Functional Mixed Effects Model Research Articles

Modeling approaches for assessing device-based measures of energy expenditure in school-based studies of body weight status

BackgroundObesity has become an important threat to children’s health, with physical and psychological impacts that extend into adulthood. Limited physical activity and sedentary behavior are associated with increased obesity risk. Because children spend approximately 6 h each day in school, researchers increasingly study how obesity is influenced by school-day physical activity and energy expenditure (EE) patterns among school-aged children by using wearable devices that collect data at frequent intervals and generate complex, high-dimensional data. Although clinicians typically define obesity in children as having an age-and sex-adjusted body mass index (BMI) value in the high percentiles, the relationships between school-based physical activity interventions and BMI are analyzed using traditional linear regression models, which are designed to assess the effects of interventions among children with average BMI, limiting insight regarding the effects of interventions among children categorized as overweight or obese.MethodsWe investigate the association between wearable device–based EE measures and age-and sex-adjusted BMI values in data from a cluster-randomized, school-based study. We express and analyze EE levels as both a scalar-valued variable and as a continuous, high-dimensional, functional predictor variable. We investigate the relationship between school-day EE (SDEE) and BMI using four models: a linear mixed-effects model (LMEM), a quantile mixed-effects model (QMEM), a functional mixed-effects model (FMEM), and a functional quantile mixed-effects model (FQMEM). The LMEM and QMEM include SDEE as a summary measure, whereas the FMEM and FQMEM allow for the modeling of SDEE as a high-dimensional covariate. The FMEM and FQMEM allow the influence of the time of day at which physical activity is performed to be assessed, which is not possible using the LMEM or the QMEM. The FMEM assesses how frequently collected SDEE data influences mean BMI, whereas the FQMEM assesses the effects on quantile levels of BMI.ResultsThe LMEM and QMEM detected a statistically significant effect of overall mean SDEE on log (BMI) (the natural logarithm of BMI) after adjusting for intervention, age, race, and sex. The FMEM and FQMEM provided evidence for statistically significant associations between SDEE and log (BMI) for only a short time interval. Being a boy or being assigned a stand-biased desk is associated with a lower log (BMI) than being a girl or being assigned a traditional desk. Across our models, age was not a statistically significant covariate, and white students had significantly lower log (BMI) than non-white students in quantile models, but this significant effect was observed for only the 10th and 50th quantile levels of BMI. The functional regression models allow for additional interpretations of the influence of EE patterns on age-and sex-adjusted BMI, whereas the quantile regression models enable the influence of EE patterns to be assessed across the entire BMI distribution.ConclusionThe FQMEM is recommended when interest lies in assessing how device-monitored SDEE patterns affect children of all body types, as this model is robust and able to assess intervention effects across the full BMI distribution. However, the sample size must be sufficiently large to adequately power determinations of covariate effects across the entire BMI distribution, including the tails.

SEMIPARAMETRIC BIVARIATE HIERARCHICAL STATE SPACE MODEL WITH APPLICATION TO HORMONE CIRCADIAN RELATIONSHIP.

The adrenocorticotropic hormone and cortisol play critical roles in stress regulation and the sleep-wake cycle. Most research has been focused on how the two hormones regulate each other in terms of short-term pulses. Few studies have been conducted on the circadian relationship between the two hormones and how it differs between normal and abnormal groups. The circadian patterns are difficult to model as parametric functions. Directly extending univariate functional mixed effects models would result in a large dimensional problem and a challenging nonparametric inference. In this article, we propose a semi-parametric bivariate hierarchical state space model, in which each hormone profile is modeled by a hierarchical state space model, with nonparametric population-average and subject-specific components. The bivariate relationship is constructed by concatenating two latent independent subject-specific random functions specified by a design matrix, leading to a parametric inference on the correlation. We propose a computationally efficient state-space EM algorithm for estimation and inference. We apply the proposed method to a study of chronic fatigue syndrome and fibromyalgia and discover an erratic regulation pattern in the patient group in contrast to a circadian regulation pattern conforming to the day-night cycle in the control group.

