Scalar-on-function regression: Estimation and inference under complex survey designs.

Increasingly, large, nationally representative health and behavioral surveys conducted under a multistage stratified sampling scheme collect high dimensional data with correlation structured along some domain (eg, wearable sensor data measured continuously and correlated over time, imaging data with spatiotemporal correlation) with the goal of associating these data with health outcomes. Analysis of this sort requires novel methodologic work at the intersection of survey statistics and functional data analysis. Here, we address this crucial gap in the literature by proposing an estimation and inferential framework for generalizable scalar-on-function regression models for data collected under a complex survey design. We propose to: (1) estimate functional regression coefficients using weighted score equations; and (2) perform inference using novel functional balanced repeated replication and survey-weighted bootstrap for multistage survey designs. This is the first frequentist study to discuss the estimation of scalar-on-function regression models in the context of complex survey studies and to assess the validity of various inferential techniques based on re-sampling methods via a comprehensive simulation study. We implement our methods to predict mortality using diurnal activity profiles measured via wearable accelerometers using the National Health and Nutrition Examination Survey 2003-2006 data. The proposed computationally efficient methods are implemented in R software package surveySoFR.

NHANES 2011-2014: Objective Physical Activity Is the Strongest Predictor of All-Cause Mortality.

INTRODUCTION: Objectively measured physical activity (PA) is a modifiable risk factor for mortality. Understanding the predictive performance of PA is essential to establish potential targets for early intervention to reduce mortality among older adults. METHODS: The study used a subset of the National Health and Nutrition Examination Survey (NHANES) 2011-2014 data consisting of participants 50 to 80 yr old ( n = 3653, 24297.5 person-years of follow-up, 416 deaths). Eight accelerometry-derived features and 14 traditional predictors of all-cause mortality were compared and ranked in terms of their individual and combined predictive performance using the 10-fold cross-validated concordance (C) from Cox regression. RESULTS: The top 3 predictors of mortality in univariate analysis were PA related: average Monitor-Independent Movement Summary (MIMS) in the 10 most active hours (C = 0.697), total MIMS per day (C = 0.686), and average log-transformed MIMS in the most 10 active hours of the day (C = 0.684), outperforming age (C = 0.676) and other traditional predictors of mortality. In multivariate regression, adding objectively measured PA to the top performing model without PA variables increased concordance from C = 0.776 to C = 0.790 ( P < 0.001). CONCLUSIONS: These findings highlight the importance of PA as a risk marker of mortality and are consistent with prior studies, confirming the importance of accelerometer-derived activity measures beyond total volume.

Integrative Modeling of Accelerometry-Derived Sleep, Physical Activity, and Circadian Rhythm Domains With Current or Remitted Major Depression.

Importance: Accelerometry has been increasingly used as an objective index of sleep, physical activity, and circadian rhythms in people with mood disorders. However, most prior research has focused on sleep or physical activity alone without consideration of the strong within- and cross-domain intercorrelations; and few studies have distinguished between trait and state profiles of accelerometry domains in major depressive disorder (MDD). Objectives: To identify joint and individual components of the domains derived from accelerometry, including sleep, physical activity, and circadian rhythmicity using the Joint and Individual Variation Explained method (JIVE), a novel multimodal integrative dimension-reduction technique; and to examine associations between joint and individual components with current and remitted MDD. Design, Setting, and Participants: This cross-sectional study examined data from the second wave of a population cohort study from Lausanne, Switzerland. Participants included 2317 adults (1164 without MDD, 185 with current MDD, and 968 with remitted MDD) with accelerometry for at least 7 days. Statistical analysis was conducted from January 2021 to June 2023. Main Outcomes and Measures: Features derived from accelerometry for 14 days; current and remitted MDD. Logistic regression adjusted for age, sex, body mass index, and anxiety and substance use disorders. Results: Among 2317 adults included in the study, 1261 (54.42%) were female, and mean (SD) age was 61.79 (9.97) years. JIVE reduced 28 accelerometry features to 3 joint and 6 individual components (1 sleep, 2 physical activity, 3 circadian rhythms). Joint components explained 58.5%, 79.5%, 54.5% of the total variation in sleep, physical activity, and circadian rhythm domains, respectively. Both current and remitted depression were associated with the first 2 joint components that were distinguished by the salience of high-intensity physical activity and amplitude of circadian rhythm and timing of both sleep and physical activity, respectively. MDD had significantly weaker circadian rhythmicity. Conclusions and Relevance: Application of a novel multimodal dimension-reduction technique demonstrates the importance of joint influences of physical activity, circadian rhythms, and timing of both sleep and physical activity with MDD; dampened circadian rhythmicity may constitute a trait marker for MDD. This work illustrates the value of accelerometry as a potential biomarker for subtypes of depression and highlights the importance of consideration of the full 24-hour sleep-wake cycle in future studies.

