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Analyzing longitudinal data in health studies is challenging due to sparse and error-prone measurements, strong within-individual correlation, missing data and various trajectory shapes. While mixed-effect models (MM) effectively address these challenges, they remain parametric models and may incur computational costs. In contrast, functional principal component analysis (FPCA) is a non-parametric approach developed for regular and dense functional data that flexibly describes temporal trajectories at a potentially lower computational cost. This article presents an empirical simulation study evaluating the behavior of FPCA with sparse and error-prone repeated measures and its robustness under different missing data schemes in comparison with MM. The results show that FPCA is well-suited in the presence of missing at random data caused by dropout, except in scenarios involving most frequent and systematic dropout. Like MM, FPCA fails under missing not at random mechanism. The FPCA was applied to describe the trajectories of four cognitive functions before clinical dementia and contrast them with those of matched controls in a case-control study nested in a population-based aging cohort. The average cognitive declines of future dementia cases showed a sudden divergence from those of their matched controls with a sharp acceleration 5 to 2.5 years prior to diagnosis.

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Sensor devices, such as accelerometers, are widely used for measuring physical activity (PA). These devices provide outputs at fine granularity (e.g., 10-100 Hz or minute-level), which while providing rich data on activity patterns, also pose computational challenges with multilevel densely sampled data, resulting in PA records that are measured continuously across multiple days and visits. On the other hand, a scalar health outcome (e.g., BMI) is usually observed only at the individual or visit level. This leads to a discrepancy in numbers of nested levels between the predictors (PA) and outcomes, raising analytic challenges. To address this issue, we proposed a multilevel longitudinal functional principal component analysis (mLFPCA) model to directly model multilevel functional PA inputs in a longitudinal study, and then implemented a longitudinal functional principal component regression (FPCR) to explore the association between PA and obesity-related health outcomes. Additionally, we conducted a comprehensive simulation study to examine the impact of imbalanced multilevel data on both mLFPCA and FPCR performance and offer guidelines for selecting optimal methods.

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Objective.We extract walking features from raw accelerometry data while accounting for varying cadence and commonality of features among subjects. Walking is the most performed type of physical activity. Thus, we explore if an individual's physical health is related to these walking features.Approach.We use data collected using ActiGraph GT3X+ devices (sampling rate = 80 Hz) as part of the developmental epidemiologic cohort study,I= 48, age =78.7±5.7years, 45.8% women. We apply structured functional principal component analysis (SFPCA) to extract features from walking signals on both, the subject-specific and the subject-spectrum-specific level of a fast-paced 400 m walk, an indicator of aerobic fitness in older adults. We also use the subject-specific level feature scores to study their associations with age and physical performance measures. Specifically, we transform the raw data into the frequency domain by applying local Fast Fourier Transform to obtain the walking spectra. SFPCA decomposes these spectra into easily interpretable walking features expressed as cadence and acceleration, which can be related to physical performance.Main results.We found that five subject-specific and 19 subject-spectrum-specific level features explained more than 85% of their respective level variation, thus significantly reducing the complexity of the data. Our results show that 54% of the total data variation arises at the subject-specific and 46% at the subject-spectrum-specific level. Moreover, we found that higher acceleration magnitude at the cadence was associated with younger age, lower BMI, faster average cadence and higher short physical performance battery scores. Lower acceleration magnitude at the cadence and higher acceleration magnitude at cadence multiples 2.5 and 3.5 are related to older age and higher blood pressure.Significance.SFPCA extracted subject-specific level empirical walking features which were meaningfully associated with several health indicators and younger age. Thus, an individual's walking pattern could shed light on subclinical stages of somatic diseases.

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Motivated by improving the prediction of the human immunodeficiency virus (HIV) suppression status using electronic health records (EHR) data, we propose a functional multivariable logistic regression model, which accounts for the longitudinal binary process and continuous process simultaneously. Specifically, the longitudinal measurements for either binary or continuous variables are modeled by functional principal components analysis, and their corresponding functional principal component scores are used to build a logistic regression model for prediction. The longitudinal binary data are linked to underlying Gaussian processes. The estimation is done using penalized spline for the longitudinal continuous and binary data. Group-lasso is used to select longitudinal processes, and the multivariate functional principal components analysis is proposed to revise functional principal component scores with the correlation. The method is evaluated via comprehensive simulation studies and then applied to predict viral suppression using EHR data for people living with HIV in South Carolina.