The time course of motor and cognitive decline in older adults and their associations with brain pathologies: a multicohort study

Many studies have reported that impaired gait precedes cognitive impairment in older people. We aimed to characterise the time course of cognitive and motor decline in older individuals and the association of these declines with the pathologies of Alzheimer's disease and related dementias. This multicohort study used data from three community-based cohort studies (Religious Orders Study, Rush Memory and Aging Project, and Minority Aging Research Study, all in the USA). The inclusion criteria for all three cohorts were no clinical dementia at the time of enrolment and consent to annual clinical assessments. Eligible participants consented to post-mortem brain donation and had post-mortem pathological assessments and three or more repeated annual measures of cognition and motor functions. Clinical and post-mortem data were analysed using functional mixed-effects models. Global cognition was based on 19 neuropsychological tests, a hand strength score was based on grip and pinch strength, and a gait score was based on the number of steps and time to walk 8 feet and turn 360°. Brain pathologies of Alzheimer's disease and related dementias were assessed at autopsy. From 1994 to 2022, there were 1570 eligible cohort participants aged 65 years or older, 1303 of whom had cognitive and motor measurements and were included in the analysis. Mean age at death was 90·3 years (SD 6·3), 905 (69%) participants were female, and 398 (31%) were male. Median follow-up time was 9 years (IQR 5-11). On average, cognition was stable from 25 to 15 years before death, when cognition began to decline. By contrast, gait function and hand strength declined during the entire study. The combinations of pathologies of Alzheimer's disease and related dementias associated with cognitive and motor decline and their onsets of associations varied; only tau tangles, Parkinson's disease pathology, and macroinfarcts were associated with decline of all three phenotypes. Tau tangles were significantly associated with cognitive decline, gait function decline, and hand function decline (p<0·0001 for each); however, the association with cognitive decline persisted for more than 11 years before death, but the association with hand strength only began 3·57 years before death and the association with gait began 3·49 years before death. By contrast, the association of macroinfarcts with declining gait function began 9·25 years before death (p<0·0001) compared with 6·65 years before death (p=0·0005) for cognitive decline and 2·66 years before death (p=0·024) for decline in hand strength. Our findings suggest that average motor decline in older adults precedes cognitive decline. Macroinfarcts but not tau tangles are associated with declining gait function that precedes cognitive decline. This suggests the need for further studies to test if gait impairment is a clinical proxy for preclinical vascular cognitive impairment. National Institutes of Health.

Classified functional mixed effects model prediction.

In nowadays biomedical research, there has been a growing demand for making accurate prediction at subject levels. In many of these situations, data are collected as longitudinal curves and display distinct individual characteristics. Thus, prediction mechanisms accommodated with functional mixed effects models (FMEM) are useful. In this paper, we developed a classified functional mixed model prediction (CFMMP) method, which adapts classified mixed model prediction (CMMP) to the framework of FMEM. Performance of CFMMP against functional regression prediction based on simulation studies and the consistency property of CFMMP estimators are explored. Real-world applications of CFMMP are illustrated using real world examples including data from the hormone research menstrual cycles and the diffusion tensor imaging.

Estimation of a clustering model for non Gaussian functional data

Model-based clustering analysis of functional data often has normality assumption. This article considers clustering non Gaussian functional data. We propose a novel non Gaussian functional mixed-effects model without the prior information and clustering number. We use transformation functions to accommodate non Gaussian functional data. Smoothing spline ANOVA and cubic B-spline approximate unknown fixed effects and random effects, respectively. A penalized likelihood is used to estimate unknown parameters, and the consistency and asymptotic normality is provided after that. We take simulations for different measurement error distribution assumptions and adopt the air quality of Italian city data. Both simulation and actual data analysis show that the proposed method performs well and has a better clustering effect.

Functional non-parametric mixed effects models for cytotoxicity assessment and clustering

A multitude of natural and synthetic chemicals are present in our environment.Through the study of a compound’s cytotoxicity, researchers can carefully set regulations regarding how much of a certain chemical in the ambient environment is tolerable. In the past, research has focused on point measurements such as the LD50. Instead, we consider entire time-dependent cellular response curves through the application of functional mixed effects models. We identify differences in such curves corresponding to the chemical’s mode of action—i.e. how the compound attacks human cells. Through such analysis, we identify curve features to be used for cluster analysis via application of both k-means and self organizing maps. The data is analyzed by making use of functional principal components as a data driven basis and separately by considering B-splines for identifying local-time features. Our analysis can be used to drastically speed up future cytotoxicity research.

