Ana-Maria Staicu

North Carolina State University | NCSU · Department of Statistics

Recent advances in multiplex imaging have enabled researchers to locate different types of cells within a tissue sample. This is especially relevant for tumor immunology, as clinical regimes corresponding to different stages of disease or responses to treatment may manifest as different spatial arrangements of tumor and immune cells. Spatial point...

This paper introduces a model for longitudinal functional data analysis that accounts for pointwise skewness. The proposed procedure decouples the marginal pointwise variation from the complex longitudinal and functional dependence using copula methodology. Pointwise variation is described through parametric distribution functions that capture vary...

Motivated by the challenges of analyzing high-dimensional ($p \gg n$) sequencing data from longitudinal microbiome studies, where samples are collected at multiple time points from each subject, we propose supervised functional tensor singular value decomposition (SupFTSVD), a novel dimensionality reduction method that leverages auxiliary informati...

Tensor-based morphometry (TBM) aims at showing local differences in brain volumes with respect to a common template. TBM images are smooth but they exhibit (especially in diseased groups) higher values in some brain regions called lateral ventricles. More specifically, our voxelwise analysis shows both a mean-variance relationship in these areas an...

This article focuses on the study of lactating sows, where the main interest is the influence of temperature, measured throughout the day, on the lower quantiles of the daily feed intake. We outline a model framework and estimation methodology for quantile regression in scenarios with longitudinal data and functional covariates. The quantile regres...

This article focuses on the study of lactating sows, where the main interest is the influence of temperature, measured throughout the day, on the lower quantiles of the daily feed intake. We outline a model framework and estimation methodology for quantile regression in scenarios with longitudinal data and functional covariates. The quantile regres...

Modern studies from a variety of fields record multiple functional observations according to either multivariate, longitudinal, spatial, or time series designs. We refer to such data as second-generation functional data because their analysis—unlike typical functional data analysis, which assumes independence of the functions—accounts for the compl...

Biological sex and gender are critical variables in biomedical research, but are complicated by the presence of sex‐specific natural hormone cycles, such as the estrous cycle in female rodents, typically divided into phases. A common feature of these cycles are fluctuating hormone levels which induce sex differences in many behaviors controlled by...

Technological advancement has made possible the collection of data from social media platforms at unprecedented speed and volume. Current methods for analyzing such data lack interpretability, are computationally intensive, or require a rigid data specification. Functional data analysis enables the development of a flexible, yet interpretable, mode...

Image-based stage and discharge measuring systems are among the most promising new non-contact technologies available for long-term hydrological monitoring. This article evaluates and reports the long-term performance of the GaugeCam (www.gaugecam.org) image-based stage measuring system in situ. For this we installed and evaluated the system over s...

Wearable devices for continuous monitoring of electronic health increased attention due to their richness in information. Often, inference is drawn from features that quantify some summary of the data, leading to a loss of information that could be useful when one utilizes the functional nature of the response. When functional trajectories are obse...

In this paper we study statistical inference in functional quantile regression for scalar response and a functional covariate. Specifically, we consider linear functional quantile model where the effect of the covariate on the quantile of the response is modeled through the inner product between the functional covariate and an unknown smooth regres...

The manuscript discusses how to incorporate random effects for quantile regression models for clustered data with focus on settings with many but small clusters. The paper has three contributions: (i) documenting that existing methods may lead to severely biased estimators for fixed effects parameters; (ii) proposing a new two-step estimation metho...

Quantile regression models with random effects are useful for studying associations between covariates and quantiles of the response distribution for clustered data. Parameter estimation is examined for a class of mixed-effects quantile regression models, with focus on settings with many but small clusters. The main contributions are the following:...

We study the problem of sparse signal detection on a spatial domain. We propose a novel approach to model continuous signals that are sparse and piecewise-smooth as the product of independent Gaussian processes (PING) with a smooth covariance kernel. The smoothness of the PING process is ensured by the smoothness of the covariance kernels of the Ga...

The study of microbiomes has become a topic of intense interest in last several decades as the development of new sequencing technologies has made DNA data accessible across disciplines. In this paper, we analyze a global dataset to investigate environmental factors that affect topsoil microbiome. As yet, much associated work has focused on linking...