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Field-based phenomic prediction employs novel features, like vegetation indices (VIs) from drone images, to predict key agronomic traits in maize, despite challenges in matching biomarker measurement time points across years or environments. This study utilized functional principal component analysis (FPCA) to summarize the variation of temporal VIs, uniquely allowing the integration of this data into phenomic prediction models tested across multiple years (2018-2021) and environments. The models, which included 1 genomic, 2 phenomic, 2 multikernel, and 1 multitrait type, were evaluated in 4 prediction scenarios (CV2, CV1, CV0, and CV00), relevant for plant breeding programs, assessing both tested and untested genotypes in observed and unobserved environments. Two hybrid populations (415 and 220 hybrids) demonstrated the visible atmospherically resistant index's strong temporal correlation with grain yield (up to 0.59) and plant height. The first 2 FPCAs explained 59.3 ± 13.9% and 74.2 ± 9.0% of the temporal variation of temporal data of VIs, respectively, facilitating predictions where flight times varied. Phenomic data, particularly when combined with genomic data, often were comparable to or numerically exceeded the base genomic model in prediction accuracy, particularly for grain yield in untested hybrids, although no significant differences in these models' performance were consistently observed. Overall, this approach underscores the effectiveness of FPCA and combined models in enhancing the prediction of grain yield and plant height across environments and diverse agricultural settings.

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BACKGROUND: Sedentary behavior (SB) is a recognized risk factor for many chronic diseases. ActiGraph and activPAL are two commonly used wearable accelerometers in SB research. The former measures body movement and the latter measures body posture. The goal of the current study is to quantify the pattern and variation of movement (by ActiGraph activity counts) during activPAL-identified sitting events, and examine associations between patterns and health-related outcomes, such as systolic and diastolic blood pressure (SBP and DBP). METHODS: The current study included 314 overweight postmenopausal women, who were instructed to wear an activPAL (at thigh) and ActiGraph (at waist) simultaneously for 24 hours a day for a week under free-living conditions. ActiGraph and activPAL data were processed to obtain minute-level time-series outputs. Multilevel functional principal component analysis (MFPCA) was applied to minute-level ActiGraph activity counts within activPAL-identified sitting bouts to investigate variation in movement while sitting across subjects and days. The multilevel approach accounted for the nesting of days within subjects. RESULTS: At least 90% of the overall variation of activity counts was explained by two subject-level principal components (PC) and six day-level PCs, hence dramatically reducing the dimensions from the original minute-level scale. The first subject-level PC captured patterns of fluctuation in movement during sitting, whereas the second subject-level PC delineated variation in movement during different lengths of sitting bouts: shorter (< 30 minutes), medium (30 -39 minutes) or longer (> 39 minute). The first subject-level PC scores showed positive association with DBP (standardized ß ^ : 2.041, standard error: 0.607, adjusted p = 0.007), which implied that lower activity counts (during sitting) were associated with higher DBP. CONCLUSION: In this work we implemented MFPCA to identify variation in movement patterns during sitting bouts, and showed that these patterns were associated with cardiovascular health. Unlike existing methods, MFPCA does not require pre-specified cut-points to define activity intensity, and thus offers a novel powerful statistical tool to elucidate variation in SB patterns and health. TRIAL REGISTRATION: ClinicalTrials.gov NCT03473145; Registered 22 March 2018; https://clinicaltrials.gov/ct2/show/NCT03473145 ; International Registered Report Identifier (IRRID): DERR1-10.2196/28684.

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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.

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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.

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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.

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Dynamically predicting patient survival probabilities using longitudinal measurements has become of great importance with routine data collection becoming more common. Many existing models utilize a multi-step landmarking approach for this problem, mostly due to its ease of use and versatility but unfortunately most fail to do so appropriately. In this article we make use of multivariate functional principal component analysis to summarize the available longitudinal information, and employ a Cox proportional hazards model for prediction. Additionally, we consider a centred functional principal component analysis procedure in an attempt to remove the natural variation incurred by the difference in age of the considered subjects. We formalize the difference between a 'relaxed' landmarking approach where only validation data is landmarked and a 'strict' landmarking approach where both the training and validation data are landmarked. We show that a relaxed landmarking approach fails to effectively use the information contained in the longitudinal outcomes, thereby producing substantially worse prediction accuracy than a strict landmarking approach.