Statistical modeling of acute and chronic pain patient-reported outcomes obtained from ecological momentary assessment.

ABSTRACT: Ecological momentary assessment (EMA) allows for the collection of participant-reported outcomes (PROs), including pain, in the normal environment at high resolution and with reduced recall bias. Ecological momentary assessment is an important component in studies of pain, providing detailed information about the frequency, intensity, and degree of interference of individuals' pain. However, there is no universally agreed on standard for summarizing pain measures from repeated PRO assessment using EMA into a single, clinically meaningful measure of pain. Here, we quantify the accuracy of summaries (eg, mean and median) of pain outcomes obtained from EMA and the effect of thresholding these summaries to obtain binary clinical end points of chronic pain status (yes/no). Data applications and simulations indicate that binarizing empirical estimators (eg, sample mean, random intercept linear mixed model) can perform well. However, linear mixed-effect modeling estimators that account for the nonlinear relationship between average and variability of pain scores perform better for quantifying the true average pain and reduce estimation error by up to 50%, with larger improvements for individuals with more variable pain scores. We also show that binarizing pain scores (eg, <3 and ≥3) can lead to a substantial loss of statistical power (40%-50%). Thus, when examining pain outcomes using EMA, the use of linear mixed models using the entire scale (0-10) is superior to splitting the outcomes into 2 groups (<3 and ≥3) providing greater statistical power and sensitivity.

A Study of Pupil Response to Light as a Digital Biomarker of Recent Cannabis Use.

Introduction: Given the traffic safety and occupational injury prevention implications associated with cannabis impairment, there is a need for objective and validated measures of recent cannabis use. Pupillary light response may offer an approach for detection. Method: Eighty-four participants (mean age: 32, 42% female) with daily, occasional, and no-use cannabis use histories participated in pupillary light response tests before and after smoking cannabis ad libitum or relaxing for 15 min (no use). The impact of recent cannabis consumption on trajectories of the pupillary light response was modeled using functional data analysis tools. Logistic regression models for detecting recent cannabis use were compared, and average pupil trajectories across cannabis use groups and times since light test administration were estimated. Results: Models revealed small, significant differences in pupil response to light after cannabis use comparing the occasional use group to the no-use control group, and similar statistically significant differences in pupil response patterns comparing the daily use group to the no-use comparison group. Trajectories of pupillary light response estimated using functional data analysis found that acute cannabis smoking was associated with less initial and sustained pupil constriction compared to no cannabis smoking. Conclusion: These analyses show the promise of pairing pupillary light response and functional data analysis methods to assess recent cannabis use.

Quantifying the time-varying association between objectively measured physical activity and mortality in US older adults over a 12-year follow-up period: the NHANES 2003-2006 study.

