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Topological data analysis (TDA) is increasingly recognized as a promising tool in the field of neuroscience, unveiling the underlying topological patterns within brain signals. However, most TDA related methods treat brain signals as if they were static, i.e., they ignore potential non-stationarities and irregularities in the statistical properties of the signals. In this study, we develop a novel fractal dimension-based testing approach that takes into account the dynamic topological properties of brain signals. By representing EEG brain signals as a sequence of Vietoris-Rips filtrations, our approach accommodates the inherent non-stationarities and irregularities of the signals. The application of our novel fractal dimension-based testing approach in analyzing dynamic topological patterns in EEG signals during an epileptic seizure episode exposes noteworthy alterations in total persistence across 0, 1, and 2-dimensional homology. These findings imply a more intricate influence of seizures on brain signals, extending beyond mere amplitude changes.
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OBJECTIVE: High-frequency oscillations (HFOs) are a promising prognostic biomarker of surgical outcome in patients with epilepsy. Their rates of occurrence and morphology have been studied extensively using recordings from electrodes of various geometries. While electrode size is a potential confounding factor in HFO studies, it has largely been disregarded due to a lack of consistent evidence. Therefore, we designed an experiment to directly test the impact of electrode size on HFO measurement. METHODS: We first simulated HFO measurement using a lumped model of the electrode-tissue interaction. Then eight human subjects were each implanted with a high-density 8x8 grid of subdural electrodes. After implantation, the electrode sizes were altered using a technique recently developed by our group, enabling intracranial EEG recordings for three different electrode surface areas from a static brain location. HFOs were automatically detected in the data and their characteristics were calculated. RESULTS: The human subject measurements were consistent with the model. Specifically, HFO rate measured per area of tissue decreased significantly as electrode surface area increased. The smallest electrodes recorded more fast ripples than ripples. Amplitude of detected HFOs also decreased as electrode surface area increased, while duration and peak frequency were unaffected. CONCLUSION: These results suggest that HFO rates measured using electrodes of different surface areas cannot be compared directly. SIGNIFICANCE: This has significant implications for HFOs as a tool for surgical planning, particularly for individual patients implanted with electrodes of multiple sizes and comparisons of HFO rate made across patients and studies.
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In this study, we explore the potential of using functional near-infrared spectroscopy (fNIRS) signals in conjunction with modern machine-learning techniques to classify specific anatomical movements to increase the number of control commands for a possible fNIRS-based brain-computer interface (BCI) applications. The study focuses on novel individual finger-tapping, a well-known task in fNIRS and fMRI studies, but limited to left/right or few fingers. Twenty-four right-handed participants performed the individual finger-tapping task. Data were recorded by using sixteen sources and detectors placed over the motor cortex according to the 10-10 international system. The event's average oxygenated Δ HbO and deoxygenated Δ HbR hemoglobin data were utilized as features to assess the performance of diverse machine learning (ML) models in a challenging multi-class classification setting. These methods include LDA, QDA, MNLR, XGBoost, and RF. A new DL-based model named "Hemo-Net" has been proposed which consists of multiple parallel convolution layers with different filters to extract the features. This paper aims to explore the efficacy of using fNRIS along with ML/DL methods in a multi-class classification task. Complex models like RF, XGBoost, and Hemo-Net produce relatively higher test set accuracy when compared to LDA, MNLR, and QDA. Hemo-Net has depicted a superior performance achieving the highest test set accuracy of 76%, however, in this work, we do not aim at improving the accuracies of models rather we are interested in exploring if fNIRS has the neural signatures to help modern ML/DL methods in multi-class classification which can lead to applications like brain-computer interfaces. Multi-class classification of fine anatomical movements, such as individual finger movements, is difficult to classify with fNIRS data. Traditional ML models like MNLR and LDA show inferior performance compared to the ensemble-based methods of RF and XGBoost. DL-based method Hemo-Net outperforms all methods evaluated in this study and demonstrates a promising future for fNIRS-based BCI applications.