Joint Modeling of Longitudinal Imaging and Survival Data

This paper considers a joint modeling framework for simultaneously examining the dynamic pattern of longitudinal and ultrahigh-dimensional images and their effects on the survival of interest. A functional mixed effects model is considered to describe the trajectories of longitudinal images. Then, a high-dimensional functional principal component analysis (HD-FPCA) is adopted to extract the principal eigenimages to reduce the ultrahigh dimensionality of imaging data. Finally, a Cox regression model is used to examine the effects of the longitudinal images and other risk factors on the hazard. A theoretical justification shows that a naive two-stage procedure that separately analyzes each part of the joint model produces biased estimation even if the longitudinal images have no measurement error. We develop a Bayesian joint estimation method coupled with efficient Markov chain Monte Carlo sampling schemes to perform statistical inference for the proposed joint model. A Monte Carlo dynamic prediction procedure is proposed to predict the future survival probabilities of subjects given their historical longitudinal images. The proposed model is assessed through extensive simulation studies and an application to Alzheimer’s Disease Neuroimaging Initiative, which turns out to hold the promise of accuracy and possess higher predictive capacity for survival outcome compared with existing methods.

Conditional functional clustering for longitudinal data with heterogeneous nonlinear patterns

In studies of cognitive aging, it is crucial to distinguish subtypes of longitudinal cognition change while accounting for the effects of given covariates. The longitudinal cognition trajectories and the covariate effects can both be nonlinear with heterogeneous shapes that do not follow a simple parametric form, where flexible functional methods are preferred. However, most functional clustering methods for longitudinal data do not allow controlling for the possible functional effects of covariates. Although traditional mixture-of-experts methods can include covariates and be extended to the functional setting, using nonlinear basis functions, satisfactory parsimonious functional methods required for robust functional coefficient estimation and clustering are still lacking. In this paper we propose a novel latent class functional mixed-effects model in which we assume the covariates have fixed functional effects, and the random curves follow a mixture of Gaussian processes that facilitates a model-based conditional clustering. A transformed penalized B-spline approach is employed for parsimonious modeling and robust model estimation. We propose a new iterative-REML method to choose the penalty parameters in heterogeneous data. The new method is applied to the latest data from the Religious Orders Study and Rush Memory and Aging Project, and four novel subtypes of cognitive changes are identified.

Functional Mixed Effects Clustering with Application to Longitudinal Urologic Chronic Pelvic Pain Syndrome Symptom Data

By clustering patients with the urologic chronic pelvic pain syndromes (UCPPS) into homogeneous subgroups and associating these subgroups with baseline covariates and other clinical outcomes, we provide opportunities to investigate different potential elements of pathogenesis, which may also guide us in selection of appropriate therapeutic targets. Motivated by the longitudinal urologic symptom data with extensive subject heterogeneity and differential variability of trajectories, we propose a functional clustering procedure where each subgroup is modeled by a functional mixed effects model, and the posterior probability is used to iteratively classify each subject into different subgroups. The classification takes into account both group-average trajectories and between-subject variabilities. We develop an equivalent state-space model for efficient computation. We also propose a cross-validation based Kullback–Leibler information criterion to choose the optimal number of subgroups. The performance of the proposed method is assessed through a simulation study. We apply our methods to longitudinal bi-weekly measures of a primary urological urinary symptoms score from a UCPPS longitudinal cohort study, and identify four subgroups ranging from moderate decline, mild decline, stable and mild increasing. The resulting clusters are also associated with the one-year changes in several clinically important outcomes, and are also related to several clinically relevant baseline predictors, such as sleep disturbance score, physical quality of life and painful urgency. Supplementary materials for this article are available online.

DADP: Dynamic abnormality detection and progression for longitudinal knee magnetic resonance images from the Osteoarthritis Initiative.

