers underscore the importance of spatial-functional statistical analysis in ecological studies involving complex, spatially functional objects. Beyond the scope of this specific case study, the application of functional data analysis shows promise for a wide array of ecological studies dealing with extensive spatial datasets.

Integrating Functional Principal Component Analysis with Data-Rich Experimentation for Enhanced Drug Substance Development

Integrating Functional Principal Component Analysis with Data-Rich Experimentation for Enhanced Drug Substance Development

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.

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. 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. 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). 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.

Age Is Associated With Dampened Circadian Patterns of Rest and Activity: The Study of Muscle, Mobility, and Aging (SOMMA).

The effects of aging on circadian patterns of behavior are insufficiently described. To address this, we characterized age-specific features of rest-activity rhythms (RAR) in community-dwelling older adults both overall, and in relation, to sociodemographic characteristics. We examined cross-sectional associations between RAR and age, sex, race, education, multimorbidity burden, financial, work, martial, health, and smoking status using assessments of older adults with wrist-worn free-living actigraphy data (N = 820, age = 76.4 years, 58.2% women) participating in the Study of Muscle, Mobility, and Aging (SOMMA). RAR parameters were determined by mapping an extension to the traditional cosine curve to activity data. Functional principal component analysis determined variables accounting for variance. Age was associated with several metrics of dampened RAR; women had stronger and more robust RAR versus men (all p < .05). Total activity (56%) and time of activity (20%) accounted for most of the RAR variance. Compared to the latest decile of acrophase, those in the earliest decile had higher average amplitude (p < .001). Compared to the latest decile of acrophase, those in the earliest and midrange categories had more total activity (p = .02). Being in a married-like relationship and a more stable financial situation were associated with stronger rhythms; higher education was associated with less rhythm strength (all p < .05). Older age was associated with dampened circadian behavior; behaviors were sexually dimorphic. Some sociodemographic characteristics were associated with circadian behavior. We identified a behavioral phenotype characterized by early time of day of peak activity, high rhythmic amplitude, and more total activity.

Projection-based two-sample inference for sparsely observed multivariate functional data.

Modern longitudinal studies collect multiple outcomes as the primary endpoints to understand the complex dynamics of the diseases. Oftentimes, especially in clinical trials, the joint variation among the multidimensional responses plays a significant role in assessing the differential characteristics between two or more groups, rather than drawing inferences based on a single outcome. We develop a projection-based two-sample significance test to identify the population-level difference between the multivariate profiles observed under a sparse longitudinal design. The methodology is built upon widely adopted multivariate functional principal component analysis to reduce the dimension of the infinite-dimensional multi-modal functions while preserving the dynamic correlation between the components. The test applies to a wide class of (non-stationary) covariance structures of the response, and it detects a significant group difference based on a single p-value, thereby overcoming the issue of adjusting for multiple p-values that arise due to comparing the means in each of components separately. Finite-sample numerical studies demonstrate that the test maintains the type-I error, and is powerful to detect significant group differences, compared to the state-of-the-art testing procedures. The test is carried out on two significant longitudinal studies for Alzheimer's disease and Parkinson's disease (PD) patients, namely, TOMMORROW study of individuals at high risk of mild cognitive impairment to detect differences in the cognitive test scores between the pioglitazone and the placebo groups, and Azillect study to assess the efficacy of rasagiline as a potential treatment to slow down the progression of PD.

Linearized maximum rank correlation estimation when covariates are functional

This paper extends the linearized maximum rank correlation (LMRC) estimation proposed by Shen et al. (2023) to the setting where the covariate is a function. However, this extension is nontrivial due to the difficulty of inverting the covariance operator, which may raise the ill-posed inverse problem, for which we integrate the functional principal component analysis to the LMRC procedure. The proposed estimator is robust to outliers in response and computationally efficient. We establish the rate of convergence of the proposed estimator, which is minimax optimal under certain smoothness assumptions. Furthermore, we extend the proposed estimation procedure to handle discretely observed functional covariates, including both sparse and dense sampling designs, and establish the corresponding rate of convergence. Simulation studies demonstrate that the proposed estimators outperform the other existing methods for some examples. Finally, we apply our method to a real data to illustrate its usefulness.

Tracking element-mineral associations with unsupervised learning and dimensionality reduction in chemical and optical image stacks of thin sections

