Geographic patterns in stroke mortality have been studied as far back as the 1960s, when a region of the southeastern United States became known as the "stroke belt" due to its unusually high rates of stroke mortality. While stroke mortality rates are known to increase exponentially with age, an investigation of spatiotemporal trends by age group at the county-level is daunting due to the preponderance of small population sizes and/or few stroke events by age group. Here, we harness the power of a complex, nonseparable multivariate space-time model which borrows strength across space, time, and age group to obtain reliable estimates of yearly county-level mortality rates from US counties between 1973 and 2013 for those aged 65+. Furthermore, we propose an alternative metric for measuring changes in event rates over time which accounts for the full trajectory of a county's event rates, as opposed to simply comparing the rates at the beginning and end of the study period. In our analysis of the stroke data, we identify differing spatiotemporal trends in mortality rates across age groups, shed light on the gains achieved in the Deep South, and provide evidence that a separable model is inappropriate for these data.
Age-specific mortality rates are often disaggregated by different attributes, such as sex, state, ethnic group and socioeconomic status. In making social policies and pricing annuity at national and subnational levels, it is important not only to forecast mortality accurately, but also to ensure that forecasts at the subnational level add up to the forecasts at the national level. This motivates recent developments in grouped functional time series methods (Shang and Hyndman, 2017) to reconcile age-specific mortality forecasts. We extend these grouped functional time series forecasting methods…
When modeling sub-national mortality rates, it is important to incorporate any possible correlation among sub-populations to improve forecast accuracy. Moreover, forecasts at the sub-national level should aggregate consistently across the forecasts at the national level. In this study, we apply a grouped multivariate functional time series to forecast Australian regional and remote age-specific mortality rates and reconcile forecasts in a group structure using various methods. Our proposed method compares favorably to a grouped univariate functional time series forecasting method by comparing …
University of the Witwatersrand（金山大学）；University of Johannesburg（约翰内斯堡大学）
Hybrid methods have been shown to outperform pure statistical and pure deep learning methods at forecasting tasks and quantifying the associated uncertainty with those forecasts (prediction intervals). One example is Exponential Smoothing Recurrent Neural Network (ES-RNN), a hybrid between a statistical forecasting model and a recurrent neural network variant. ES-RNN achieves a 9.4\% improvement in absolute error in the Makridakis-4 Forecasting Competition. This improvement and similar outperformance from other hybrid models have primarily been demonstrated only on univariate datasets. Difficu…
When modeling sub-national mortality rates, we should consider three features: (1) how to incorporate any possible correlation among sub-populations to potentially improve forecast accuracy through multi-population joint modeling; (2) how to reconcile sub-national mortality forecasts so that they aggregate adequately across various levels of a group structure; (3) among the forecast reconciliation methods, how to combine their forecasts to achieve improved forecast accuracy. To address these issues, we introduce an extension of grouped univariate functional time series method. We first conside…
A common class of methods for analyzing of multivariate time series, stationary and nonstationary, decomposes the observed series into latent sources. Methods such as principal compoment analysis (PCA), independent component analysis (ICA) and Stationary Subspace Analysis (SSA) assume the observed multivariate process is generated by latent sources that are stationary or nonstationary. We develop a method that tracks changes in the complexity of a 32-channel local field potential (LFP) signal from a rat following an experimentally induced stroke. We study complexity through the latent sources …
Exposure to air pollution is associated with increased morbidity and mortality. Recent technological advancements permit the collection of time-resolved personal exposure data. Such data are often incomplete with missing observations and exposures below the limit of detection, which limit their use in health effects studies. In this paper we develop an infinite hidden Markov model for multiple asynchronous multivariate time series with missing data. Our model is designed to include covariates that can inform transitions among hidden states. We implement beam sampling, a combination of slice sa…
We study the importance of group structure in grouped functional time series. Due to the non-uniqueness of group structure, we investigate different disaggregation structures in grouped functional time series. We address a practical question on whether or not the group structure can affect forecast accuracy. Using a dynamic multivariate functional time series method, we consider joint modeling and forecasting multiple series. Illustrated by Japanese sub-national age-specific mortality rates from 1975 to 2016, we investigate one- to 15-step-ahead point and interval forecast accuracies for the t…