Objectively measuring physical activity (PA) has consistently shown an association with reduced all-cause mortality risk in cross-sectional studies. However, the strength of this association may change over time. We quantify the time-varying, covariate-adjusted association between the total volume of PA and all-cause mortality over a 12-year follow-up period using Cox regression with a time varying effect of population-referenced quantile total activity count adjusted for traditional risk factors. Analyses focus on participants 50-84 years old with adequate accelerometer wear time and without missing covariates. The findings suggest that (1) the use of baseline PA in Cox models with long follow-up periods may be inappropriate without time-varying effects and (2) the use of accelerometry derived volume of PA in risk score calculations may be most appropriate for short-term to medium-term risk scores.

Association Between Electronic Diary-Rated Sleep, Mood, Energy, and Stress With Incident Headache in a Community-Based Sample.

BACKGROUND AND OBJECTIVES: The aim of this study was to examine the diurnal links between average and changes in average levels of prospectively rated mood, sleep, energy, and stress as predictors of incident headache in a community-based sample. METHODS: This observational study included structured clinical diagnostic assessment of both headache syndromes and mental disorders and electronic diaries that were administered 4 times per day for 2 weeks yielding a total of 4,974 assessments. The chief outcomes were incident morning (am) and later-day (pm) headaches. Generalized linear mixed-effects models were used to evaluate the average and lagged values of predictors including subjectively rated mood, anxiety, energy, stress, and sleep quality and objectively measured sleep duration and efficiency on incident am and pm headaches. RESULTS: The sample included 477 participants (61% female), aged 7 through 84 years. After adjusting for demographic and clinical covariates and emotional states, incident am headache was associated with lower average (ß = -0.206*; confidence intervals: -0.397 to -0.017) and a decrease in average sleep quality on the prior day (ß = -0.172*; confidence interval: -0.305, -0.039). Average stress and changes in subjective energy levels on the prior day were associated with incident headaches but with different valence for am (decrease) (ß = -0.145* confidence interval: -0.286, -0.005) and pm (increase) (ß = 0.157*; confidence interval: 0.032, 0.281) headache. Mood and anxiety disorders were not significantly associated with incident headache after controlling for history of a diagnosis of migraine. DISCUSSION: Both persistent and acute changes in arousal states manifest by subjective sleep quality and energy are salient precursors of incident headaches. Whereas poorer sleep quality and decreased energy on the prior day were associated with incident morning headache, an increase in energy and greater average stress were associated with headache onsets later in the day. Different patterns of predictors of morning and later-day incident headache highlight the role of circadian rhythms in the manifestations of headache. These findings may provide insight into the pathophysiologic processes underlying migraine and inform clinical intervention and prevention. Tracking these systems in real time with mobile technology provides a valuable ancillary tool to traditional clinical assessments.

Gender difference in "second-shift" physical activity: New insights from analyzing accelerometry data in a nationally representative sample.

The gendered organization of daily activities results in differential contexts of physical activity (PA) for the working population, especially during the "second shift" - a time window dominated by household-based activities. Existing research predominantly relies on self-reported leisure-time activities, yielding a partial understanding of gender difference in the source, timing, and accumulation pattern of PA. To address these limitations, this study draws on the interplay between work and family to understand how they shape gender difference in household-based PA across occupational groups. It combines work schedule and accelerometry PA data from the 2005-2006 National Health and Nutrition Examination Survey (NHANES), which permits our study of second-shift PA on workdays among full-time workers, aged 20 to 49, with a regular daytime schedule. To capture different aspects of second-shift PA, the PA outcomes are measured as both volume and accumulation patterns during time windows following (i.e., 6pm-9pm) and prior to typical working hours (7:30am-8:30am). Using generalized estimating equations, we estimate gender differences in the volume and fragmentation of second-shift PA. Overall, women with a full-time job exhibit both higher volume and higher fragmentation of second-shift PA than their male counterparts. The occupational group moderates such gender difference in PA. The gender gaps in PA volume and fragmentation are only evident for professional workers, whereas the second shift represents a gender-neutral context for PA accumulation for non-professional groups. These findings are supported by a secondary analysis when analyzing the whole-day PA data using functional data analysis. Such social patterning of second-shift PA calls for further research on gendered PA under the interplay of work and family beyond the usual focus on leisure activities.

