Recent advances in directional statistics

Mainstream statistical methodology is generally applicable to data observed in Euclidean space. There are, however, numerous contexts of considerable scientific interest in which the natural supports for the data under consideration are Riemannian manifolds like the unit circle, torus, sphere and their extensions. Typically, such data can be represented using one or more directions, and directional statistics is the branch of statistics that deals with their analysis. In this paper we provide a review of the many recent developments in the field since the publication of Mardia and Jupp (1999), still the most comprehensive text on directional statistics. Many of those developments have been stimulated by interesting applications in fields as diverse as astronomy, medicine, genetics, neurology, aeronautics, acoustics, image analysis, text mining, environmetrics, and machine learning. We begin by considering developments for the exploratory analysis of directional data before progressing to distributional models, general approaches to inference, hypothesis testing, regression, nonparametric curve estimation, methods for dimension reduction, classification and clustering, and the modelling of time series, spatial and spatio-temporal data. An overview of currently available software for analysing directional data is also provided, and potential future developments discussed.Comment: 61 page

Cost-effectiveness analysis of 3-D computerized tomography colonography versus optical colonoscopy for imaging symptomatic gastroenterology patients.

BACKGROUND: When symptomatic gastroenterology patients have an indication for colonic imaging, clinicians have a choice between optical colonoscopy (OC) and computerized tomography colonography with three-dimensional reconstruction (3-D CTC). 3-D CTC provides a minimally invasive and rapid evaluation of the entire colon, and it can be an efficient modality for diagnosing symptoms. It allows for a more targeted use of OC, which is associated with a higher risk of major adverse events and higher procedural costs. A case can be made for 3-D CTC as a primary test for colonic imaging followed if necessary by targeted therapeutic OC; however, the relative long-term costs and benefits of introducing 3-D CTC as a first-line investigation are unknown. AIM: The aim of this study was to assess the cost effectiveness of 3-D CTC versus OC for colonic imaging of symptomatic gastroenterology patients in the UK NHS. METHODS: We used a Markov model to follow a cohort of 100,000 symptomatic gastroenterology patients, aged 50 years or older, and estimate the expected lifetime outcomes, life years (LYs) and quality-adjusted life years (QALYs), and costs (£, 2010-2011) associated with 3-D CTC and OC. Sensitivity analyses were performed to assess the robustness of the base-case cost-effectiveness results to variation in input parameters and methodological assumptions. RESULTS: 3D-CTC provided a similar number of LYs (7.737 vs 7.739) and QALYs (7.013 vs 7.018) per individual compared with OC, and it was associated with substantially lower mean costs per patient (£467 vs £583), leading to a positive incremental net benefit. After accounting for the overall uncertainty, the probability of 3-D CTC being cost effective was around 60 %, at typical willingness-to-pay values of £20,000-£30,000 per QALY gained. CONCLUSION: 3-D CTC is a cost-saving and cost-effective option for colonic imaging of symptomatic gastroenterology patients compared with OC

A semiparametric regression model for paired longitudinal outcomes with application in childhood blood pressure development

This research examines the simultaneous influences of height and weight on longitudinally measured systolic and diastolic blood pressure in children. Previous studies have shown that both height and weight are positively associated with blood pressure. In children, however, the concurrent increases of height and weight have made it all but impossible to discern the effect of height from that of weight. To better understand these influences, we propose to examine the joint effect of height and weight on blood pressure. Bivariate thin plate spline surfaces are used to accommodate the potentially nonlinear effects as well as the interaction between height and weight. Moreover, we consider a joint model for paired blood pressure measures, that is, systolic and diastolic blood pressure, to account for the underlying correlation between the two measures within the same individual. The bivariate spline surfaces are allowed to vary across different groups of interest. We have developed related model fitting and inference procedures. The proposed method is used to analyze data from a real clinical investigation.Comment: Published in at http://dx.doi.org/10.1214/12-AOAS567 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

Conditional Spectral Analysis of Replicated Multiple Time Series with Application to Nocturnal Physiology

This article considers the problem of analyzing associations between power spectra of multiple time series and cross-sectional outcomes when data are observed from multiple subjects. The motivating application comes from sleep medicine, where researchers are able to non-invasively record physiological time series signals during sleep. The frequency patterns of these signals, which can be quantified through the power spectrum, contain interpretable information about biological processes. An important problem in sleep research is drawing connections between power spectra of time series signals and clinical characteristics; these connections are key to understanding biological pathways through which sleep affects, and can be treated to improve, health. Such analyses are challenging as they must overcome the complicated structure of a power spectrum from multiple time series as a complex positive-definite matrix-valued function. This article proposes a new approach to such analyses based on a tensor-product spline model of Cholesky components of outcome-dependent power spectra. The approach flexibly models power spectra as nonparametric functions of frequency and outcome while preserving geometric constraints. Formulated in a fully Bayesian framework, a Whittle likelihood based Markov chain Monte Carlo (MCMC) algorithm is developed for automated model fitting and for conducting inference on associations between outcomes and spectral measures. The method is used to analyze data from a study of sleep in older adults and uncovers new insights into how stress and arousal are connected to the amount of time one spends in bed