In many modern applications, a dependent functional response is observed for each subject over repeated time, leading to longitudinal functional data. In this paper, we propose a novel statistical procedure to test whether the mean function varies over time. Our approach relies on reducing the dimension of the response using data-driven orthogonal...

Osteoarthritis (OA) is a chronic condition often associated with pain, affecting approximately fourteen percent of the population, and increasing in prevalence. A globally aging population have made treating OA-associated pain as well as maintaining mobility and activity a public health priority. OA affects all mammals, and the use of spontaneous a...

Observational longitudinal studies are a common means to study treatment efficacy and safety in chronic mental illness. In many such studies, treatment changes may be initiated by either the patient or by their clinician and can thus vary widely across patients in their timing, number, and type. Indeed, in the observational longitudinal pathway of...

Wearable devices including accelerometers are increasingly being used to collect high-frequency human activity data in situ. There is tremendous potential to use such data to inform medical decision making and public health policies. However, modeling such data is challenging as they are high-dimensional, heterogeneous, and subject to informative m...

To study trends in extreme precipitation across the United States over the years 1951–2017, we analyze 10 climate indexes that represent extreme precipitation, such as annual maximum of daily precipitation and annual maximum of consecutive five-day average precipitation. We consider the gridded data produced by the CLIMDEX project (http://www.climd...

We propose a novel modeling framework to study the effect of covariates of various types on the conditional distribution of the response. The methodology accommodates flexible model structure, allows for joint estimation of the quantiles at all levels, and involves a computationally efficient estimation algorithm. Extensive numerical investigation...

Scalar-on-function linear models are commonly used to regress functional predictors on a scalar response. However, functional models are more difficult to estimate and interpret than traditional linear models, and may be unnecessarily complex for a data application. Hypothesis testing can be used to guide model selection by determining if a functio...

Generalized linear mixed models (GLMMs) are used to model responses from exponential families with a combination of fixed and random effects. For variance components in GLMMs, we propose an approximate restricted likelihood ratio test that conducts testing on the working responses used in penalized quasi-likelihood estimation. This presents the hyp...

To study trends in extreme precipitation across US over the years 1951-2017, we consider 10 climate indexes that represent extreme precipitation, such as annual maximum of daily precipitation, annual maximum of consecutive 5-day average precipitation, which exhibit spatial correlation as well as mutual dependence. We consider the gridded data, prod...

In this paper, we consider a Dirichlet process mixture of spatial skew-$t$ processes that can flexibly model the extremes as well as the bulk, with separate parameters controlling spatial dependence in these two parts of the distribution. The proposed model has nonstationary mean and covariance structure and also nonzero spatial asymptotic dependen...

Wearable devices including accelerometers are increasingly being used to collect high-frequency human activity data in situ. There is tremendous potential to use such data to inform medical decision making and public health policies. However, modeling such data is challenging as they are high-dimensional, heterogeneous, and subject to informative m...

Functional data methods are often applied to longitudinal data as they provide a more flexible way to capture dependence across repeated observations. However, there is no formal testing procedure to determine if functional methods are actually necessary. We propose a goodness‐of‐fit test for comparing parametric covariance functions against genera...

The perceptual decoupling hypothesis suggests a general mechanism that while mind wandering, our attention is detached from our environment, resulting in diminished processing of external stimuli. This study focused on examining two possible specific mechanisms: the global suppression of all external stimuli, and a combination of reduced target fac...

The advent of high-throughput sequencing technologies has made data from DNA material readily available, leading to a surge of microbiome-related research establishing links between markers of microbiome health and specific outcomes. However, to harness the power of microbial communities we must understand not only how they affect us, but also how...

A joint design for sampling functional data is proposed to achieve optimal prediction of both functional data and a scalar outcome. The motivating application is fetal growth, where the objective is to determine the optimal times to collect ultrasound measurements in order to recover fetal growth trajectories and to predict child birth outcomes. Th...

Additional simulations and data application and software.

We study the problem of sparse signal detection on a spatial domain. We propose a novel approach to model continuous signals that are sparse and piecewise smooth as product of independent Gaussian processes (PING) with a smooth covariance kernel. The smoothness of the PING process is ensured by the smoothness of the covariance kernels of Gaussian c...