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Brain functional connectivity (FC) networks inferred from functional magnetic resonance imaging (fMRI) have shown altered or aberrant brain functional connectome in various neuropsychiatric disorders. Recent application of deep neural networks to connectome-based classification mostly relies on traditional convolutional neural networks (CNNs) using input FCs on a regular Euclidean grid to learn spatial maps of brain networks neglecting the topological information of the brain networks, leading to potentially sub-optimal performance in brain disorder identification. We propose a novel graph deep learning framework that leverages non-Euclidean information inherent in the graph structure for classifying brain networks in major depressive disorder (MDD). We introduce a novel graph autoencoder (GAE) architecture, built upon graph convolutional networks (GCNs), to embed the topological structure and node content of large fMRI networks into low-dimensional representations. For constructing the brain networks, we employ the Ledoit-Wolf (LDW) shrinkage method to efficiently estimate high-dimensional FC metrics from fMRI data. We explore both supervised and unsupervised techniques for graph embedding learning. The resulting embeddings serve as feature inputs for a deep fully-connected neural network (FCNN) to distinguish MDD from healthy controls (HCs). Evaluating our model on resting-state fMRI MDD dataset, we observe that the GAE-FCNN outperforms several state-of-the-art methods for brain connectome classification, achieving the highest accuracy when using LDW-FC edges as node features. The graph embeddings of fMRI FC networks also reveal significant group differences between MDD and HCs. Our framework demonstrates the feasibility of learning graph embeddings from brain networks, providing valuable discriminative information for diagnosing brain disorders.
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Encefalopatías , Conectoma , Trastorno Depresivo Mayor , Humanos , Trastorno Depresivo Mayor/diagnóstico por imagen , Encéfalo/diagnóstico por imagen , Conectoma/métodos , Imagen por Resonancia Magnética/métodos , Redes Neurales de la ComputaciónRESUMEN
OBJECTIVE: The aim of this study was to identify the potential electrophysiological biomarkers of human responses by comparing the electroencephalogram brain wave changes towards lavender versus normal saline in a healthy human population. METHOD: This study included a total of 44 participants without subjective olfactory disturbances. Lavender and normal saline were used as the olfactory stimulant and control. Electroencephalogram was recorded and power spectra were analysed by the spectral analysis for each alpha, beta, delta, theta and gamma bandwidth frequency upon exposure to lavender and normal saline independently. RESULTS: The oscillatory brain activities in response to the olfactory stimulant indicated that the lavender smell decreased the beta activity in the left frontal (F7 electrode) and central region (C3 electrode) with a reduction in the gamma activity in the right parietal region (P4 electrode) (p < 0.05). CONCLUSION: Olfactory stimulants result in changes of electrical brain activities in different brain regions, as evidenced by the topographical brain map and spectra analysis of each brain wave.
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Ondas Encefálicas , Solución Salina , Humanos , Odorantes , Electroencefalografía , Olfato/fisiología , EncéfaloRESUMEN
Topological data analysis (TDA) provide tools that are becoming increasingly popular for analyzing multivariate time series data. One key aspect in analyzing multivariate time series is dependence between components. One application is on brain signal analysis. In particular, various dependence patterns in brain networks may be linked to specific tasks and cognitive processes. These dependence patterns may be altered by various neurological and cognitive impairments such as Alzheimer's and Parkinson's diseases, as well as attention deficit hyperactivity disorder (ADHD). Because there is no ground-truth with known dependence patterns in real brain signals, testing new TDA methods on multivariate time series is still a challenge. Our goal here is to develop novel statistical inference procedures via simulations. Simulations are useful for generating some null distributions of a test statistic (for hypothesis testing), forming confidence regions, and for evaluating the performance of proposed TDA methods. To the best of our knowledge, there are no methods that simulate multivariate time series data with potentially complex user-specified connectivity patterns. In this paper we present a novel approach to simulate multivariate time series with specific number of cycles/holes in its dependence network. Furthermore, we also provide a procedure for generating higher dimensional topological features.
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Over the last two decades, topological data analysis (TDA) has emerged as a very powerful data analytic approach that can deal with various data modalities of varying complexities. One of the most commonly used tools in TDA is persistent homology (PH), which can extract topological properties from data at various scales. The aim of this article is to introduce TDA concepts to a statistical audience and provide an approach to analyzing multivariate time series data. The application's focus will be on multivariate brain signals and brain connectivity networks. Finally, this paper concludes with an overview of some open problems and potential application of TDA to modeling directionality in a brain network, as well as the casting of TDA in the context of mixed effect models to capture variations in the topological properties of data collected from multiple subjects.
