Johns Hopkins University, Dept. of Biostatistics Working Papers

Structured Functional Principal Component Analysis

Haochang Shou et al. — Tue, 30 Apr 2013 09:35:21 PDT

Motivated by modern observational studies, we introduce a class of functional models that expands nested and crossed designs. These models account for the natural inheritance of correlation structure from sampling design in studies where the fundamental sampling unit is a function or image. Inference is based on functional quadratics and their relationship with the underlying covariance structure of the latent processes. A computationally fast and scalable estimation procedure is developed for ultra-high dimensional data. Methods are illustrated in three examples: high-frequency accelerometer data for daily activity, pitch linguistic data for phonetic analysis, and EEG data for studying electrical brain activity during sleep.

PENALIZED FUNCTION-ON-FUNCTION REGRESSION

Andrada E. Ivanescu et al. — Tue, 23 Apr 2013 09:50:30 PDT

We propose a general framework for smooth regression of a functional response on one or multiple functional predictors. 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 response as well as multiple functional predictors that are observed: 1) on the same or different domains than the functional response; 2) on a dense or sparse grid; and 3) with or without noise. It also allows for seamless integration of continuous or categorical covariates and provides approximate confidence intervals as a by-product of the mixed model inference. The proposed methods are accompanied by easy to use and robust software implemented in the pffr function of the R package refund. Methodological developments are general, but were inspired by and applied to a Diffusion Tensor Imaging (DTI) brain tractography dataset.

OPTIMAL TESTS OF TREATMENT EFFECTS FOR THE OVERALL POPULATION AND TWO SUBPOPULATIONS IN RANDOMIZED TRIALS, USING SPARSE LINEAR PROGRAMMING

Michael Rosenblum et al. — Tue, 23 Apr 2013 06:49:10 PDT

We propose new, optimal methods for analyzing randomized trials, when it is suspected that treatment effects may differ in two predefined subpopulations. Such sub-populations could be defined by a biomarker or risk factor measured at baseline. The goal is to simultaneously learn which subpopulations benefit from an experimental treatment, while providing strong control of the familywise Type I error rate. We formalize this as a multiple testing problem and show it is computationally infeasible to solve using existing techniques. Our solution involves a novel approach, in which we first transform the original multiple testing problem into a large, sparse linear program. We then solve this problem using advanced optimization techniques. This general method can solve a variety of multiple testing problems and decision theory problems related to optimal trial design, for which no solution was previously available. In particular, we construct new multiple testing procedures that satisfy minimax and Bayes optimality criteria. For a given optimality criterion, our new approach yields the optimal tradeoff between power to detect an effect in the overall population versus power to detect effects in subpopulations. We demonstrate our approach in examples motivated by two randomized trials of new treatments for HIV.

Homotopic Group ICA for Multi-Subject Brain Imaging Data

Juemin Yang et al. — Thu, 07 Mar 2013 11:53:29 PST

Independent Component Analysis (ICA) is a computational technique for revealing latent factors that underlie sets of measurements or signals. It has become a standard technique in functional neuroimaging. In functional neuroimaging, so called group ICA (gICA) seeks to identify and quantify networks of correlated regions across subjects. This paper reports on the development of a new group ICA approach, Homotopic Group ICA (H-gICA), for blind source separation of resting state functional magnetic resonance imaging (fMRI) data. Resting state brain functional homotopy is the similarity of spontaneous fluctuations between bilaterally symmetrically opposing regions (i.e. those symmetric with respect to the mid-sagittal plane) (Zuo et al., 2010). The approach we proposed improves network estimates by leveraging this known brain functional homotopy. H-gICA increases the potential for network discovery, effectively by averaging information across hemispheres. It is theoretically proven to be identical to standard group ICA when the true sources are both perfectly homotopic and noise-free, while simulation studies and data explorations demonstrate its benefits in the presence of noise. Moreover, compared to commonly applied group ICA algorithms, the structure of the H-gICA input data leads to significant improvement in computational efficiency. A simulation study comfirms its effectiveness in homotopic, non-homotopic and mixed settings, as well as on the landmark ADHD-200 dataset. From a relatively small subset of data, several brain networks were found including: the visual, the default mode and auditory networks, as well as others. These were shown to be more contiguous and clearly delineated than the corresponding ordinary group ICA. Finally, in addition to improving network estimation, H-gICA facilitates the investigation of functional homotopy via ICA-based networks.

