Permutation-Based Inference for Function-on-Scalar Regression With an Application in PET Brain Imaging.

The density of various proteins throughout the human brain can be studied through the use of positron emission tomography (PET) imaging. We report here on data from a study of serotonin transporter (5-HTT) binding. While PET imaging data analysis is most commonly performed on data that are aggregated into several discrete a priori regions of interest, in this study, primary interest is on measures of 5-HTT binding potential that are made at many locations along a continuous anatomically defined tract, one that was chosen to follow serotonergic axons. Our goal is to characterize the binding patterns along this tract and also to determine how such patterns differ between control subjects and depressed patients. Due to the nature of our data, we utilize function-on-scalar regression modeling to make optimal use of our data. Inference on both main effects (position along the tract; diagnostic group) and their interactions is made using permutation testing strategies that do not require distributional assumptions. Also, to investigate the question of homogeneity we implement a permutation testing strategy, which adapts a "block bootstrapping" approach from time series analysis to the functional data setting.

A functional generalized F-test for signal detection with applications to event-related potentials significance analysis.

Motivated by the analysis of complex dependent functional data such as event-related brain potentials (ERP), this paper considers a time-varying coefficient multivariate regression model with fixed-time covariates for testing global hypotheses about population mean curves. Based on a reduced-rank modeling of the time correlation of the stochastic process of pointwise test statistics, a functional generalized F-test is proposed and its asymptotic null distribution is derived. Our analytical results show that the proposed test is more powerful than functional analysis of variance testing methods and competing signal detection procedures for dependent data. Simulation studies confirm such power gain for data with patterns of dependence similar to those observed in ERPs. The new testing procedure is illustrated with an analysis of the ERP data from a study of neural correlates of impulse control.

Functional modeling of pedaling kinematics for the Stroke patients.

Understanding deficits in motor control through the analysis of pedaling biomechanics plays a key role in the treatment of stroke patients. A thorough study of the impact of different exercise patterns and workloads on the change between pre- and post-treatment movement patterns in the patients is therefore of utmost importance to the clinicians. The objective of this study was to analyze the difference between pre- and post-treatment pedaling torques when the patients are subject to different exercise groups with varying workloads. The effects of affected vs unaffected side along with the covariates age and BMI have also been accounted for in this work. Two different three-way ANOVA-based approaches have been implemented here. In the first approach, a random projection-based ANOVA technique has been performed treating the pedaling torques as functional response, whereas the second approach utilizes distance measures to summarize the difference between pre- and post-treatment torques and perform nonparametric tests on it. Bayesian bootstrap has been used here to perform tests on the median distance. A group of stroke patients have been studied in the Cleveland Clinic categorizing them into different exercise groups and workload patterns. The data obtained have been analyzed with the aforementioned techniques, and the results have been reported here. These techniques turn out to be promising and will help clinicians recommend personalized treatment to stroke patients for optimal results.

Experimental design for multi-drug combination studies using signaling networks.

Combinations of multiple drugs are an important approach to maximize the chance for therapeutic success by inhibiting multiple pathways/targets. Analytic methods for studying drug combinations have received increasing attention because major advances in biomedical research have made available large number of potential agents for testing. The preclinical experiment on multi-drug combinations plays a key role in (especially cancer) drug development because of the complex nature of the disease, the need to reduce development time and costs. Despite recent progresses in statistical methods for assessing drug interaction, there is an acute lack of methods for designing experiments on multi-drug combinations. The number of combinations grows exponentially with the number of drugs and dose-levels and it quickly precludes laboratory testing. Utilizing experimental dose-response data of single drugs and a few combinations along with pathway/network information to obtain an estimate of the functional structure of the dose-response relationship in silico, we propose an optimal design that allows exploration of the dose-effect surface with the smallest possible sample size in this article. The simulation studies show our proposed methods perform well.

Semiparametric Factor Analysis for Item-Level Response Time Data.

Item-level response time (RT) data can be conveniently collected from computer-based test/survey delivery platforms and have been demonstrated to bear a close relation to a miscellany of cognitive processes and test-taking behaviors. Individual differences in general processing speed can be inferred from item-level RT data using factor analysis. Conventional linear normal factor models make strong parametric assumptions, which sacrifices modeling flexibility for interpretability, and thus are not ideal for describing complex associations between observed RT and the latent speed. In this paper, we propose a semiparametric factor model with minimal parametric assumptions. Specifically, we adopt a functional analysis of variance representation for the log conditional densities of the manifest variables, in which the main effect and interaction functions are approximated by cubic splines. Penalized maximum likelihood estimation of the spline coefficients can be performed by an Expectation-Maximization algorithm, and the penalty weight can be empirically determined by cross-validation. In a simulation study, we compare the semiparametric model with incorrectly and correctly specified parametric factor models with regard to the recovery of data generating mechanism. A real data example is also presented to demonstrate the advantages of the proposed method.