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BACKGROUND: Differences in mortality exist between sexes because of biological, genetic, and social factors. Sex differentials are well documented in children younger than 5 years but have not been systematically examined for ages 5-24 years. We aimed to estimate the sex ratio of mortality from birth to age 24 years and reconstruct trends in sex-specific mortality between 1990 and 2021 for 200 countries, major regions, and the world. METHODS: We compiled comprehensive databases on the mortality sex ratio (ratio of male to female mortality rates) for individuals aged 0-4 years, 5-14 years, and 15-24 years. The databases contain mortality rates from death registration systems, full birth and sibling histories from surveys, and reports on household deaths in censuses. We modelled the sex ratio of age-specific mortality as a function of the mortality in both sexes using Bayesian hierarchical time-series models. We report the levels and trends of sex ratios and estimate the expected female mortality and excess female mortality rates (the difference between the estimated female mortality and the expected female mortality) to identify countries with outlying sex ratios. FINDINGS: Globally, the mortality sex ratio was 1·13 (ie, boys were more likely to die than girls of the same age) for ages 0-4 years (90% uncertainty interval 1·11 to 1·15) in 2021. This ratio increased with age to 1·16 (1·12 to 1·20) for 5-14 years, reaching 1·65 for 15-24 years (1·52 to 1·75). In all age groups, the global sex ratio of mortality increased between 1990 and 2021, driven by faster declines in female mortality. In 2021, the probability of a newborn male reaching age 25 years was 94·1% (93·7 to 94·4), compared with 95·1% for a newborn female (94·7 to 95·3). We found a disadvantage of females versus males (compared with countries with similar total mortality) in 2021 in five countries for ages 0-4 years (Algeria, Bangladesh, Egypt, India, and Iran), one country (Suriname) for ages 5-14 years, and 13 countries for ages 15-24 years (including Bangladesh and India). We found the reverse pattern (disadvantage of males vs females compared with countries of similar total mortality) in one country in ages 0-4 years (Vietnam) and eight countries in ages 15-24 years (including Brazil and Mexico). Globally, the number of excess female deaths from birth to age 24 years was 86â563 (-6059 to 164â000) in 2021, down from 544â636 (453â982 to 633â265) in 1990. INTERPRETATION: The global sex ratio of mortality for all age groups in the first 25 years of life increased between 1990 and 2021. Targeted interventions should focus on countries with outlying sex ratios of mortality to reduce disparities due to discrimination in health care, nutrition, and violence. FUNDING: The Bill & Melinda Gates Foundation, US Agency for International Development, and King Abdullah University of Science and Technology.
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Caracteres Sexuales , Conducta Sexual , Recién Nacido , Humanos , Femenino , Adolescente , Niño , Masculino , Teorema de Bayes , Bangladesh , BrasilRESUMEN
Objective.Intracranial electroencephalogram (iEEG) plays a critical role in the treatment of neurological diseases, such as epilepsy and Parkinson's disease, as well as the development of neural prostheses and brain computer interfaces. While electrode geometries vary widely across these applications, the impact of electrode size on iEEG features and morphology is not well understood. Some insight has been gained from computer simulations, as well as experiments in which signals are recorded using electrodes of different sizes concurrently in different brain regions. Here, we introduce a novel method to record from electrodes of different sizes in the exact same location by changing the size of iEEG electrodes after implantation in the brain.Approach.We first present a theoretical model and anin vitrovalidation of the method. We then report the results of anin vivoimplementation in three human subjects with refractory epilepsy. We recorded iEEG data from three different electrode sizes and compared the amplitudes, power spectra, inter-channel correlations, and signal-to-noise ratio (SNR) of interictal epileptiform discharges, i.e. epileptic spikes.Main Results.We found that iEEG amplitude and power decreased as electrode size increased, while inter-channel correlation did not change significantly with electrode size. The SNR of epileptic spikes was generally highest in the smallest electrodes, but 39% of spikes had maximal SNR in larger electrodes. This likely depends on the precise location and spatial spread of each spike.Significance.Overall, this new method enables multi-scale measurements of electrical activity in the human brain that can facilitate our understanding of neurophysiology, treatment of neurological disease, and development of novel technologies.