Quantifying the Association between Objectively Measured Physical Activity and Multiple Sclerosis in the UK Biobank.

INTRODUCTION: Objectively measured physical activity (PA) data were collected in the accelerometry substudy of the UK Biobank. UK Biobank also contains information about multiple sclerosis (MS) diagnosis at the time of and after PA collection. This study aimed to 1) quantify the difference in PA between prevalent MS cases and matched healthy controls, and 2) evaluate the predictive performance of objective PA measures for incident MS cases. METHODS: The first analysis compared eight accelerometer-derived PA summaries between MS patients ( N = 316) and matched controls (30 controls for each MS case). The second analysis focused on predicting time to MS diagnosis among participants who were not diagnosed with MS. A total of 19 predictors including eight measures of objective PA were compared using Cox proportional hazards models (number of events = 47; 585,900 person-years of follow-up). RESULTS: In the prevalent MS study, the difference between MS cases and matched controls was statistically significant for all PA summaries ( P < 0.001). In the incident MS study, the most predictive variable of progression to MS in univariate Cox regression models was lower age ( C = 0.604), and the most predictive PA variable was lower relative amplitude (RA, C = 0.594). A two-stage forward selection using Cox regression resulted in a model with concordance C = 0.693 and four predictors: age ( P = 0.015), stroke ( P = 0.009), Townsend deprivation index ( P = 0.874), and RA ( P = 0.004). A model including age, stroke, and RA had a concordance of C = 0.691. CONCLUSIONS: Objective PA summaries were significantly different and consistent with lower activity among study participants who had MS at the time of the accelerometry study. Among individuals who did not have MS, younger age, stroke history, and lower RA were significantly associated with a higher risk of a future MS diagnosis.

Specificity of affective dynamics of bipolar and major depressive disorder.

OBJECTIVE: Here, we examine whether the dynamics of the four dimensions of the circumplex model of affect assessed by ecological momentary assessment (EMA) differ among those with bipolar disorder (BD) and major depressive disorder (MDD). METHODS: Participants aged 11-85 years (n = 362) reported momentary sad, anxious, active, and energetic dimensional states four times per day for 2 weeks. Individuals with lifetime mood disorder subtypes of bipolar-I, bipolar-II, and MDD derived from a semistructured clinical interview were compared to each other and to controls without a lifetime history of psychiatric disorders. Random effects from individual means, inertias, innovation (residual) variances, and cross-lags across the four affective dimensions simultaneously were derived from multivariate dynamic structural equation models. RESULTS: All mood disorder subtypes were associated with higher levels of sad and anxious mood and lower energy than controls. Those with bipolar-I had lower average activation, and lower energy that was independent of activation, compared to MDD or controls. However, increases in activation were more likely to perpetuate in those with bipolar-I. Bipolar-II was characterized by higher lability of sad and anxious mood compared to bipolar-I and controls but not MDD. Compared to BD and controls, those with MDD exhibited cross-augmentation of sadness and anxiety, and sadness blunted energy. CONCLUSION: Bipolar-I is more strongly characterized by activation and energy than sad and anxious mood. This distinction has potential implications for both specificity of intervention targets and differential pathways underlying these dynamic affective systems. Confirmation of the longer term stability and generalizability of these findings in future studies is necessary.

Evaluating the prediction performance of objective physical activity measures for incident Parkinson's disease in the UK Biobank.