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@#Objective To develop a shake-flask stage culture process for E.coli with higher biomass and higher bacterial viability based on Quality by Design(QbD)concept.Methods Using different shake-flask configurations as the investigation factors,and A600value of the bacterial suspension,wet weight of the culture and viability value of the bacteria as the indicators for investigation of the culture results,ANOVA was used for the analysis of culture results to obtain the third amplification flask configurations with high biomass and high bacterial viability.The two-factor two-level full-factor test was carried out with the shaker temperature and shaker speed as the test factors,the A value of bacterial suspension as the response value,the culture accumulation time as a variable factor,and the real-time online temperature and self-test speed of the shaker as the supplemented variable factors.The functional principal component analysis(FPCA)method was used to perform a generalized regression model to model the quasi-growth curve,and the optimized culture stop time and culture process were obtained by the growth curve model.The design space of the shaker culture process was optimized again using Monte Carlo simulation(MCS)with random noise added to the response value.The worst condition in the design space was selected as the setting condition for verification test,and serial 10 batch verification tests were performed in stages with different culture stop time.Results The third amplification shake-flask configurations:5 L disposable high-efficiency shakeflask and large area breathable film cover.The culture process design space:shaker temperature of 36.5-37.5 ℃,shaker speed of 220-230 r/min,and the design culture stop time of 18 h.The worst condition verification test showed that when the culture was stopped for 16 h,the culture results of higher cell viability value and lower biomass could be obtained,and when the culture was stopped for 18 h,the results of higher biomass and bacterial viability value could be obtained.Conclusion The shake-flask stage culture process for E.coli designed in this study has the characteristics of high biomass and high bacterial viability,and can be adjusted according to the adaptability of this culture process to meet different culture needs.

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Modern medical devices are increasingly producing complex data that could offer deeper insights into physiological mechanisms of underlying diseases. One type of complex data that arises frequently in medical imaging studies is functional data, whose sampling unit is a smooth continuous function. In this work, with the goal of establishing the scientific validity of experiments involving modern medical imaging devices, we focus on the problem of evaluating reliability and reproducibility of multiple functional data that are measured on the same subjects by different methods (i.e. different technologies or raters). Specifically, we develop a series of intraclass correlation coefficient and concordance correlation coefficient indices that can assess intra-method, inter-method, and total (intra + inter) agreement based on multivariate multilevel functional data consisting of replicated functional data measurements produced by each of the different methods. For efficient estimation, the proposed indices are expressed using variance components of a multivariate multilevel functional mixed effect model, which can be smoothly estimated by functional principal component analysis. Extensive simulation studies are performed to assess the finite-sample properties of the estimators. The proposed method is applied to evaluate the reliability and reproducibility of renogram curves produced by a high-tech radionuclide image scan used to non-invasively detect kidney obstruction.

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Human mortality patterns and trajectories in closely related populations are likely linked together and share similarities. It is always desirable to model them simultaneously while taking their heterogeneity into account. This article introduces two new models for joint mortality modelling and forecasting multiple subpopulations using the multivariate functional principal component analysis techniques. The first model extends the independent functional data model to a multipopulation modelling setting. In the second one, we propose a novel multivariate functional principal component method for coherent modelling. Its design primarily fulfils the idea that when several subpopulation groups have similar socio-economic conditions or common biological characteristics such close connections are expected to evolve in a non-diverging fashion. We demonstrate the proposed methods by using sex-specific mortality data. Their forecast performances are further compared with several existing models, including the independent functional data model and the Product-Ratio model, through comparisons with mortality data of ten developed countries. The numerical examples show that the first proposed model maintains a comparable forecast ability with the existing methods. In contrast, the second proposed model outperforms the first model as well as the existing models in terms of forecast accuracy.

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BACKGROUND: A substantial body of clinical research involving individuals infected with severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) has evaluated the association between in-hospital biomarkers and severe SARS-CoV-2 outcomes, including intubation and death. However, most existing studies considered each of multiple biomarkers independently and focused analysis on baseline or peak values. METHODS: We propose a two-stage analytic strategy combining functional principal component analysis (FPCA) and sparse-group LASSO (SGL) to characterize associations between biomarkers and 30-day mortality rates. Unlike prior reports, our proposed approach leverages: 1) time-varying biomarker trajectories, 2) multiple biomarkers simultaneously, and 3) the pathophysiological grouping of these biomarkers. We apply this method to a retrospective cohort of 12, 941 patients hospitalized at Massachusetts General Hospital or Brigham and Women's Hospital and conduct simulation studies to assess performance. RESULTS: Renal, inflammatory, and cardio-thrombotic biomarkers were associated with 30-day mortality rates among hospitalized SARS-CoV-2 patients. Sex-stratified analysis revealed that hematogolical biomarkers were associated with higher mortality in men while this association was not identified in women. In simulation studies, our proposed method maintained high true positive rates and outperformed alternative approaches using baseline or peak values only with respect to false positive rates. CONCLUSIONS: The proposed two-stage approach is a robust strategy for identifying biomarkers that associate with disease severity among SARS-CoV-2-infected individuals. By leveraging information on multiple, grouped biomarkers' longitudinal trajectories, our method offers an important first step in unraveling disease etiology and defining meaningful risk strata.