Osteoarthritis (OA) is the most common disabling joint disease. Magnetic resonance (MR) imaging has been commonly used to assess knee joint degeneration due to its distinct advantage in detecting morphologic cartilage changes. Although several statistical methods over conventional radiography have been developed to perform quantitative cartilage analyses, little work has been done capturing the development and progression of cartilage lesions (or abnormal regions) and how they naturally progress. There are two major challenges, including (i) the lack of building spatial-temporal correspondences and correlations in cartilage thickness and (ii) the spatio-temporal heterogeneity in abnormal regions. The goal of this work is to propose a dynamic abnormality detection and progression (DADP) framework for quantitative cartilage analysis, while addressing the two challenges. First, spatial correspondences are established on flattened 2D cartilage thickness maps extracted from 3D knee MR images both across time within each subject and across all subjects. Second, a dynamic functional mixed effects model (DFMEM) is proposed to quantify abnormality progression across time points and subjects, while accounting for the spatio-temporal heterogeneity. We systematically evaluate our DADP using simulations and real data from the Osteoarthritis Initiative (OAI). Our results show that DADP not only effectively detects subject-specific dynamic abnormal regions, but also provides population-level statistical disease mapping and subgroup analysis.

Model-based joint curve registration and classification

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

Automated Analysis Using a Bayesian Functional Mixed-Effects Model With Gaussian Process Responses for Wavelet Spectra of Spatiotemporal Colonic Manometry Signals.

Manual analysis of human high-resolution colonic manometry data is time consuming, non-standardized and subject to laboratory bias. In this article we present a technique for spectral analysis and statistical inference of quasiperiodic spatiotemporal signals recorded during colonic manometry procedures. Spectral analysis is achieved by computing the continuous wavelet transform and cross-wavelet transform of these signals. Statistical inference is achieved by modeling the resulting time-averaged amplitudes in the frequency and frequency-phase domains as Gaussian processes over a regular grid, under the influence of categorical and numerical predictors specified by the experimental design as a functional mixed-effects model. Parameters of the model are inferred with Hamiltonian Monte Carlo. Using this method, we re-analyzed our previously published colonic manometry data, comparing healthy controls and patients with slow transit constipation. The output from our automated method, supports and adds to our previous manual analysis. To obtain these results took less than two days. In comparison the manual analysis took 5 weeks. The proposed mixed-effects model approach described here can also be used to gain an appreciation of cyclical activity in individual subjects during control periods and in response to any form of intervention.

Bayesian Functional Mixed-effects Models with Grouped Smoothness for Analyzing Time-course Gene Expression Data

Objective: As a result of the development of microarray technologies, gene expression levels of thousands of genes involved in a given biological process can be measured simultaneously, and it is important to study their temporal behavior to understand their mechanisms. Since the dependence between gene expression levels over time for a given gene is often too complicated to model parametrically, sparse functional data analysis has received an increasing amount of attention for analyzing such data. Methods: We propose a new functional mixed-effects model for analyzing time-course gene expression data. Specifically, the model groups individual functions with heterogeneous smoothness. The proposed method utilizes the mixed-effects model representation of penalized splines for both the mean function and the individual functions. Given noninformative or weakly informative priors, Bayesian inference on the proposed models was developed, and Bayesian computation was implemented by using Markov chain Monte Carlo methods. Results: The performance of our new model was studied by two simulation studies and illustrated using a yeast cell cycle gene expression dataset. Simulation results suggest that our proposed methods can outperform the previously used methods in terms of the mean integrated squared error. The yeast gene expression data application suggests that the proposed model with two latent groups should be used on this dataset. Conclusion: The new Bayesian functional mixed-effects model that assumes multiple groups of functions with different smoothing parameters provides an enhanced approach to analyzing timecourse gene expression data.

Online anomaly detection of profiles with varying coefficients via functional mixed effects modelling

In this paper, a novel online sequential monitoring scheme is proposed for real-time detection of anomalies in the incoming profile data. A profile data, in the present context, consists of the response affected by multiple time-dependent covariates and is subject to within-profile correlation. The proposed scheme is based on a functional mixed-effects model, where the response variable is influenced simultaneously by functional fixed-effect and random-effect terms. The baseline functional mixed-effects model is first estimated based on in-control historical profiles during appropriate Phase-I analysis. Subsequently, a Phase-II exponentially weighted moving average scheme is implemented using a monitoring statistic based on penalized spline smoothing for sequential monitoring of the online profile data. Theoretical results and extensive simulation studies show the effectiveness of the proposed charting scheme. Moreover, the proposed method is validated by an application example from the drying process of tobacco manufacturing. Technical details are given in the Appendix.