Early recognition of risky trajectories during an Intensive Care Unit (ICU) stay is one of the key steps towards improving patient survival. Learning trajectories from physiological signals continuously measured during an ICU stay requires learning time-series features that are robust and discriminative across diverse patient populations. Patients within different ICU populations (referred here as domains) vary by age, conditions and interventions. Thus, mortality prediction models using patient data from a particular ICU population may perform suboptimally in other populations because the fea…
This paper proposes a cluster-based method to analyze the evolution of multivariate time series and applies this to the COVID-19 pandemic. On each day, we partition countries into clusters according to both their case and death counts. The total number of clusters and individual countries' cluster memberships are algorithmically determined. We study the change in both quantities over time, demonstrating a close similarity in the evolution of cases and deaths. The changing number of clusters of the case counts precedes that of the death counts by 32 days. On the other hand, there is an optimal …
A multiple objective space-time forecasting approach is presented involving cyclical curve log-regression, and multivariate time series spatial residual correlation analysis. Specifically, the mean quadratic loss function is minimized in the framework of trigonometric regression. While, in our subsequent spatial residual correlation analysis, maximization of the likelihood allows us to compute the posterior mode in a Bayesian multivariate time series soft-data framework. The presented approach is applied to the analysis of COVID-19 mortality in the first wave affecting the Spanish Communities,…
The goal of this paper is to develop a measure for characterizing complex dependence between stationary time series that cannot be captured by traditional measures such as correlation and coherence. Our approach is to use copula models of functionals of the Fourier coefficients which is a generalization of coherence. Here, we use standard parametric copula models with a single parameter both from elliptical and Archimedean families. Our approach is to analyze changes in local field potentials in the rat cortex prior to and immediately following the onset of stroke. We present the necessary the…
Tracking and estimating Daily Fine Particulate Matter (PM2.5) is very important as it has been shown that PM2.5 is directly related to mortality related to lungs, cardiovascular system, and stroke. That is, high values of PM2.5 constitute a public health problem in the US, and it is important that we precisely estimate PM2.5 to aid in public policy decisions. Thus, we propose a Bayesian hierarchical model for high-dimensional "multi-type" responses. By "multi-type" responses we mean a collection of correlated responses that have different distributional assumptions (e.g., continuous skewed obs…
Functional data are often extremely high-dimensional and exhibit strong dependence structures but can often prove valuable for both prediction and inference. The literature on functional data analysis is well developed; however, there has been very little work involving functional data in complex survey settings. Motivated by physical activity monitor data from the National Health and Nutrition Examination Survey (NHANES), we develop a Bayesian model for functional covariates that can properly account for the survey design. Our approach is intended for non-Gaussian data and can be applied in m…
The analysis of samples of random objects that do not lie in a vector space is gaining increasing attention in statistics. An important class of such object data is univariate probability measures defined on the real line. Adopting the Wasserstein metric, we develop a class of regression models for such data, where random distributions serve as predictors and the responses are either also distributions or scalars. To define this regression model, we utilize the geometry of tangent bundles of the space of random measures endowed with the Wasserstein metric for mapping distributions to tangent s…
University College London（伦敦大学学院）；Biomediq A/S（Biomediq公司）；University of Copenhagen（哥本哈根大学）；Cerebriu A/S（Cerebriu公司）
Learning temporal patterns from multivariate longitudinal data is challenging especially in cases when data is sporadic, as often seen in, e.g., healthcare applications where the data can suffer from irregularity and asynchronicity as the time between consecutive data points can vary across features and samples, hindering the application of existing deep learning models that are constructed for complete, evenly spaced data with fixed sequence lengths. In this paper, a novel deep learning-based model is developed for modeling multiple temporal features in sporadic data using an integrated deep …
Deep neural networks have shown promising results for various clinical prediction tasks such as diagnosis, mortality prediction, predicting duration of stay in hospital, etc. However, training deep networks -- such as those based on Recurrent Neural Networks (RNNs) -- requires large labeled data, high computational resources, and significant hyperparameter tuning effort. In this work, we investigate as to what extent can transfer learning address these issues when using deep RNNs to model multivariate clinical time series. We consider transferring the knowledge captured in an RNN trained on se…
College of Information and Computer Sciences（信息与计算机科学学院）；University of Massachusetts Amherst（马萨诸塞大学阿默斯特分校）