In-situ chemical analysis on thin sections is a cornerstone of geochemical research. Despite massive advances in digital image analysis, the interpretation of such data within the optical petrological context of the thin section has largely remained an analogue task in geochemistry. In this contribution, we registered optical and micro-chemical images from large thin section areas. Chemical datasets from scanning electron microscopy energy dispersive spectrometry (SEM-EDX) and Synchrotron X-ray fluorescence microscopy (S-XFM) were exported from proprietary software. We then evaluated two dimensionality reduction techniques against false-colour images and phase maps to test whether previously unnoticed features became discoverable. Principal component analysis (PCA) and deep sparse autoencoder (DSA) neural networks were used to summarise the multi-channel SEM-EDX and S-XFM into one single red-green-blue (RGB) representation each.Applied to an oceanic gabbro, a cratonic peridotite, and a pelagic limestone, the PCA-based dimensionality reduction was found to produce crisp RGB maps of phases with less noise than false-colour three-element RGB maps. They were registered with optical images to form a simple multi-channel input for pixel-based classification into classes (i.e., semantic segmentation). This was fast and worked well for typical igneous and metamorphic rocks (1–3 h routine). In the chemically quite homogenous limestone, the combined optical and S-XFM PCA input was successfully classified into many phases that were unclassifiable on the conventional SEM-EDX phase map. From the segmented optical and S-XFM PCA map, we exported pixel locations of classified accessory phases back into the original proprietary S-XFM software. This allowed quantification of trace elements whose X-ray peaks were invisible in the original S-XFM quantification.The DSA-based approach yielded phase maps with greater noise, but the technique was very strong at detecting subtle features. In the gabbro sample, the DSA image identified cryptic relict cores in clinopyroxene more clearly than in the previously used Cr concentration map. A DSA training set can be obtained on a small ROI to generate a consistent large area DSA image from which more fragmental cores were observed. For a ROI on the gabbro thin section, the DSA representation map and the blended optical image were segmented and inspected with a loupe tool. This allowed us to generate interactive histograms and bin-scatter concentration plots of selected phases and to search for co-variations of element concentrations. This approach can be expanded to include data from any in situ geochemical acquisition tools and may help discover previously unseen features in complex elemental imagery.

Forecasting high-dimensional functional time series: Application to sub-national age-specific mortality

We study the modeling and forecasting of high-dimensional functional time series (HDFTS), which can be cross-sectionally correlated and temporally dependent. We introduce a decomposition of the HDFTS into two distinct components: a deterministic component and a residual component that varies over time. The decomposition is derived through the estimation of two-way functional analysis of variance. A functional time series forecasting method, based on functional principal component analysis, is implemented to produce forecasts for the residual component. By combining the forecasts of the residual component with the deterministic component, we obtain forecast curves for multiple populations. We apply the model to age- and sex-specific mortality rates in the United States, France, and Japan, in which there are 51 states, 95 departments, and 47 prefectures, respectively. The proposed method is capable of delivering more accurate point and interval forecasts in forecasting multi-population mortality than several benchmark methods considered.

Deciphering temporal growth patterns in maize: integrative modeling of phenotype dynamics and underlying genomic variations.

Quantifying the temporal or longitudinal growth dynamics of crops in diverse environmental conditions is crucial for understanding plant development, requiring further modeling techniques. In this study, we analyzed the growth patterns of two different maize (Zea mays L.) populations using high-throughput phenotyping with a maize population consisting of 515 recombinant inbred lines (RILs) grown in Texas and a hybrid population containing 1090 hybrids grown in Missouri. Two models, Gaussian peak and functional principal component analysis (FPCA), were employed to study the Normalized Green-Red Difference Index (NGRDI) scores. The Gaussian peak model showed strong correlations (c. 0.94 for RILs and c. 0.97 for hybrids) between modeled and non-modeled temporal trajectories. Functional principal component analysis differentiated NGRDI trajectories in RILs under different conditions, capturing substantial variability (75%, 20%, and 5% for RILs; 88% and 12% for hybrids). By comparing these models with conventional BLUP values, common quantitative trait loci (QTLs) were identified, containing candidate genes of brd1, pin11, zcn8 and rap2. The harmony between these loci's additive effects and growing degree days, as well as the differentiation of RIL haplotypes across growth stages, underscores the significant interplay of these loci in driving plant development. These findings contribute to advancing understanding of plant-environment interactions and have implications for crop improvement strategies.

Modeling correlated pairs of mammogram images.

Mammography remains the primary screening strategy for breast cancer, which continues to be the most prevalent cancer diagnosis among women globally. Because screening mammograms capture both the left and right breast, there is a nonnegligible correlation between the pair of images. Previous studies have explored the concept of averaging between the pair of images after proper image registration; however, no comparison has been made in directly utilizing the paired images. In this paper, we extend the bivariate functional principal component analysis over triangulations to jointly characterize the pair of imaging data bounded in an irregular domain and then nest the extracted features within the survival model to predict the onset of breast cancer. The method is applied to our motivating data from the Joanne Knight Breast Health Cohort at Siteman Cancer Center. Our findings indicate that there was no statistically significant difference in model discrimination performance between averaging the pair of images and jointly modeling the two images. Although the breast cancer study did not reveal any significant difference, it is worth noting that the methods proposed here can be readily extended to other studies involving paired or multivariate imaging data.

Risk adjustment-based statistical control charts with a functional covariate

ABSTRACT In real applications, there are situations in which quality characteristics are significantly affected by function-valued covariates such as electrocardiogram (ECG) signals; however, previous surveillance methods with covariate adjustment mainly use scalar-valued covariates to construct control charts to investigate the stability of nonindustrial processes, such as in the medical and public health fields. Few existing approaches address the infinite-dimensional regression encountered with function-valued covariates. Thus, an applicable scheme needs to be developed. Here, by relaxing the assumption of normality, a novel surveillance strategy for functional logistic regression (FLR) is proposed. In this approach, the response is a binary variable, and the covariate information is obtained from functional data. To address the above problems, functional principal component analysis (FPCA) is used to extend the score test to situations with functional covariates. Moreover, the score statistic is integrated into an exponentially weighted moving average (EWMA) charting scheme to detect abnormal changes in the location and scale parameters based on additional information. The simulation results show that the proposed approach is more efficient than previous approaches in detecting small to moderate shifts. Finally, the proposed charting scheme is applied to a real case study to demonstrate its utility and applicability.