PREDICTING HUMAN MOVEMENT TYPE BASED ON MULTIPLE ACCELEROMETERS USING MOVELETS

Bing He et al. — Thu, 07 Mar 2013 11:52:56 PST

We introduce statistical methods for prediction of types of human movement based on three tri-axial accelerometers worn simultaneously at the hip, left, and right wrist. We compare the individual performance of the three accelerometers using movelets and propose a new prediction algorithm that integrates the information from all three accelerometers. The development is motivated by a study of 20 older subjects who were instructed to perform 15 different types of activities during in-laboratory sessions. The differences in the prediction performance for different activity types among the three accelerometers reveal subtle yet important insights into how the intrinsic physical features of human movements could be effectively utilized in prediction. The proposed integrative movelet method takes into account those findings to augment the prediction accuracy and improve our understanding of human movement measurements.

Adaptive Group Sequential Designs that Balance the Benefits and Risks of Expanding Inclusion Criteria

Michael Rosenblum et al. — Mon, 04 Feb 2013 10:03:35 PST

In designing a Phase III randomized trial, care must be taken in selecting the target population. Advantages of enrolling from a larger population include wider generalizability of results and faster recruitment. However, since earlier trials (e.g. Phase II trials) may only have enrolled participants from a relatively narrow population, little data may be available on the larger population. This makes a Phase III trial that enrolls from the larger population more risky. We propose new adaptive, group sequential designs aimed at gaining the advantages of wider generalizability and faster recruitment, while mitigating the risks of including a population for which there is little prior data. These designs use preplanned rules for changing the enrollment criteria if the participants from predefined subpopulations are not benefiting from the new treatment. We demonstrate these adaptive designs in the context of a Phase III trial of a new treatment for stroke, and compare them to standard designs in terms of expected sample size and trial duration. In this context, we investigate the tradeoff between sample size and trial duration that arises in designs with preplanned rules for changing the enrollment criteria.

FAST COVARIANCE ESTIMATION FOR HIGH-DIMENSIONAL FUNCTIONAL DATA

Luo Xiao et al. — Wed, 09 Jan 2013 09:11:16 PST

We propose a fast covariance smoothing method and associated software that scale up linearly to very large matrices. The main idea is to exploit a very fast new bivariate penalized spline smoothing approach and focus on the practicality and scalability of the method. Currently available methods and software cannot smooth covariance matrices of dimension J > 500, whereas our approach provides fast smoothing for matrices of dimension J > 10; 000. An R function, simulations, and data analysis provide ready to use, reproducible, and scalable tools for practical data analysis of noisy high-dimensional functional data.

LONGITUDINAL FUNCTIONAL MODELS WITH STRUCTURED PENALTIES

Madan G. Kundu et al. — Fri, 02 Nov 2012 11:29:56 PDT

Collection of functional data is becoming increasingly common including longitudinal observations in many studies. For example, we use magnetic resonance (MR) spectra collected over a period of time from late stage HIV patients. MR spectroscopy (MRS) produces a spectrum which is a mixture of metabolite spectra, instrument noise and baseline profile. Analysis of such data typically proceeds in two separate steps: feature extraction and regression modeling. In contrast, a recently-proposed approach, called partially empirical eigenvectors for regression (PEER) (Randolph, Harezlak and Feng, 2012), for functional linear models incorporates a priori knowledge via a scientifically-informed penalty operator in the regression function estimation process. We extend the scope of PEER to the longitudinal setting with continuous outcomes and longitudinal functional covariates. The method presented in this paper: 1) takes into account external information; and 2) allows for a time-varying regression function. In the proposed approach, we express the time-varying regression function as linear combination of several time-invariant component functions; the time dependence enters into the regression function through their coefficients. The estimation procedure is easy to implement due to its mixed model equivalence. We derive the precision and accuracy of the estimates and discuss their connection with the generalized singular value decomposition. Real MRS data and simulations are used to illustrate the concepts.