In this paper we illustrate the application of modern functional data analysis methods to study the spatiotemporal variability of particulate matter components across the United States. The approach models the pollutant annual profiles in a way that describes the dynamic behavior over time and space. This new technique allows us to predict yearly p...

We propose a flexible regression model to study the association between a functional response and multiple functional covariates that are observed on the same domain. Specifically, we relate the mean of the current response to current values of the covariates by a sum of smooth unknown bivariate functions, where each of the functions depends on the...

A scalar-response functional model describes the association between a scalar response and a set of functional covariates. An important problem in the functional data literature is to test the nullity or linearity of the effect of the functional covariate in the context of scalar-on-function regression. This article provides an overview of the exis...

A scalar-response functional model describes the association between a scalar response and a set of functional covariates. An important problem in the functional data literature is to test the nullity or linearity of the effect of the functional covariate in the context of scalar-on-function regression. This article provides an overview of the exis...

Neurologists and radiologists often use magnetic resonance imaging (MRI) in the management of subjects with multiple sclerosis (MS) because it is sensitive to inflammatory and demyelinative changes in the white matter of the brain and spinal cord. Two conventional modalities used for identifying lesions are T1-weighted (T1) and T2-weighted fluid-at...

Medical imaging data with thousands of spatially correlated data points are common in many fields. Methods that account for spatial correlation often require cumbersome matrix evaluations which are prohibitive for data of this size, and thus current work has either used low-rank approximations or analyzed data in blocks. We propose a method that ac...

We study additive function-on-function regression where the mean response at a particular time point depends on the time point itself, as well as the entire covariate trajectory. We develop a computationally efficient estimation methodology based on a novel combination of spline bases with an eigenbasis to represent the trivariate kernel function....

Evidence-based personalized medicine formalizes treatment selection as an individualized treatment regime that maps up-to-date patient information into the space of possible treatments. Available patient information may include static features such race, gender, family history, genetic and genomic information, as well as longitudinal information in...

Introduction and objectives Accelerometry is used as an objective measure of physical activity in humans and veterinary species. In cats, one important use of accelerometry is in the study of therapeutics designed to treat degenerative joint disease (DJD) associated pain, where it serves as the most widely applied objective outcome measure. These a...

Activity (A) and intensity (B) profiles for cats in the two DJD groups. Log transformed activity for all cats is shown in gray with time (in hours) along the horizontal axis. The group mean for activity and intensity are shown for the Low-dose study (red) and FMPI study (yellow). (TIF)

Results of FPCA for Intensity for the Normal cats. (A) The top three eigenfunctions of intensity profiles for activity during the weekend (black) and weekday (blue). The first component describes approximately 40% of the total variance for both weekends and weekdays and picks up the two peaks seen in the activity profiles. (TIF)

Functional regression analysis for intensity in the DJD group. Depicted are the smooth effects of Age (years), BCS, AGE*BCS (standard deviations away from the mean), standardized TDJD score and TPain score on the intensity of DJD cats, when model (2) is assumed. Results are shown for weekends in the top row and weekdays in the bottom row, with func...

Results of FPCA for Intensity for the DJD cats. The top three eigenfunctions of intensity profiles for activity during the weekend (dark blue) and weekday (light blue). The first component describes approximately 34% of the total variance for the weekends and approximately 37% for the weekdays and picks up the two peaks seen in the activity profile...

Functional regression analysis for intensity in the Normal group. Depicted are the smooth effects of Age (years, left panels), BCS (middle panels) and AGE*BCS (standard deviations away from the mean, right panels) on the intensity of Normal cats, when model (1) is assumed. Results are shown for weekends in the top row and weekdays in the bottom row...

This article develops flexible methodology to study the association between scalar outcomes and functional predictors observed over time, at many instances, in longitudinal studies. We propose a parsimonious modeling framework to study time-varying regression that leads to superior prediction properties and allows to reconstruct full trajectories o...

This article develops flexible methodology to study the association between scalar outcomes and functional predictors observed over time, at many instances, in longitudinal studies. We propose a parsimonious modeling framework to study time-varying regression that leads to superior prediction properties and allows to reconstruct full trajectories o...