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BACKGROUND: Suboptimal rest-activity patterns in adolescence are associated with worse health outcomes in adulthood. Understanding sociodemographic factors associated with rest-activity rhythms may help identify subgroups who may benefit from interventions. This study aimed to investigate the association of rest-activity rhythm with demographic and socioeconomic characteristics in adolescents. METHODS: Using cross-sectional data from the nationally representative National Health and Nutrition Examination Survey (NHANES) 2011-2014 adolescents (N = 1814), this study derived rest-activity profiles from 7-day 24-hour accelerometer data using functional principal component analysis. Multiple linear regression was used to assess the association between participant characteristics and rest-activity profiles. Weekday and weekend specific analyses were performed in addition to the overall analysis. RESULTS: Four rest-activity rhythm profiles were identified, which explained a total of 82.7% of variance in the study sample, including (1) High amplitude profile; (2) Early activity window profile; (3) Early activity peak profile; and (4) Prolonged activity/reduced rest window profile. The rest-activity profiles were associated with subgroups of age, sex, race/ethnicity, and household income. On average, older age was associated with a lower value for the high amplitude and early activity window profiles, but a higher value for the early activity peak and prolonged activity/reduced rest window profiles. Compared to boys, girls had a higher value for the prolonged activity/reduced rest window profiles. When compared to Non-Hispanic White adolescents, Asian showed a lower value for the high amplitude profile, Mexican American group showed a higher value for the early activity window profile, and the Non-Hispanic Black group showed a higher value for the prolonged activity/reduced rest window profiles. Adolescents reported the lowest household income had the lowest average value for the early activity window profile. CONCLUSIONS: This study characterized main rest-activity profiles among the US adolescents, and demonstrated that demographic and socioeconomic status factors may shape rest-activity behaviors in this population.

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BACKGROUND: Within-breath oscillations in arterial oxygen tension (PaO2) can be detected using fast responding intra-arterial oxygen sensors in animal models. These PaO2 signals, which rise in inspiration and fall in expiration, may represent cyclical recruitment/derecruitment and, therefore, a potential clinical monitor to allow titration of ventilator settings in lung injury. However, in hypovolaemia models, these oscillations have the potential to become inverted, such that they decline, rather than rise, in inspiration. This inversion suggests multiple aetiologies may underlie these oscillations. A correct interpretation of the various PaO2 oscillation morphologies is essential to translate this signal into a monitoring tool for clinical practice. We present a pilot study to demonstrate the feasibility of a new analysis method to identify these morphologies. METHODS: Seven domestic pigs (average weight 31.1 kg) were studied under general anaesthesia with muscle relaxation and mechanical ventilation. Three underwent saline-lavage lung injury and four were uninjured. Variations in PEEP, tidal volume and presence/absence of lung injury were used to induce different morphologies of PaO2 oscillation. Functional principal component analysis and k-means clustering were employed to separate PaO2 oscillations into distinct morphologies, and the cardiorespiratory physiology associated with these PaO2 morphologies was compared. RESULTS: PaO2 oscillations from 73 ventilatory conditions were included. Five functional principal components were sufficient to explain ≥ 95% of the variance of the recorded PaO2 signals. From these, five unique morphologies of PaO2 oscillation were identified, ranging from those which increased in inspiration and decreased in expiration, through to those which decreased in inspiration and increased in expiration. This progression was associated with the estimates of the first functional principal component (P < 0.001, R2 = 0.88). Intermediate morphologies demonstrated waveforms with two peaks and troughs per breath. The progression towards inverted oscillations was associated with increased pulse pressure variation (P = 0.03). CONCLUSIONS: Functional principal component analysis and k-means clustering are appropriate to identify unique morphologies of PaO2 waveform associated with distinct cardiorespiratory physiology. We demonstrated novel intermediate morphologies of PaO2 waveform, which may represent a development of zone 2 physiologies within the lung. Future studies of PaO2 oscillations and modelling should aim to understand the aetiologies of these morphologies.