Testing For Functional Effects

Bruce J. Swihart et al. — Tue, 07 Aug 2012 13:38:17 PDT

The goal of our article is to provide a transparent, robust, and computationally feasible statistical approach for testing in the context of functional linear models. In particular, we are interested in testing for the necessity of functional effects against standard linear models. Our approach is to express the coefficient function so that the null model includes the average of functional predictors as a scalar covariate. Two specific methods are utilized: the first is a modified version of the now-standard functional principal components regression; and the second is a flexible spline approach that induces smoothness in a linear mixed model framework. In the first method testing is accomplished using a standard likelihood ratio test, while in the second testing is performed using (restricted) likelihood ratio tests for zero variance components. We extend the methodology to be of use when multiple functional predictors are observed and when observations are made longitudinally. Our methods are motivated by and applied to a large longitudinal study involving diffusion tensor imaging of intracranial white matter tracts in a susceptible cohort. In the context of this study, we conduct hypothesis tests that are motivated by anatomical knowledge and which support recent findings regarding the relationship between cognitive impairment and white matter demyelination. Accompanying R code from an upcoming release of the R-package refund is provided.

Component extraction of Complex Biomedical signal and performance analysis based on different algorithm

hemant pasusangai kasturiwale — Sat, 14 Jul 2012 12:07:46 PDT

Biomedical signals can arise from one or many sources including heart ,brains and endocrine systems. Multiple sources poses challenge to researchers which may have contaminated with artifacts and noise. The Biomedical time series signal are like electroencephalogram(EEG),electrocardiogram(ECG),etc The morphology of the cardiac signal is very important in most of diagnostics based on the ECG. The diagnosis of patient is based on visual observation of recorded ECG,EEG,etc, may not be accurate. To achieve better understanding , PCA (Principal Component Analysis) and ICA algorithms helps in analyzing ECG signals . The immense scope in the field of biomedical-signal processing Independent Component Analysis( ICA ) is gaining momentum due to huge data base requirement for quality testing This paper describes some algorithms of ICA in brief, such as Fast-ICA, Kernel-ICA, MS –ICA, JADE, EGLD-ICA ,Robust ICA etc. The quality & performance of some of the ICA algorithms are tested and analysis of each can be done with respect to Noise/Artifacts, SIR(Signal Interference Ratio),PI(performance Index). The most common bioelectric signals are EEG and ECG. The experimental results presented in the paper show that the proposed here to indentify the various components with higher accuracy in the particular algorithm based on classifying biomedical data.

ANALYTIC PROGRAMMING WITH fMRI DATA: A QUICK-START GUIDE FOR STATISTICIANS USING R

Ani Eloyan et al. — Sat, 14 Jul 2012 12:07:18 PDT

Functional magnetic resonance imaging (fMRI) is a thriving field that plays an important role in medical imaging analysis, biological and neuroscience research and practice. This manuscript gives a didactic introduction to the statistical analysis of fMRI data using the R project along with the relevant R code. The goal is to give tatisticians who would like to pursue research in this area a quick start for programming with fMRI data along with the available data visualization tools.

MODELING SLEEP FRAGMENTATION IN POPULATIONS OF SLEEP HYPNOGRAMS

Bruce J. Swihart et al. — Tue, 05 Jun 2012 09:21:01 PDT

We introduce methods for the analysis of large populations of sleep architectures (hypnograms) that respect the 5-state 20-transition-type structure defined by the American Academy of Sleep Medicine. By applying these methods to the hypnograms of 5598 subjects from the Sleep Heart Health Study we: 1) provide the firrst analysis of sleep hypnogram data of such size and complexity in a community cohort with a 4-level comorbidity; 2) compare 5-state 20-transition-type sleep to 3-state 6-transition-type sleep for a check of feasibility and information-loss; 3) extend current approaches to multivariate survival data analysis to populations of time-to-transition processes; and 4) provide scalable solutions for data analyses required by the case study. This allows us to provide detailed new insights into the association between sleep apnea and sleep architecture. Supporting R as well as SAS code and data are included in the online supplementary materials.