We extend four tests common in classical regression ? Wald, score, likelihood ratio and F tests ? to functional linear regression, for testing the null hypothesis, that there is no association between a scalar response and a functional covariate. Using functional principal component analysis, we re-express the functional linear model as a standard...

We propose simple inferential approaches for the fixed effects in complex functional mixed effects models. We estimate the fixed effects under the independence of functional residuals assumption and then bootstrap independent units (e.g. subjects) to estimate the variability of and conduct inference in the form of hypothesis testing on the fixed ef...

We propose simple inferential approaches for the fixed effects in complex functional mixed effects models. We estimate the fixed effects under the independence of functional residuals assumption and then bootstrap independent units (e.g. subjects) to estimate the variability of and conduct inference in the form of hypothesis testing on the fixed ef...

Non-Gaussian functional data are considered and modeling through functional principal components analysis (FPCA) is discussed. The direct extension of popular FPCA techniques to the generalized case incorrectly uses a marginal mean estimate for a model that has an inherently conditional interpretation, and thus leads to biased estimates of populati...

We study additive function-on-function regression where the mean response at a particular time point depends on the time point itself as well as the entire covariate trajectory. We develop a computationally efficient estimation methodology based on a novel combination of spline bases with an eigenbasis to represent the trivariate kernel function. W...

We propose a novel modeling framework to study the effect of covariates of various types on the conditional distribution of the response. The methodology accommodates flexible model structure, allows for joint estimation of the quantiles at all levels, and involves a computationally efficient estimation algorithm. Extensive numerical investigation...

The focus of this work is on spatial variable selection for scalar-on-image regression. We propose a new class of Bayesian nonparametric models, soft-thresholded Gaussian processes and develop the efficient posterior computation algorithms. Theoretically, soft-thresholded Gaussian processes provide large prior support for the spatially varying coef...

Motivated by an imaging study, the paper develops a non-parametric testing procedure for testing the null hypothesis that two samples of curves observed at discrete grids and with noise have the same underlying distribution. The objective is to compare formally white matter tract profiles between healthy individuals and multiple-sclerosis patients,...

In this paper, we study statistical inference in functional quantile regression for scalar response and a functional covariate. Specifically, we consider a functional linear quantile regression model where the effect of the covariate on the quantile of the response is modeled through the inner product between the functional covariate and an unknown...

A functional regression model with a scalar response and multiple functional predictors is proposed that accommodates two-way interactions in addition to their main effects. The proposed estimation procedure models the main effects using penalized regression splines, and the interaction effect by a tensor product basis. Extensions to generalized li...

Abstract: We consider non-linear regression models for functional responses and functional predictors observed on possible different domains. We introduce a flexible model that relates the value of response variable at a particular time point to the entire profile of the covariate as well as the time point of the response. There are two innovations...

We observe a group of pigs over a period of about 100 days. Using high frequency radio frequency identification, it is recorded when each pig is feeding, leading to very dense binary functional data for each pig and day. One aim of the data analysis is to find pig-specific feeding profiles showing us the typical feeding pattern of each pig. For mod...

Mountain glacier retreat is an important problem related to temperature increase caused by global climate change. The retreat of mountain glaciers has been studied from the ground, but there exists a need for automated methods to catalog glacial change with a wider scope. A viable approach is to extract intensity profiles from Landsat images along...

A general framework for smooth regression of a functional response on one or multiple functional predictors is proposed. Using the mixed model representation of penalized regression expands the scope of function-on-function regression to many realistic scenarios. In particular, the approach can accommodate a densely or sparsely sampled functional r...

Multiple sclerosis (MS) is an immune-mediated neurological disease that causes morbidity and disability. In patients with MS, the accumulation of lesions in the white matter of the brain is associated with disease progression and worse clinical outcomes. Breakdown of the blood-brain barrier in newer lesions is indicative of more active disease-rela...

We introduce a class of covariate-adjusted skewed functional models (cSFM) designed for functional data exhibiting location-dependent marginal distributions. We propose a semi-parametric copula model for the pointwise marginal distributions, which are allowed to depend on covariates, and the functional dependence, which is assumed covariate invaria...