Identification of Drug-Induced Multichannel Block and Proarrhythmic Risk in Humans Using Continuous T Vector Velocity Effect Profiles Derived From Surface Electrocardiograms.

We present continuous T vector velocity (TVV) effect profiles as a new method for identifying drug effects on cardiac ventricular repolarization. TVV measures the temporal change in the myocardial action potential distribution during repolarization. The T vector dynamics were measured as the time required to reach p percent of the total T vector trajectory length, denoted as Tr(p), with p in {1, …, 100%}. The Tr(p) values were individually corrected for heart rate at each trajectory length percentage p. Drug effects were measured by evaluating the placebo corrected changes from baseline of Tr(p)c jointly for all p using functional mixed effects models. The p-dependent model parameters were implemented as cubic splines, providing continuous drug effect profiles along the entire ventricular repolarization process. The effect profile distributions were approximated by bootstrap simulations. We applied this TVV-based analysis approach to ECGs available from three published studies that were conducted in the CiPA context. These studies assessed the effect of 10 drugs and drug combinations with different ion channel blocking properties on myocardial repolarization in a total of 104 healthy volunteers. TVV analysis revealed that blockade of outward potassium currents alone presents an effect profile signature of continuous accumulation of delay throughout the entire repolarization interval. In contrast, block of inward sodium or calcium currents involves acceleration, which accumulates during early repolarization. The balance of blocking inward versus outward currents was reflected in the percentage pzero of the T vector trajectory length where accelerated repolarization transitioned to delayed repolarization. Binary classification using a threshold pzero = 43% separated predominant hERG channel blocking drugs with potentially higher proarrhythmic risk (moxifloxacin, dofetilide, quinidine, chloroquine) from multichannel blocking drugs with low proarrhythmic risk (ranolazine, verapamil, lopinavir/ritonavir) with sensitivity 0.99 and specificity 0.97. The TVV-based effect profile provides a detailed view of drug effects throughout the entire ventricular repolarization interval. It enables the evaluation of drug-induced blocks of multiple cardiac repolarization currents from clinical ECGs. The proposed pzero parameter enhances identification of the proarrhythmic risk of a drug beyond QT prolongation, and therefore constitutes an important tool for cardiac arrhythmia risk assessment.

Examination of Nonlinear and Functional Mixed-Effects Models with Nonparametrically Generated Data

Previous research has shown functional mixed-effects models and traditional mixed-effects models perform similarly when recovering individual trajectories when data were generated following a parametric structure. We extend this previous work and compare nonlinear mixed-effects (NMEM) and functional mixed-effects models’ (FMEM) ability to recover underlying trajectories when generated from an inherently nonparametric process. Nonlinear trajectories were generated using B-splines, NMEMs and FMEMs were estimated, and the accuracy of the estimated curves was examined. Sample size, number of time points per curve, and measurement design were varied across simulation conditions. Results showed the FMEMs recovered the underlying mean curve more accurately than the NMEMs, and that, the FMEMs tended to recover the underlying individual curves more accurately than the NMEMs. Progesterone cycle data were then analyzed to demonstrate the utility of both approaches, and models performed similarly when analyzing these data.

Normative Cognitive Decline in Old Age.