LIKELIHOOD RATIO TESTS FOR THE MEAN STRUCTURE OF CORRELATED FUNCTIONAL PROCESSES

Ana-Maria Staicu et al. — Wed, 02 May 2012 09:29:29 PDT

The paper introduces a general framework for testing hypotheses about the structure of the mean function of complex functional processes. Important particular cases of the proposed framework are: 1) testing the null hypotheses that the mean of a functional process is parametric against a nonparametric alternative; and 2) testing the null hypothesis that the means of two possibly correlated functional processes are equal or differ by only a simple parametric function. A global pseudo likelihood ratio test is proposed and its asymptotic distribution is derived. The size and power properties of the test are confirmed in realistic simulation scenarios. Finite sample power results indicate that the proposed test is much more powerful than competing alternatives. Methods are applied to testing the equality between the means of normalized δ-power of sleep electroencephalograms of subjects with sleep-disordered breathing and matched controls.

AUTOMATED DIAGNOSES OF ATTENTION DEFICIT HYPERACTIVE DISORDER USING MAGNETIC RESONANCE IMAGING

Ani Eloyan et al. — Fri, 27 Apr 2012 15:02:56 PDT

Successful automated diagnoses of attention de.cit hyperactive disorder (ADHD) using imaging and functional biomarkers would have fundamental consequences on the public health impact of the disease. In this work, we show results on the predictability of ADHD using imaging biomarkers and discuss the scienti.c and diagnostic impacts of the research. We created a prediction model using the landmark ADHD 200 data set focusing on resting state functional connectivity (rs-fc) and structural brain imaging. We predicted ADHD status and subtype, obtained by behavioral examination, using imaging data, intelligence quotients and other covariates. The novel contributions of this manuscript include a thorough exploration of prediction and image feature extraction methodology on this form of data, including the use of singular value decompositions, CUR decompositions, random forest, gradient boosting, bagging, voxel-based morphometry and support vector machines as well as important insights into the value, and potentially lack thereof, of imaging biomarkers of disease. The key results include the CUR-based decomposition of the rs-fc-fMRI along with gradient boosting and the prediction algorithm based on a motor network parcellation and random forest algorithm. We conjecture that the CUR decomposition is largely diagnosing common population directions of head motion. Of note, a byproduct of this research is a potential automated method for detecting subtle in-scanner motion. The .nal prediction algorithm, a weighted combination of several algorithms, had an external test set speci.city of 94% with sensitivity of 21%. The most promising imaging biomarker was a correlation graph from a motor network parcellation. In summary, we have undertaken a large-scale statistical exploratory prediction exercise on the unique ADHD 200 data set. The exercise produced several potential leads for future scienti.c exploration of the neurological basis of ADHD.

CONFIDENCE INTERVALS FOR THE SELECTED POPULATION IN RANDOMIZED TRIALS THAT ADAPT THE POPULATION ENROLLED

Michael Rosenblum — Wed, 04 Apr 2012 13:46:45 PDT

It is a challenge to design randomized trials when it is suspected that a treatment may benefit only certain subsets of the target population. In such situations, trial designs have been proposed that modify the population enrolled based on an interim analysis, in a preplanned manner. For example, if there is early evidence that the treatment only benefits a certain subset of the population, enrollment may then be restricted to this subset. At the end of such a trial, it is desirable to draw inferences about the selected population. We focus on constructing confidence intervals for the average treatment effect in the selected population. Confidence interval methods that fail to account for the adaptive nature of the design may fail to have the desired coverage probability. We provide a new procedure for constructing confidence intervals having at least 95% coverage probability, uniformly over a large class of possible data generating distributions. We prove an optimality property for our confidence interval procedure in terms of minimizing the average confidence interval widths.

Flexible Distributed Lag Models using Random Functions with Application to Estimating Mortality Displacement from Heat-Related Deaths