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Electrocorticografía , Epilepsia , Humanos , Electrocorticografía/métodos , Electroencefalografía/métodos , Encéfalo , ElectrodosRESUMEN
We propose a model-based approach that combines Bayesian variable selection tools, a novel spatial kernel convolution structure, and autoregressive processes for detecting a subject's brain activation at the voxel level in complex-valued functional magnetic resonance imaging (CV-fMRI) data. A computationally efficient Markov chain Monte Carlo algorithm for posterior inference is developed by taking advantage of the dimension reduction of the kernel-based structure. The proposed spatiotemporal model leads to more accurate posterior probability activation maps and less false positives than alternative spatial approaches based on Gaussian process models, and other complex-valued models that do not incorporate spatial and/or temporal structure. This is illustrated in the analysis of simulated data and human task-related CV-fMRI data. In addition, we show that complex-valued approaches dominate magnitude-only approaches and that the kernel structure in our proposed model considerably improves sensitivity rates when detecting activation at the voxel level.
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Mapeo Encefálico , Imagen por Resonancia Magnética , Humanos , Mapeo Encefálico/métodos , Imagen por Resonancia Magnética/métodos , Teorema de Bayes , Encéfalo/diagnóstico por imagen , Encéfalo/fisiología , AlgoritmosRESUMEN
For decades, psychostimulants have been the gold standard pharmaceutical treatment for attention-deficit/hyperactivity disorder (ADHD). In the United States, an astounding 9% of all boys and 4% of girls will be prescribed stimulant drugs at some point during their childhood. Recent meta-analyses have revealed that individuals with ADHD have reduced brain volume loss later in life (>60 y.o.) compared to the normal aging brain, which suggests that either ADHD or its treatment may be neuroprotective. Crucially, these neuroprotective effects were significant in brain regions (e.g., hippocampus, amygdala) where severe volume loss is linked to cognitive impairment and Alzheimer's disease. Historically, the ADHD diagnosis and its pharmacotherapy came about nearly simultaneously, making it difficult to evaluate their effects in isolation. Certain evidence suggests that psychostimulants may normalize structural brain changes typically observed in the ADHD brain. If ADHD itself is neuroprotective, perhaps exercising the brain, then psychostimulants may not be recommended across the lifespan. Alternatively, if stimulant drugs are neuroprotective, then this class of medications may warrant further investigation for their therapeutic effects. Here, we take a bottom-up holistic approach to review the psychopharmacology of ADHD in the context of recent models of attention. We suggest that future studies are greatly needed to better appreciate the interactions amongst an ADHD diagnosis, stimulant treatment across the lifespan, and structure-function alterations in the aging brain.
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The standard approach to analyzing brain electrical activity is to examine the spectral density function (SDF) and identify frequency bands, defined a priori, that have the most substantial relative contributions to the overall variance of the signal. However, a limitation of this approach is that the precise frequency and bandwidth of oscillations are not uniform across different cognitive demands. Thus, these bands should not be arbitrarily set in any analysis. To overcome this limitation, the Bayesian mixture auto-regressive decomposition (BMARD) method is proposed, as a data-driven approach that identifies (i) the number of prominent spectral peaks, (ii) the frequency peak locations, and (iii) their corresponding bandwidths (or spread of power around the peaks). Using the BMARD method, the standardized SDF is represented as a Dirichlet process mixture based on a kernel derived from second-order auto-regressive processes which completely characterize the location (peak) and scale (bandwidth) parameters. A Metropolis-Hastings within the Gibbs algorithm is developed for sampling the posterior distribution of the mixture parameters. Simulations demonstrate the robust performance of the proposed method. Finally, the BMARD method is applied to analyze local field potential (LFP) activity from the hippocampus of laboratory rats across different conditions in a non-spatial sequence memory experiment, to identify the most prominent frequency bands and examine the link between specific patterns of brain oscillatory activity and trial-specific cognitive demands.
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High-dimensionality is ubiquitous in various scientific fields such as imaging genetics, where a deluge of functional and structural data on brain-relevant genetic polymorphisms are investigated. It is crucial to identify which genetic variations are consequential in identifying neurological features of brain connectivity compared to merely random noise. Statistical inference in high-dimensional settings poses multiple challenges involving analytical and computational complexity. A widely implemented strategy in addressing inference goals is penalized inference. In particular, the role of the ridge penalty in high-dimensional prediction and estimation has been actively studied in the past several years. This study focuses on ridge-penalized tests in high-dimensional hypothesis testing problems by proposing and examining a class of methods for choosing the optimal ridge penalty. We present our findings on strategies to improve the statistical power of ridge-penalized tests and what determines the optimal ridge penalty for hypothesis testing. The application of our work to an imaging genetics study and biological research will be presented.