Do Different Models Induce Changes in Mortality Indicators? That Is a Key Question for Extending the Lee-Carter Model.

The parametric model introduced by Lee and Carter in 1992 for modeling mortality rates in the USA was a seminal development in forecasting life expectancies and has been widely used since then. Different extensions of this model, using different hypotheses about the data, constraints on the parameters, and appropriate methods have led to improvements in the model's fit to historical data and the model's forecasting of the future. This paper's main objective is to evaluate if differences between models are reflected in different mortality indicators' forecasts. To this end, nine sets of indicator predictions were generated by crossing three models and three block-bootstrap samples with each of size fifty. Later the predicted mortality indicators were compared using functional ANOVA. Models and block bootstrap procedures are applied to Spanish mortality data. Results show model, block-bootstrap, and interaction effects for all mortality indicators. Although it was not our main objective, it is essential to point out that the sample effect should not be present since they must be realizations of the same population, and therefore the procedure should lead to samples that do not influence the results. Regarding significant model effect, it follows that, although the addition of terms improves the adjustment of probabilities and translates into an effect on mortality indicators, the model's predictions must be checked in terms of their probabilities and the mortality indicators of interest.

Regional and temporal patterns of influenza: Application of functional data analysis.

BACKGROUND: The accurate estimation of temporal patterns of influenza may help in utilizing hospital resources and guiding influenza surveillance. This paper proposes functional data analysis (FDA) to improve the prediction of temporal patterns of influenza. METHODS: We illustrate FDA methods using the weekly Influenza-like Illness (ILI) activity level data from the U.S. We propose to use the Fourier basis function for transforming discrete weekly data to the smoothed functional ILI activities. Functional analysis of variance (FANOVA) is used to examine the regional differences in temporal patterns and the impact of state's political orientation. RESULTS: The ILI activity has a very distinct peak at the beginning and end of the year. There are significant differences in average level of ILI activities among geographic regions. However, the temporal patterns in terms of the peak and flat time are quite consistent across regions. The geographic and temporal patterns of ILI activities also depend on the political make-up of states. The states affiliated with Republicans had higher ILI activities than those affiliated with Democrats across the whole year. The influence of political party affiliation on temporal pattern is quite different among geographic regions. CONCLUSIONS: Functional data analysis can help us to reveal the temporal variability in average ILI levels, rate of change in ILI levels, and the effect of geographical regions. Consideration should be given to wider application of FDA to generate more accurate estimates in public health and biomedical research.

A Statistical Method to Enhance the Analysis of the Differences Among High-Resolution Melting (HRM) Curves of PCR-Amplified DNA Fragments.

Consistent differences among melting curves of PCR-amplified DNA fragments are treated by normalizing the relative fluorescence units (RFU) and performing a clustering analysis, but statistically significant differences among curves are not usually determined. In the present study, an analysis based on functional data analysis (FDA) was implemented to evaluate the existence of statistically significant differences between normalized RFU curves obtained from PCR-HRM (high-resolution melting) analysis by using ANOVA for functional data. The effectiveness of the FDA method was analyzed with data from a set of samples of eight animal species of interest in food analysis, as well as mixtures of DNA from these species, analyzed by PCR-HRM to differentiate them. The statistical method described in this study has been demonstrated to be a robust and precise tool to discriminate among melting curves derived from HRM analysis. This method has advantages over the current comparison methods. PRACTICAL APPLICATION: As long as food fraud and mislabeling exist, new techniques for species identification are needed. High-resolution melting (HRM) has been shown to be a rapid, reliable and inexpensive species identification method. In the present study, functional data analysis (FDA) was applied to HRM curves of DNA from eight animal species used for food, as well as to mixtures of these species in different proportions. FDA has advantages over the usual methods, providing a deeper statistical analysis and facilitating the data interpretation as shown by the HRM analysis for a clearer comparison among individual species and mixtures of species.

Systematic Discovery of Archaeal Transcription Factor Functions in Regulatory Networks through Quantitative Phenotyping Analysis.