While the volume of electronic health records (EHR) data continues to grow, it remains rare for hospital systems to capture dense physiological data streams, even in the data-rich intensive care unit setting. Instead, typical EHR records consist of sparse and irregularly observed multivariate time series, which are well understood to present particularly challenging problems for machine learning methods. In this paper, we present a new deep learning architecture for addressing this problem based on the use of a semi-parametric interpolation network followed by the application of a prediction n…
A common goal in modeling demographic rates is to compare two or more groups. For ex- ample comparing mortality rates between men and women or between geographic regions may reveal health inequalities. A popular class of models for all-cause mortality as well as incidence of specific diseases like cancer is the age-period-cohort (APC) model. Extending this model to the multivariate setting is not straightforward because the univariate APC model suffers from well-known identifiability problems. Often APC models are fit separately for each strata, and then comparisons are made post hoc. This pap…
State-space representation of early-life child mortality dynamics: linking event history analysis and orbit-based models
School of Computer Science and Applied Mathematics, University of the Witwatersrand（威特沃特斯兰德大学计算机科学与应用数学学院）；Department of Mathematics and Applied Mathematics, University of Johannesburg（约翰内斯堡大学数学与应用数学系）；National Institute for Theoretical and Computational Sciences (NITheCS)（国家理论与计算科学研究所）
Electronic records contain sequences of events, some of which take place all at once in a single visit, and others that are dispersed over multiple visits, each with a different timestamp. We postulate that fine temporal detail, e.g., whether a series of blood tests are completed at once or in rapid succession should not alter predictions based on this data. Motivated by this intuition, we propose models for analyzing sequences of multivariate clinical time series data that are invariant to this temporal clustering. We propose an efficient data augmentation technique that exploits the postulat…
We introduce efficient Markov chain Monte Carlo methods for inference and model determination in multivariate and matrix-variate Gaussian graphical models. Our framework is based on the G-Wishart prior for the precision matrix associated with graphs that can be decomposable or non-decomposable. We extend our sampling algorithms to a novel class of conditionally autoregressive models for sparse estimation in multivariate lattice data, with a special emphasis on the analysis of spatial data. These models embed a great deal of flexibility in estimating both the correlation structure across outcom…
Regional aggregates of health outcomes over delineated administrative units (e.g., states, counties, zip codes), or areal units, are widely used by epidemiologists to map mortality or incidence rates and capture geographic variation. To capture health disparities over regions, we seek "difference boundaries" that separate neighboring regions with significantly different spatial effects. Matters are more challenging with multiple outcomes over each unit, where we capture dependence among diseases as well as across the areal units. Here, we address multivariate difference boundary detection for …
Local field potentials (LFPs) are signals that measure electrical activity in localized cortical regions from implanted tetrodes in the human or animal brain. The LFP signals are curves observed at multiple tetrodes which are implanted across a patch on the surface of the cortex. Hence, they can be treated as multi-group functional data, where the trajectories collected across temporal epochs from one tetrode are viewed as a group of functions. In many cases, multi-tetrode LFP trajectories contain both global variation patterns (which are shared in common to all groups, due to signal synchrony…
A Bayesian location-scale joint model for time-to-event and multivariate longitudinal data with association based on within-individual variability
MRC Biostatistics Unit, University of Cambridge（剑桥大学MRC生物统计单元）；Department of Medical Statistics, London School of Hygiene & Tropical Medicine（伦敦卫生与热带医学院医学统计学系）；Royal Brompton Hospital, part of Guy’s and St Thomas’ NHS Foundation Trust（皇家布龙普顿医院（盖伊和圣托马斯NHS基金会信托旗下））；National Heart and Lung Institute, Imperial College（帝国理工学院国家心肺研究所）；Divisions of Biostatistics and Epidemiology and Pulmonary Medicine, Cincinnati Children’s Hospital Medical Center（辛辛那提儿童医院医疗中心生物统计、流行病学和肺病科）；Department of Pediatrics, University of Cincinnati（辛辛那提大学儿科系）；Department of Public Health, Policy and Systems, University of Liverpool（利物浦大学公共卫生、政策和系统系）；Cardiovascular Epidemiology Unit, University of Cambridge（剑桥大学心血管流行病学单元）；Ohio University Heritage College of Osteopathic Medicine（俄亥俄大学遗产骨科医学院）；University of Edinburgh（爱丁堡大学）
Joint models are used in ageing studies to investigate the association between longitudinal markers and a time-to-event, and have been extended to multiple markers and/or competing risks. The competing risk of death must be considered in the elderly because death and dementia have common risk factors. Moreover, in cohort studies, time-to-dementia is interval-censored because dementia is only assessed intermittently. So subjects can become demented and die between two follow-up visits without being diagnosed. To study pre-dementia cognitive decline, we propose a joint latent class model combini…
