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Hierarchical Adaptive Regression Kernels for Regression with Functional Predictors.

ABSTRACT: We propose a new method for regression using a parsimonious and scientifically interpretable representation of functional predictors. Our approach is designed for data that exhibit features such as spikes, dips, and plateaus whose frequency, location, size, and shape varies stochastically across subjects. We propose Bayesian inference of the joint functional and exposure models, and give a method for efficient computation. We contrast our approach with existing state-of-the-art methods for regression with functional predictors, and show that our method is more effective and efficient for data that include features occurring at varying locations. We apply our methodology to a large and complex dataset from the Sleep Heart Health Study, to quantify the association between sleep characteristics and health outcomes. Software and technical appendices are provided in online supplemental materials.

SUBMITTER: Woodard DB

PROVIDER: S-EPMC3842620 | biostudies-literature | 2013

REPOSITORIES: biostudies-literature

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Hierarchical Adaptive Regression Kernels for Regression with Functional Predictors.

Woodard Dawn B DB Crainiceanu Ciprian C Ruppert David D

Journal of computational and graphical statistics : a joint publication of American Statistical Association, Institute of Mathematical Statistics, Interface Foundation of North America 20130101 4

We propose a new method for regression using a parsimonious and scientifically interpretable representation of functional predictors. Our approach is designed for data that exhibit features such as spikes, dips, and plateaus whose frequency, location, size, and shape varies stochastically across subjects. We propose Bayesian inference of the joint functional and exposure models, and give a method for efficient computation. We contrast our approach with existing state-of-the-art methods for regre ...[more]

PMID: 24293988

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Project description:PurposeUnderstanding how early adaptive schemas, cognitive flexibility, and emotional regulation influence eating disorder (ED) symptoms, and whether this differs across diagnostic subtypes is critical to optimising treatment. The current study investigated the relationship between these variables and ED symptomology in individuals self-reporting an ED diagnosis and healthy controls.MethodsA dataset of 1576 online survey responses yielded subsamples for anorexia nervosa (n = 155), bulimia nervosa (n = 55), binge eating disorder (n = 33), other specified feeding or eating disorder (n = 93), and healthy participants (n = 505). The hierarchical linear regression analysis included Eating Disorder Examination Questionnaire 6.0 Global Score as the dependent variable; Young Positive Schema Questionnaire, Emotional Regulation Questionnaire, and Cognitive Flexibility Inventory subscale scores as the independent variables; and demographic measures as the covariates.ResultsThe number of significant predictors varied considerably by ED sub-group. Amongst the anorexia nervosa, bulimia nervosa, and healthy subsamples, the adaptive schema Self-Compassion and Realistic Expectations was associated with lower ED symptom severity. In comparison, age and body mass index were the strongest predictors for binge eating disorder, whilst the Expressive Suppression (a subscale of the Emotional Regulation Questionnaire) was the strongest predictor for other specified feeding or eating disorders.ConclusionEarly adaptive schemas, cognitive flexibility, and emotional regulation vary across ED subtype, suggesting the need for tailored treatment that disrupts the self-reinforcing cycle of ED psychopathology. Future research investigating how early adaptive schemas may predict or be associated with treatment response across diagnostic subtypes is needed.Level of evidenceLevel IV, evidence obtained from multiple time-series with or without the intervention, such as case studies.

Project description:Functional data are increasingly encountered in scientific studies, and their high dimensionality and complexity lead to many analytical challenges. Various methods for functional data analysis have been developed, including functional response regression methods that involve regression of a functional response on univariate/multivariate predictors with nonparametrically represented functional coefficients. In existing methods, however, the functional regression can be sensitive to outlying curves and outlying regions of curves, so is not robust. In this paper, we introduce a new Bayesian method, robust functional mixed models (R-FMM), for performing robust functional regression within the general functional mixed model framework, which includes multiple continuous or categorical predictors and random effect functions accommodating potential between-function correlation induced by the experimental design. The underlying model involves a hierarchical scale mixture model for the fixed effects, random effect and residual error functions. These modeling assumptions across curves result in robust nonparametric estimators of the fixed and random effect functions which down-weight outlying curves and regions of curves, and produce statistics that can be used to flag global and local outliers. These assumptions also lead to distributions across wavelet coefficients that have outstanding sparsity and adaptive shrinkage properties, with great flexibility for the data to determine the sparsity and the heaviness of the tails. Together with the down-weighting of outliers, these within-curve properties lead to fixed and random effect function estimates that appear in our simulations to be remarkably adaptive in their ability to remove spurious features yet retain true features of the functions. We have developed general code to implement this fully Bayesian method that is automatic, requiring the user to only provide the functional data and design matrices. It is efficient enough to handle large data sets, and yields posterior samples of all model parameters that can be used to perform desired Bayesian estimation and inference. Although we present details for a specific implementation of the R-FMM using specific distributional choices in the hierarchical model, 1D functions, and wavelet transforms, the method can be applied more generally using other heavy-tailed distributions, higher dimensional functions (e.g. images), and using other invertible transformations as alternatives to wavelets.

Project description:BACKGROUND:Emerging resistance to anti-malarial drugs has led malaria researchers to investigate what covariates (parasite and host factors) are associated with resistance. In this regard, investigation of how covariates impact malaria parasites clearance is often performed using a two-stage approach in which the WWARN Parasite Clearance Estimator or PCE is used to estimate parasite clearance rates and then the estimated parasite clearance is regressed on the covariates. However, the recently developed Bayesian Clearance Estimator instead leads to more accurate results for hierarchial regression modelling which motivated the authors to implement the method as an R package, called "bhrcr". METHODS:Given malaria parasite clearance profiles of a set of patients, the "bhrcr" package performs Bayesian hierarchical regression to estimate malaria parasite clearance rates along with the effect of covariates on them in the presence of "lag" and "tail" phases. In particular, the model performs a linear regression of the log clearance rates on covariates to estimate the effects within a Bayesian hierarchical framework. All posterior inferences are obtained by a "Markov Chain Monte Carlo" based sampling scheme which forms the core of the package. RESULTS:The "bhrcr" package can be utilized to study malaria parasite clearance data, and specifically, how covariates affect parasite clearance rates. In addition to estimating the clearance rates and the impact of covariates on them, the "bhrcr" package provides tools to calculate the WWARN PCE estimates of the parasite clearance rates as well. The fitted Bayesian model to the clearance profile of each individual, as well as the WWARN PCE estimates, can also be plotted by this package. CONCLUSIONS:This paper explains the Bayesian Clearance Estimator for malaria researchers including describing the freely available software, thus making these methods accessible and practical for modelling covariates' effects on parasite clearance rates.

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Hierarchical Adaptive Regression Kernels for Regression with Functional Predictors.

Publications

Hierarchical Adaptive Regression Kernels for Regression with Functional Predictors.

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