To characterize trajectories of normative cognitive aging. Older persons without dementia at study enrollment (n = 1,010) had annual cognitive testing for up to 24 years (mean = 9.9 years, standard deviation = 5.0), died, and underwent a neuropathologic examination to quantify 9 postmortem markers of common neurodegenerative and cerebrovascular conditions. To accommodate the heterogeneity in cognitive trajectories, we used functional mixed effects models, which allow individuals to have different patterns of cognitive decline under a unified model structure. In a functional mixed effects model, postmortem markers (Alzheimer disease pathology, Lewy bodies, transactive response DNA-binding protein 43 pathology, hippocampal sclerosis, atherosclerosis, gross infarcts) were associated with global cognitive decline. Residual global cognitive decline after adjustment for neuropathologic burden was weakly related to age at death; it occurred in only about one-third of participants, mostly proximate to death. Results were comparable after eliminating the initial cognitive assessments to minimize retest learning or controlling for frailty proximate to death. Analyses were also conducted with composite measures of episodic memory and perceptual speed. Residual decline not attributable to neuropathologic burden was confined to a subset for each outcome and was most evident proximate to death. Age at death was unrelated to residual decline in episodic memory but was related to residual decline in perceptual speed. Late life cognitive loss mainly reflects non-normative pathologic and mortality-related processes rather than normative age-related processes. ANN NEUROL 2020;87:816-829.

An Examination of a Functional Mixed-Effects Modeling Approach to the Analysis of Longitudinal Data

Growth curve modeling is one of the main analytical approaches to study change over time. Growth curve models are commonly estimated in the linear and nonlinear mixed-effects modeling framework in which both the mean and person-specific curves are modeled parametrically with functions of time such as the linear, quadratic, and exponential. However, when more complex nonlinear trajectories need to be estimated and researchers do not have a priori knowledge of an appropriate functional form of growth, parametric models may be too restrictive. This paper reviews functional mixed-effects models, a nonparametric extension of mixed-effects models that permit both the mean and person-specific curves to be estimated without assuming a prespecified functional form of growth. Details of the model are presented along with results from a simulation study and an empirical example. The simulation study showed functional mixed-effects models performed reasonably well under various conditions commonly associated with longitudinal panel data, such as few time points per person, irregularly spaced time points across persons, missingness, and nonlinear trajectories. The usefulness of functional mixed-effects models is illustrated by analyzing empirical data from the Early Childhood Longitudinal Study – Kindergarten Class of 1998–1999.

FMEM: Functional Mixed Effects Models for Longitudinal Functional Responses.

The aim of this paper is to conduct a systematic and theoretical analysis of estimation and inference for a class of functional mixed effects models (FMEM). Such FMEMs consist of fixed effects that characterize the association between longitudinal functional responses and covariates of interest and random effects that capture the spatial-temporal correlations of longitudinal functional responses. We propose local linear estimates of refined fixed effect functions and establish their weak convergence along with a simultaneous confidence band for each fixed-effect function. We propose a global test for the linear hypotheses of varying coefficient functions and derive the associated asymptotic distribution under the null hypothesis and the asymptotic power under the alternative hypothesis are derived. We also establish the convergence rates of the estimated spatial-temporal covariance operators and their associated eigenvalues and eigenfunctions. We conduct extensive simulations and apply our method to a white-matter fiber data set from a national database for autism research to examine the finite-sample performance of the proposed estimation and inference procedures.

Functional Mixed-Effects Modeling of Longitudinal Duchenne Muscular Dystrophy Electrical Impedance Myography Data Using State-Space Approach.

Electrical impedance myography (EIM) is a quantitative and objective tool to evaluate muscle status. EIM offers the possibility to replace conventional physical functioning scores or quality of life measures, which depend on patient cooperation and mood. Here, we propose a functional mixed-effects model using a state-space approach to describe the response trajectories of EIM data measured on 16 boys with Duchenne muscular dystrophy and 12 healthy controls, both groups measured over a period of two years. The modeling framework presented imposes a smoothing spline structure on EIM data collected at each visit and taking into account of within subject correlations of these curves along the longitudinal measurements. The modeling framework is recast in a state-space approach, thereby allowing for the employment of computationally efficient diffuse Kalman filtering and smoothing algorithms for the model estimation, as well as the estimates of the posterior variance-covariance matrix for the construction of the Bayesian [Formula: see text] confidence bands. The proposed model allows us to simultaneously adjust for baseline variables, differentiate the longitudinal changes in the smooth functional response and estimate the subject and subject-time specific deviations from the population-averaged response curves. The code is made publicly available in the supplementary material. The modeling approach presented will potentially enhance EIM capability to serve as a biomarker for testing therapeutic efficacy in DMD and other clinical trials.