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BACKGROUND: The sex ratio at birth (SRB; ratio of male to female births) in Nepal has been reported around the normal level on the national level. However, the national SRB could mask the disparity within the country. Given the demographic and cultural heterogeneities in Nepal, it is crucial to model Nepal SRB on the subnational level. Prior studies on subnational SRB in Nepal are mostly based on reporting observed values from surveys and census, and no study has provided probabilistic projections. We aim to estimate and project SRB for the seven provinces of Nepal from 1980 to 2050 using a Bayesian modeling approach. METHODS: We compiled an extensive database on provincial SRB of Nepal, consisting 2001, 2006, 2011, and 2016 Nepal Demographic and Health Surveys and 2011 Census. We adopted a Bayesian hierarchical time series model to estimate and project the provincial SRB, with a focus on modelling the potential SRB imbalance. RESULTS: In 2016, the highest SRB is estimated in Province 5 (Lumbini Pradesh) at 1.102, corresponding to 110.2 male births per 100 female births, with a 95% credible interval (1.044, 1.127) and the lowest SRB is in Province 2 at 1.053 (1.035, 1.109). The SRB imbalance probabilities in all provinces are generally low and vary from 16% in Province 2 to 81% in Province 5 (Lumbini Pradesh). SRB imbalances are estimated to have begun at the earliest in 2001 in Province 5 (Lumbini Pradesh) with a 95% credible interval (1992, 2022) and the latest in 2017 (1998, 2040) in Province 2. We project SRB in all provinces to begin converging back to the national baseline in the mid-2030s. By 2050, the SRBs in all provinces are projected to be around the SRB baseline level. CONCLUSIONS: Our findings imply that the majority of provinces in Nepal have low risks of SRB imbalance for the period 1980-2016. However, we identify a few provinces with higher probabilities of having SRB inflation. The projected SRB is an important illustration of potential future prenatal sex discrimination and shows the need to monitor SRB in provinces with higher possibilities of SRB imbalance.
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Parto , Razón de Masculinidad , Teorema de Bayes , Censos , Femenino , Humanos , Recién Nacido , Masculino , Nepal/epidemiología , EmbarazoRESUMEN
We consider the challenges in extracting stimulus-related neural dynamics from other intrinsic processes and noise in naturalistic functional magnetic resonance imaging (fMRI). Most studies rely on inter-subject correlations (ISC) of low-level regional activity and neglect varying responses in individuals. We propose a novel, data-driven approach based on low-rank plus sparse ( [Formula: see text]) decomposition to isolate stimulus-driven dynamic changes in brain functional connectivity (FC) from the background noise, by exploiting shared network structure among subjects receiving the same naturalistic stimuli. The time-resolved multi-subject FC matrices are modeled as a sum of a low-rank component of correlated FC patterns across subjects, and a sparse component of subject-specific, idiosyncratic background activities. To recover the shared low-rank subspace, we introduce a fused version of principal component pursuit (PCP) by adding a fusion-type penalty on the differences between the columns of the low-rank matrix. The method improves the detection of stimulus-induced group-level homogeneity in the FC profile while capturing inter-subject variability. We develop an efficient algorithm via a linearized alternating direction method of multipliers to solve the fused-PCP. Simulations show accurate recovery by the fused-PCP even when a large fraction of FC edges are severely corrupted. When applied to natural fMRI data, our method reveals FC changes that were time-locked to auditory processing during movie watching, with dynamic engagement of sensorimotor systems for speech-in-noise. It also provides a better mapping to auditory content in the movie than ISC.
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Encéfalo , Imagen por Resonancia Magnética , Algoritmos , Encéfalo/diagnóstico por imagen , Encéfalo/fisiología , Mapeo Encefálico/métodos , Humanos , Imagen por Resonancia Magnética/métodos , Películas CinematográficasRESUMEN
Assessing the impact of complex interventions on measurable health outcomes is a growing concern in health care and health policy. Interrupted time series (ITS) designs borrow from traditional case-crossover designs and function as quasi-experimental methodology able to retrospectively analyze the impact of an intervention. Statistical models used to analyze ITS designs primarily focus on continuous-valued outcomes. We propose the "Generalized Robust ITS" (GRITS) model appropriate for outcomes whose underlying distribution belongs to the exponential family of distributions, thereby expanding the available methodology to adequately model binary and count responses. GRITS formally implements a test for the existence of a change point in discrete ITS. The methodology proposed is able to test for the existence of and estimate the change point, borrow information across units in multi-unit settings, and test for differences in the mean function and correlation pre- and post-intervention. The methodology is illustrated by analyzing patient falls from a hospital that implemented and evaluated a new care delivery model in multiple units.