BACKGROUND: Parkinson's disease (PD) is the fastest-growing neurological condition with over 10 million cases worldwide. While age and sex are known predictors of incident PD, there is a need to identify other predictors. This study compares the prediction performance of accelerometry-derived physical activity (PA) measures and traditional risk factors for incident PD in the UK Biobank. METHODS: The study population consisted of 92,352 UK Biobank participants without PD at baseline (43.8% male, median age 63 years with interquartile range 43-69). 245 participants were diagnosed with PD by April 1, 2021 (586,604 person-years of follow-up). The incident PD prediction performances of 10 traditional predictors and 8 objective PA measures were compared using single- and multi-variable Cox models. Prediction performance was assessed using a novel, stable statistic: the repeated cross-validated concordance (rcvC). Sensitivity analyses were conducted where PD cases diagnosed within the first six months, one year, and two years were deleted. RESULTS: Single-predictor Cox regression models indicated that all PA measures were statistically significant (p-values < 0.0001). The highest-performing individual predictors were total acceleration (TA) (rcvC = 0.813) among PA measures, and age (rcvC = 0.757) among traditional predictors. The two-step forward-selection process produced a model containing age, sex, and TA (rcvC = 0.851). Adding TA to the model increased the rcvC by 9.8% (p-value < 0.0001). Results were largely unchanged in sensitivity analyses. CONCLUSIONS: Objective PA summaries have better single-predictor model performance than known risk factors and increase the prediction performance substantially when added to models with age and sex.

Objectively assessed sleep and physical activity in depression subtypes and its mediating role in their association with cardiovascular risk factors.

The aims of this study were to investigate the associations of major depressive disorder (MDD) and its subtypes (atypical, melancholic, combined, unspecified) with actigraphy-derived measures of sleep, physical activity and circadian rhythms; and test the potentially mediating role of sleep, physical activity and circadian rhythms in the well-established associations of the atypical MDD subtype with Body Mass Index (BMI) and the metabolic syndrome (MeS). The sample consisted of 2317 participants recruited from an urban area, who underwent comprehensive somatic and psychiatric evaluations. MDD and its subtypes were assessed via semi-structured diagnostic interviews. Sleep, physical activity and circadian rhythms were measured using actigraphy. MDD and its subtypes were associated with several actigraphy-derived variables, including later sleep midpoint, low physical activity, low inter-daily stability and larger intra-individual variability of sleep duration and relative amplitude. Sleep midpoint and physical activity fulfilled criteria for partial mediation of the association between atypical MDD and BMI, and physical activity also for partial mediation of the association between atypical MDD and MeS. Our findings confirm associations of MDD and its atypical subtype with sleep and physical activity, which are likely to partially mediate the associations of atypical MDD with BMI and MeS, although most of these associations are not explained by sleep and activity variables. This highlights the need to consider atypical MDD, sleep and sedentary behavior as cardiovascular risk factors.

A case study of glucose levels during sleep using multilevel fast function on scalar regression inference.

Continuous glucose monitors (CGMs) are increasingly used to measure blood glucose levels and provide information about the treatment and management of diabetes. Our motivating study contains CGM data during sleep for 174 study participants with type II diabetes mellitus measured at a 5-min frequency for an average of 10 nights. We aim to quantify the effects of diabetes medications and sleep apnea severity on glucose levels. Statistically, this is an inference question about the association between scalar covariates and functional responses observed at multiple visits (sleep periods). However, many characteristics of the data make analyses difficult, including (1) nonstationary within-period patterns; (2) substantial between-period heterogeneity, non-Gaussianity, and outliers; and (3) large dimensionality due to the number of study participants, sleep periods, and time points. For our analyses, we evaluate and compare two methods: fast univariate inference (FUI) and functional additive mixed models (FAMMs). We extend FUI and introduce a new approach for testing the hypotheses of no effect and time invariance of the covariates. We also highlight areas for further methodological development for FAMM. Our study reveals that (1) biguanide medication and sleep apnea severity significantly affect glucose trajectories during sleep and (2) the estimated effects are time invariant.

Fingerprinting walking using wrist-worn accelerometers.