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BACKGROUND: The gait pattern of adults with class I obesity [30 ≤ body mass index < 35kg/m2] was characterized by altered three-dimensional ground reaction force signals compared to lean adults (18.5 ≤ body mass index < 25 kg/m2). However, results might not be generalizable to adults with severe obesity (class II and III; body mass index ≥ 35 kg/m2). Hence, the purpose of the present study was to investigate the differences in relative ground reaction force signals, i.e., normalized by body weight, between adults with severe obesity and lean adults using functional principal component analysis. METHODS: Thirteen lean and eighteen sedentary adults with severe obesity performed a 5-min walking trial (1.11 m/s) on an instrumented treadmill. The first five functional principal components of the relative force signals (mediolateral, anterior-posterior, and vertical directions) were obtained using functional principal component analysis. Functional principal component scores were compared between groups using an analysis of covariance with age as covariable. FINDINGS: Functional principal component analysis reported a statistically significant group effect for first functional principal component score for mediolateral (P = 0.004), and second and fifth functional principal component scores for anterior-posterior (P ≤ 0.02) force signals. Adults with severe obesity displayed a greater mediolateral force during most of the stance but similar magnitudes of the anterior-posterior and vertical forces compared to lean adults. INTERPRETATION: Therefore, increasing the obesity level accentuates differences in mediolateral force but promotes no specific changes in anterior-posterior force likely due to chronic loading adaptation.

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In animal behavior studies, a common goal is to investigate the causal pathways between an exposure and outcome, and a mediator that lies in between. Causal mediation analysis provides a principled approach for such studies. Although many applications involve longitudinal data, the existing causal mediation models are not directly applicable to settings where the mediators are measured on irregular time grids. In this paper, we propose a causal mediation model that accommodates longitudinal mediators on arbitrary time grids and survival outcomes simultaneously. We take a functional data analysis perspective and view longitudinal mediators as realizations of underlying smooth stochastic processes. We define causal estimands of direct and indirect effects accordingly and provide corresponding identification assumptions. We employ a functional principal component analysis approach to estimate the mediator process and propose a Cox hazard model for the survival outcome that flexibly adjusts the mediator process. We then derive a g-computation formula to express the causal estimands using the model coefficients. The proposed method is applied to a longitudinal data set from the Amboseli Baboon Research Project to investigate the causal relationships between early adversity, adult physiological stress responses, and survival among wild female baboons. We find that adversity experienced in early life has a significant direct effect on females' life expectancy and survival probability, but find little evidence that these effects were mediated by markers of the stress response in adulthood. We further developed a sensitivity analysis method to assess the impact of potential violation to the key assumption of sequential ignorability. Supplementary materials accompanying this paper appear on-line.

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We introduce fast multilevel functional principal component analysis (fast MFPCA), which scales up to high dimensional functional data measured at multiple visits. The new approach is orders of magnitude faster than and achieves comparable estimation accuracy with the original MFPCA (Di et al., 2009). Methods are motivated by the National Health and Nutritional Examination Survey (NHANES), which contains minute-level physical activity information of more than 10000 participants over multiple days and 1440 observations per day. While MFPCA takes more than five days to analyze these data, fast MFPCA takes less than five minutes. A theoretical study of the proposed method is also provided. The associated function mfpca.face() is available in the R package refund.

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Multi-source functional block-wise missing data arise more commonly in medical care recently with the rapid development of big data and medical technology, hence there is an urgent need to develop efficient dimension reduction to extract important information for classification under such data. However, most existing methods for classification problems consider high-dimensional data as covariates. In the paper, we propose a novel multinomial imputed-factor Logistic regression model with multi-source functional block-wise missing data as covariates. Our main contribution is to establishing two multinomial factor regression models by using the imputed multi-source functional principal component scores and imputed canonical scores as covariates, respectively, where the missing factors are imputed by both the conditional mean imputation and the multiple block-wise imputation approaches. Specifically, the univariate FPCA is carried out for the observable data of each data source firstly to obtain the univariate principal component scores and the eigenfunctions. Then, the block-wise missing univariate principal component scores instead of the block-wise missing functional data are imputed by the conditional mean imputation method and the multiple block-wise imputation method, respectively. After that, based on the imputed univariate factors, the multi-source principal component scores are constructed by using the relationship between the multi-source principal component scores and the univariate principal component scores; and at the same time, the canonical scores are obtained by the multiple-set canonial correlation analysis. Finally, the multinomial imputed-factor Logistic regression model is established with the multi-source principal component scores or the canonical scores as factors. Numerical simulations and real data analysis on ADNI data show the proposed method works well.

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