Gene regulatory networks (GRNs) are critical for dynamic transcriptional responses to environmental stress. However, the mechanisms by which GRN regulation adjusts physiology to enable stress survival remain unclear. Here we investigate the functions of transcription factors (TFs) within the global GRN of the stress-tolerant archaeal microorganism Halobacterium salinarum. We measured growth phenotypes of a panel of TF deletion mutants in high temporal resolution under heat shock, oxidative stress, and low-salinity conditions. To quantitate the noncanonical functional forms of the growth trajectories observed for these mutants, we developed a novel modeling framework based on Gaussian process regression and functional analysis of variance (FANOVA). We employ unique statistical tests to determine the significance of differential growth relative to the growth of the control strain. This analysis recapitulated known TF functions, revealed novel functions, and identified surprising secondary functions for characterized TFs. Strikingly, we observed that the majority of the TFs studied were required for growth under multiple stress conditions, pinpointing regulatory connections between the conditions tested. Correlations between quantitative phenotype trajectories of mutants are predictive of TF-TF connections within the GRN. These phenotypes are strongly concordant with predictions from statistical GRN models inferred from gene expression data alone. With genome-wide and targeted data sets, we provide detailed functional validation of novel TFs required for extreme oxidative stress and heat shock survival. Together, results presented in this study suggest that many TFs function under multiple conditions, thereby revealing high interconnectivity within the GRN and identifying the specific TFs required for communication between networks responding to disparate stressors. IMPORTANCE To ensure survival in the face of stress, microorganisms employ inducible damage repair pathways regulated by extensive and complex gene networks. Many archaea, microorganisms of the third domain of life, persist under extremes of temperature, salinity, and pH and under other conditions. In order to understand the cause-effect relationships between the dynamic function of the stress network and ultimate physiological consequences, this study characterized the physiological role of nearly one-third of all regulatory proteins known as transcription factors (TFs) in an archaeal organism. Using a unique quantitative phenotyping approach, we discovered functions for many novel TFs and revealed important secondary functions for known TFs. Surprisingly, many TFs are required for resisting multiple stressors, suggesting cross-regulation of stress responses. Through extensive validation experiments, we map the physiological roles of these novel TFs in stress response back to their position in the regulatory network wiring. This study advances understanding of the mechanisms underlying how microorganisms resist extreme stress. Given the generality of the methods employed, we expect that this study will enable future studies on how regulatory networks adjust cellular physiology in a diversity of organisms.

Growth curve registration for evaluating salinity tolerance in barley.

BACKGROUND: Smarthouses capable of non-destructive, high-throughput plant phenotyping collect large amounts of data that can be used to understand plant growth and productivity in extreme environments. The challenge is to apply the statistical tool that best analyzes the data to study plant traits, such as salinity tolerance, or plant-growth-related traits. RESULTS: We derive family-wise salinity sensitivity (FSS) growth curves and use registration techniques to summarize growth patterns of HEB-25 barley families and the commercial variety, Navigator. We account for the spatial variation in smarthouse microclimates and in temporal variation across phenotyping runs using a functional ANOVA model to derive corrected FSS curves. From FSS, we derive corrected values for family-wise salinity tolerance, which are strongly negatively correlated with Na but not significantly with K, indicating that Na content is an important factor affecting salinity tolerance in these families, at least for plants of this age and grown in these conditions. CONCLUSIONS: Our family-wise methodology is suitable for analyzing the growth curves of a large number of plants from multiple families. The corrected curves accurately account for the spatial and temporal variations among plants that are inherent to high-throughput experiments.

Assessing a learning process with functional ANOVA estimators of EEG power spectral densities.

We propose to assess the process of learning a task using electroencephalographic (EEG) measurements. In particular, we quantify changes in brain activity associated to the progression of the learning experience through the functional analysis-of-variances (FANOVA) estimators of the EEG power spectral density (PSD). Such functional estimators provide a sense of the effect of training in the EEG dynamics. For that purpose, we implemented an experiment to monitor the process of learning to type using the Colemak keyboard layout during a twelve-lessons training. Hence, our aim is to identify statistically significant changes in PSD of various EEG rhythms at different stages and difficulty levels of the learning process. Those changes are taken into account only when a probabilistic measure of the cognitive state ensures the high engagement of the volunteer to the training. Based on this, a series of statistical tests are performed in order to determine the personalized frequencies and sensors at which changes in PSD occur, then the FANOVA estimates are computed and analyzed. Our experimental results showed a significant decrease in the power of [Formula: see text] and [Formula: see text] rhythms for ten volunteers during the learning process, and such decrease happens regardless of the difficulty of the lesson. These results are in agreement with previous reports of changes in PSD being associated to feature binding and memory encoding.