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We propose a ridge-penalized adaptive Mantel test (AdaMant) for evaluating the association of two high-dimensional sets of features. By introducing a ridge penalty, AdaMant tests the association across many metrics simultaneously. We demonstrate how ridge penalization bridges Euclidean and Mahalanobis distances and their corresponding linear models from the perspective of association measurement and testing. This result is not only theoretically interesting but also has important implications in penalized hypothesis testing, especially in high-dimensional settings such as imaging genetics. Applying the proposed method to an imaging genetic study of visual working memory in healthy adults, we identified interesting associations of brain connectivity (measured by electroencephalogram coherence) with selected genetic features.
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Encéfalo , Encéfalo/diagnóstico por imagen , Humanos , Modelos LinealesRESUMEN
The sex ratio at birth (SRB, i.e., the ratio of male to female births) in Vietnam has been imbalanced since the 2000s. Previous studies have revealed a rapid increase in the SRB over the past 15 years and the presence of important variations across regions. More recent studies suggested that the nation's SRB may have plateaued during the 2010s. Given the lack of exhaustive birth registration data in Vietnam, it is necessary to estimate and project levels and trends in the regional SRBs in Vietnam based on a reproducible statistical approach. We compiled an extensive database on regional Vietnam SRBs based on all publicly available surveys and censuses and used a Bayesian hierarchical time series mixture model to estimate and project SRB in Vietnam by region from 1980 to 2050. The Bayesian model incorporates the uncertainties from the observations and year-by-year natural fluctuation. It includes a binary parameter to detect the existence of sex ratio transitions among Vietnamese regions. Furthermore, we model the SRB imbalance using a trapezoid function to capture the increase, stagnation, and decrease of the sex ratio transition by Vietnamese regions. The model results show that four out of six Vietnamese regions, namely, Northern Midlands and Mountain Areas, Northern Central and Central Coastal Areas, Red River Delta, and South East, have existing sex imbalances at birth. The rise in SRB in the Red River Delta was the fastest, as it took only 12 years and was more pronounced, with the SRB reaching the local maximum of 1.146 with a 95% credible interval (1.129, 1.163) in 2013. The model projections suggest that the current decade will record a sustained decline in sex imbalances at birth, and the SRB should be back to the national SRB baseline level of 1.06 in all regions by the mid-2030s.
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Dinámica Poblacional/tendencias , Razón de Masculinidad , Teorema de Bayes , Certificado de Nacimiento , Femenino , Predicción/métodos , Historia del Siglo XX , Historia del Siglo XXI , Humanos , Masculino , Dinámica Poblacional/historia , Dinámica Poblacional/estadística & datos numéricos , VietnamRESUMEN
BACKGROUND: Various interacting and interdependent components comprise complex interventions. These components create difficulty in assessing the true impact of interventions designed to improve patient-centered outcomes. Interrupted time series (ITS) designs borrow from case-crossover designs and serve as quasi-experimental methodology able to retrospectively assess the impact of an intervention while accounting for temporal correlation. While ITS designs are aptly situated for studying the impacts of large-scale public health policies, existing ITS software implement rigid ITS methodology that often assume the pre- and post-intervention phases are fully differentiated (by a known change-point or set of time points) and do not allow for changes in both the mean functions and correlation structure. RESULTS: This article describes the Robust Interrupted Time Series (RITS) toolbox, a stand-alone user-friendly application researchers can use to implement flexible ITS models that estimate the lagged effect of an intervention on an outcome, level and trend changes, and post-intervention changes in the correlation structure, for single and multiple ITS. The RITS toolbox incorporates a formal test for the existence of a change in the outcome and estimates a change-point over a set of possible change-points defined by the researcher. In settings with multiple ITS, RITS provides a global over-all units change-point and allows for unit-specific changes in the mean functions and correlation structures. CONCLUSIONS: The RITS toolbox is the first piece of software that allows researchers to use flexible ITS models that test for the existence of a change-point, estimate the change-point (if estimation is desired), and allow for changes in both the mean functions and correlation structures at the change point. RITS does not require any knowledge of a statistical (or otherwise) programming language, is freely available to the community, and may be downloaded and used on a local machine to ensure data protection.