Roger D. Peng — Wed, 14 Dec 2011 08:00:09 PST

TESTS THAT REJECT AT LEAST ONE SUBPOPULATION NULL HYPOTHESIS AFTER REJECTING FOR OVERALL POPULATION

Michael Rosenblum — Wed, 30 Nov 2011 08:45:42 PST

It is often of interest to determine treatment effects in the overall study population, as well as in certain subpopulations. These subpopulations could be defined by a risk factor, such as a biomarker, measured at baseline. We consider situations where the overall population is
partitioned into two subpopulations of interest.
If the null hypothesis of no treatment effect in the overall population is rejected, a natural question is what can be said about these subpopulations.
Whenever there is a treatment effect in the overall population, it follows logically that there must be a treatment effect in at least one of these
subpopulations. Therefore, it would be desirable to reject at least one subpopulation null hypothesis whenever the null hypothesis for the overall
population is rejected. Furthermore, it would be desirable to do so without sacrificing any power for detecting a treatment effect in the overall population. We give the first multiple testing procedure that has both these properties and that strongly controls the familywise Type I error rate at
level 0.05. Our procedure is simple to implement and can be used with binary, continuous, or time-to-event outcomes. In addition, this procedure is the first to satisfy a certain maximin optimality property in this setting. The proofs of these properties rely on a general method for transforming analytically difficult expressions arising in some multiple testing problems
into more tractable nonlinear optimization problems, which are then solved using intensive computation.

Assessing Association for Bivariate Survival Data with Interval Sampling: A Copula Model Approach with Application to AIDS Study

Hong Zhu et al. — Wed, 16 Nov 2011 09:33:19 PST

In disease surveillance systems or registries, bivariate survival data are typically collected under interval sampling. It refers to a situation when entry into a registry is at the time of the first failure event (e.g., HIV infection) within a calendar time interval, the time of the initiating event (e.g., birth) is retrospectively identified for all the cases in the registry, and subsequently the second failure event (e.g., death) is observed during the follow-up. Sampling bias is induced due to the selection process that the data are collected conditioning on the first failure event occurs within a time interval. Consequently, the first failure time is doubly truncated, and the second failure time is informatively right censored. A copula model under semi-stationary condition is considered to assess the association between the bivariate survival times with interval sampling. Estimation and inference are carried out by a two-stage procedure. We first obtain bias-corrected estimators of marginal survival functions, then a pseudo conditional likelihood method is developed to study the association parameter. Asymptotic properties of the proposed estimators are established, and finite sample performance is evaluated by simulation studies. The method is applied to a motivating community-based AIDS study in Rakai to investigate the effect of age at infection on survival time of HIV seroconverters.

LONGITUDINAL HIGH-DIMENSIONAL DATA ANALYSIS

Vadim Zipunnikov et al. — Wed, 16 Nov 2011 09:21:39 PST

We develop a flexible framework for modeling high-dimensional functional and imaging data observed longitudinally. The approach decomposes the observed variability of high-dimensional observations measured at multiple visits into three additive components: a subject-specific functional random intercept that quantifies the cross-sectional variability, a subject-specific functional slope that quantifies the dynamic irreversible deformation over multiple visits, and a subject-visit specific functional deviation that quantifies exchangeable or reversible visit-to-visit changes. The proposed method is very fast, scalable to studies including ultra-high dimensional data, and can easily be adapted to and executed on modest computing infrastructures. The method is applied to the longitudinal analysis of diffusion tensor imaging (DTI) data of the corpus callosum of multiple sclerosis (MS) subjects. The study includes 176 subjects observed at 466 visits. For each subject and visit the study contains a registered DTI scan of the corpus callosum at roughly 30,000 voxels.

CORRECTED CONFIDENCE BANDS FOR FUNCTIONAL DATA USING PRINCIPAL COMPONENTS

Jeff Goldsmith et al. — Wed, 09 Nov 2011 11:20:37 PST

Functional principal components (FPC) analysis is widely used to decompose and express functional observations. Curve estimates implicitly condition on basis functions and other quantities derived from FPC decompositions; however these objects are unknown in practice. In this paper, we propose a method for obtaining correct curve estimates by accounting for uncertainty in FPC decompositions. Additionally, pointwise and simultaneous confidence intervals that account for both model- based and decomposition-based variability are constructed. Standard mixed-model representations of functional expansions are used to construct curve estimates and variances conditional on a specific decomposition. A bootstrap procedure is implemented to understand the uncertainty in principal component decomposition quantities. Iterated expectation and variance formulas combine both sources of uncertainty by combining model-based conditional estimates across the distribution of decompositions. Our method compares favorably to competing approaches in simulation studies that include both densely- and sparsely-observed functions. We apply our method to sparse observations of CD4 cell counts and to dense white-matter tract profiles. Code for the analyses and simulations is publicly available, and our method is implemented as the IVfpca() function in the R package refund on CRAN.