BACKGROUND: Identifying an individual from accelerometry data collected during walking without reliance on step-cycle detection has not been achieved with high accuracy. RESEARCH QUESTION: We propose an open-source reproducible method to: (1) create a unique, person-specific "walking fingerprint" from a sample of un-landmarked high-resolution data collected by a wrist-worn accelerometer; and (2) predict who an individual is from their walking fingerprint. METHODS: Accelerometry data were collected during walking from 32 individuals (23-52 y.o., 19 females) for at least 380 s each. For this study's purpose, data are not landmarked, nor synchronized. Individual walking fingerprints were created by: (1) partitioning the accelerometer time series in adjacent, non-overlapping one-second intervals; (2) transforming all one-second interval data for a given individual into a three-dimensional (3D) image obtained by plotting each one-second interval time series by the lagged time series for a series of lags; (3) partitioning these resulting participant-specific 3D images into a grid of cells; and (4) identifying the combinations of cells (areas in the 3D image) that best predict the individual. For every participant, the first 200 s of data were used as training and the last 180 s as testing. This approach does not use segmentation methods for individual strides, which reduces dependence on complementary algorithms and increases its generalizability. RESULTS: The method correctly identified 100 % of the participants in the test data and highlighted unique features of walking that characterize the individuals. SIGNIFICANCE: Predicting the identity of an individual from their walking pattern has immediate implications that can complement or replace those of actual fingerprinting, voice, and image recognition. Furthermore, as walking may change with age or disease burden, individual walking fingerprints may be used as biomarkers of change in health status with potential clinical and epidemiologic implications.

Cardiovascular mortality risk prediction using objectively measured physical activity phenotypes in NHANES 2003-2006.

Increased physical activity (PA) has been associated with a decreased risk of cardiovascular disease (CVD) and mortality. However, most previous studies use self-reported PA instead of objectively measured PA assessed by wearable accelerometers. To the best of our knowledge, there have not been studies that quantified the univariate and multivariate ability of objectively measured PA summaries to predict the risk of CVD mortality. We investigate the ability of objectively measured PA summary variables to predict CVD mortality: as individual predictors, as part of the best multivariate model incorporating traditional predictors, and as additions to the best multivariate model using only traditional CVD predictors. Data were collected in the National Health and Nutrition Examination Survey 2003-2006 waves for US participants aged 50-85. The predictive ability was measured using Concordance, sometimes referred to as the C-statistic. Specifically, we calculated 10-fold cross-validated concordance (CVC) in survey-weighted Cox proportional hazard models. The best univariate predictor of CVD mortality was total activity count (outperformed age). In multivariate models, two of the eight predictors identified using the improvement in CVC threshold of 0.001 were PA measures (CVC = 0.844). The best model without physical activity (7 predictors) had CVC of 0.830. The addition of PA measures to the best traditional model was significantly better at predicting CVD mortality (P < 0.001). Accelerometer-derived PA measures have excellent cardiovascular mortality prediction performance. Wearable accelerometers have a potential for assessment of individuals' CVD mortality risks.

Comparison of Accelerometry-Based Measures of Physical Activity: Retrospective Observational Data Analysis Study.