We propose an L2L2-norm based global testing procedure for the null hypothesis that multiple group mean functions are equal, for functional data with complex dependence structure. Specifically, we consider the setting of functional data with a multilevel structure of the form groups–clusters or subjects–units, where the unit-level profiles are spat...

We introduce the functional generalized additive model (FGAM), a novel regression model for association studies between a scalar response and a functional predictor. We model the link-transformed mean response as the integral with respect to t of F{X(t), t} where F( ·, ·) is an unknown regression function and X(t) is a functional covariate. Rather...

Modern research data, where a large number of functional predictors is collected on few subjects are becoming increasingly common. In this paper we propose a variable selection technique, when the predictors are functional and the response is scalar. Our approach is based on adopting a generalized functional linear model framework and using a penal...

We provide insights into new methodology for the analysis of multilevel binary data observed longitudinally, when the repeated longitudinal measurements are correlated. The proposed model is logistic functional regression conditioned on three latent processes describing the within- and between-variability, and describing the cross-dependence of the...

We propose nonparametric inference methods on the mean difference between two correlated functional processes. We compare methods that (1) incorporate different levels of smoothing of the mean and covariance; (2) preserve the sampling design; and (3) use parametric and nonparametric estimation of the mean functions. We apply our method to estimatin...

The detection of distributional shifts in functional data has become increasingly popular in recent years and has important applications in neuroscience. Over the past decade, many innovative methodologies have been developed, within the framework of functional principal component analysis, to detect differences in the mean functions, eigenfunction...

We propose an extensive framework for additive regression models for correlated functional responses, allowing for multiple partially nested or crossed functional random effects with flexible correlation structures for, e.g., spatial, temporal, or longitudinal functional data. Additionally, our framework includes linear and nonlinear effects of fun...

We propose a novel class of models for functional data exhibiting skewness or other shape characteristics that vary with spatial or temporal location. We use copulas so that the marginal distributions and the dependence structure can be modeled independently. Dependence is modeled with a Gaussian or t-copula, so that there is an underlying latent G...

We present new approaches to analyzing case-control studies using prospective likelihood methods. In the classical framework, we extend the equality of the profile likelihoods to the Barndorff-Nielsen modified profile likelihoods for prospective and retrospective models. This enables simple and accurate approximate conditional inference for stratif...

Second order approximate ancillaries have evolved as the primary ingredient for recent likelihood development in statistical inference. This uses quantile functions rather than the equivalent distribution functions, and the intrinsic ancillary contour is given explicitly as the plug-in estimate of the vector quantile function. The derivation uses a...

We propose a new methodological framework for the analysis of hierarchical functional data when the functions at the lowest level of the hierarchy are correlated. For small data sets, our methodology leads to a computational algorithm that is orders of magnitude more efficient than its closest competitor (seconds versus hours). For large data sets,...

This paper concerns the approximate ancillary needed for higher order asymptotic likelihood inference. The existence of an exact or approximate ancillary is the key to such inference. The exact ancillary is, however, only available for transformation model and an approximate ancillary is typically very difficult to find. Fraser (1988) revealed that...

We introduce Generalized Multilevel Functional Linear Models (GMFLMs), a novel statistical framework for regression models where exposure has a multilevel functional structure. We show that GMFLMs are, in fact, generalized multilevel mixed models (GLMMs). Thus, GMFLMs can be analyzed using the mixed effects inferential machinery and can be generali...

In this paper we revisit the classical problem of interval estimation for one-binomial parameter and for the log odds ratio of two binomial parameters. We examine the confidence intervals provided by two versions of the modified log likelihood root: the usual Barndorff-Nielsen's r* and a Bayesian version of the r* test statistic.For the one-binomia...

First-order probability matching priors are priors for which Bayesian and frequentist inference, in the form of posterior quantiles, or confidence intervals, agree to a second order of approximation. The authors show that the matching priors developed by Peers (1965) and Tibshirani (1989) are readily and uniquely implemented in a third-order approx...

Probability matching priors are priors for which Bayesian and frequentist inference, in the form of posterior quantiles, or confidence intervals, agree to some order of approximation. These priors are constructed by solving a first order partial differential equation, that may be difficult to solve. However, Peers (1965) and Tibshirani (1989) showe...