BACKGROUND: Given the evolution of processing and analysis methods for accelerometry data over the past decade, it is important to understand how newer summary measures of physical activity compare with established measures. OBJECTIVE: We aimed to compare objective measures of physical activity to increase the generalizability and translation of findings of studies that use accelerometry-based data. METHODS: High-resolution accelerometry data from the Baltimore Longitudinal Study on Aging were retrospectively analyzed. Data from 655 participants who used a wrist-worn ActiGraph GT9X device continuously for a week were summarized at the minute level as ActiGraph activity count, monitor-independent movement summary, Euclidean norm minus one, mean amplitude deviation, and activity intensity. We calculated these measures using open-source packages in R. Pearson correlations between activity count and each measure were quantified both marginally and conditionally on age, sex, and BMI. Each measures pair was harmonized using nonparametric regression of minute-level data. RESULTS: Data were from a sample (N=655; male: n=298, 45.5%; female: n=357, 54.5%) with a mean age of 69.8 years (SD 14.2) and mean BMI of 27.3 kg/m2 (SD 5.0). The mean marginal participant-specific correlations between activity count and monitor-independent movement summary, Euclidean norm minus one, mean amplitude deviation, and activity were r=0.988 (SE 0.0002324), r=0.867 (SE 0.001841), r=0.913 (SE 0.00132), and r=0.970 (SE 0.0006868), respectively. After harmonization, mean absolute percentage errors of predicting total activity count from monitor-independent movement summary, Euclidean norm minus one, mean amplitude deviation, and activity intensity were 2.5, 14.3, 11.3, and 6.3, respectively. The accuracies for predicting sedentary minutes for an activity count cut-off of 1853 using monitor-independent movement summary, Euclidean norm minus one, mean amplitude deviation, and activity intensity were 0.981, 0.928, 0.904, and 0.960, respectively. An R software package called SummarizedActigraphy, with a unified interface for computation of the measures from raw accelerometry data, was developed and published. CONCLUSIONS: The findings from this comparison of accelerometry-based measures of physical activity can be used by researchers and facilitate the extension of knowledge from existing literature by demonstrating the high correlation between activity count and monitor-independent movement summary (and other measures) and by providing harmonization mapping.

Fast Univariate Inference for Longitudinal Functional Models.

We propose fast univariate inferential approaches for longitudinal Gaussian and non-Gaussian functional data. The approach consists of three steps: (1) fit massively univariate pointwise mixed effects models; (2) apply any smoother along the functional domain; and (3) obtain joint confidence bands using analytic approaches for Gaussian data or a bootstrap of study participants for non-Gaussian data. Methods are motivated by two applications: (1) Diffusion Tensor Imaging (DTI) measured at multiple visits along the corpus callosum of multiple sclerosis (MS) patients; and (2) physical activity data measured by body-worn accelerometers for multiple days. An extensive simulation study indicates that model fitting and inference are accurate and much faster than existing approaches. Moreover, the proposed approach was the only one that was computationally feasible for the physical activity data application. Methods are accompanied by R software, though the method is "read-and-use", as it can be implemented by any analyst who is familiar with mixed effects model software.

Fixed-effects inference and tests of correlation for longitudinal functional data.

We propose an inferential framework for fixed effects in longitudinal functional models and introduce tests for the correlation structures induced by the longitudinal sampling procedure. The framework provides a natural extension of standard longitudinal correlation models for scalar observations to functional observations. Using simulation studies, we compare fixed effects estimation under correctly and incorrectly specified correlation structures and also test the longitudinal correlation structure. Finally, we apply the proposed methods to a longitudinal functional dataset on physical activity. The computer code for the proposed method is available at https://github.com/rli20ST758/FILF.

Genome-wide association studies of 27 accelerometry-derived physical activity measurements identified novel loci and genetic mechanisms.

Physical inactivity (PA) is an important risk factor for a wide range of diseases. Previous genome-wide association studies (GWAS), based on self-reported data or a small number of phenotypes derived from accelerometry, have identified a limited number of genetic loci associated with habitual PA and provided evidence for involvement of central nervous system in mediating genetic effects. In this study, we derived 27 PA phenotypes from wrist accelerometry data obtained from 88,411 UK Biobank study participants. Single-variant association analysis based on mixed-effects models and transcriptome-wide association studies (TWAS) together identified 5 novel loci that were not detected by previous studies of PA, sleep duration and self-reported chronotype. For both novel and previously known loci, we discovered associations with novel phenotypes including active-to-sedentary transition probability, light-intensity PA, activity during different times of the day and proxy phenotypes to sleep and circadian patterns. Follow-up studies including TWAS, colocalization, tissue-specific heritability enrichment, gene-set enrichment and genetic correlation analyses indicated the role of the blood and immune system in modulating the genetic effects and a secondary role of the digestive and endocrine systems. Our findings provided important insights into the genetic architecture of PA and its underlying mechanisms.