Hidden Markov random field and FRAME modelling for TCA-image analysis

Tooth Cementum Annulation (TCA) is an age estimation method carried out on thin cross sections of the root of human teeth. Age is computed by adding the tooth eruption age to the count of annual incremental lines that are called tooth rings and appear in the cementum band. Algorithms to denoise and segment the digital image of the tooth section are considered a crucial step towards computer-assisted TCA. The approach pursued in this paper relies on modelling the images as hidden Markov random fields, where gray values are assumed to be pixelwise conditionally independent and normally distributed, given a hidden random field of labels. These unknown labels have to be estimated to segment the image. To account for long-range dependence among the observed values and for periodicity in the placement of tooth rings, the Gibbsian label distribution is specified by a potential function that incorporates macro-features of the TCA-image (a FRAME model). Estimation of the model parameters is carried out by an EM-algorithm that exploits the mean field approximation of the label distribution. Segmentation is based on the predictive distribution of the labels given the observed gray values. KEYWORDS: EM, FRAME, Gibbs distribution, (hidden) Markov random field, mean field approximation, TCA

A missing composite covariate in survival analysis: a case study of the Chinese Longitudinal Health and Longevity Survey

We estimate a Cox proportional hazards model where one of the covariates measures the level of a subject´s cognitive functioning by grading the total score obtained by the subject on the items of a questionnaire. A case study is presented where the sample includes partial respondents, who did not answer some or all of the questionnaire items. The total score takes hence the form of an interval-censored variable and, as a result, the level of cognitive functioning is missing on some subjects. We handle partial respondents by taking a likelihood-based approach where survival time is jointly modelled with the censored total score and the size of the censoring interval. Parameter estimates are obtained by an E-M-type algorithm that essentially reduces to the iterative maximization of three complete log-likelihood functions derived from two augmented datasets with case weights, alternated with weights updating. This methodology is exploited to assess the Mini Mental State Examination index as a prognostic factor of survival in a sample of Chinese older adults.China, health

Segmenting toroidal time series by nonhomogeneous hidden semi-Markov models

Motivated by classification issues in marine studies, we propose a hidden semi-Markov model to segment toroidal time series according to a finite number of latent regimes. The time spent in a given regime and the chances of a regime switching event are separately modeled by a battery of regression models that depend on time-varying covariates

DYNAMIC MIXTURES OF FACTOR ANALYZERS TO CHARACTERIZE MULTIVARIATE AIR POLLUTANT EXPOSURES

The assessment of pollution exposure is based on the analysis of multivariate time series that include the concentrations of several pollutants as well as the measurements of multiple atmospheric variables. It typically requires methods of dimensionality reduction that are capable to identify potentially dangerous combinations of pollutants and, simultaneously, to segment exposure periods according to air quality conditions. When the data are high-dimensional, however, efficient methods of dimensionality reduction are challenging because of the formidable structure of cross-correlations that arise from the dynamic interaction between weather conditions and natural/anthropogenic pollution sources. In order to assess pollution exposure in an urban area while taking the above mentioned difficulties into account, we develop a class of parsimonious hidden Markov models. In a multivariate time-series setting, this approach allows to simultaneously perform temporal segmentation and dimensionality reduction. We specifically approximate the distribution of multiple pollutant concentrations by mixtures of factor analysis models, whose parameters evolve according to a latent Markov chain. Covariates are included as predictors of the chain transition probabilities. Parameter constraints on the factorial component of the model are exploited to tune the flexibility of dimensionality reduction. In order to estimate the model parameters efficiently, we propose a novel three-step Alternating Expected Conditional Maximization (AECM) algorithm, which is also assessed in a simulation study. In the case study, the proposed methods were capable (1) to describe the exposure to pollution in terms of a few latent regimes, (2) to associate these regimes with specific combinations of pollutant concentration levels as well as distinct correlation structures between concentrations, and (3) to capture the influence of weather conditions on transitions between regime

A circular nonhomogeneous hidden Markov field for the spatial segmentation of wildfire occurrences

This is the pre-peer reviewed version of the following article: Ameijeiras‐Alonso, J, Lagona, F, Ranalli, M, Crujeiras, RM. A circular nonhomogeneous hidden Markov field for the spatial segmentation of wildfire occurrences. Environmetrics. 2019; 30:e2501. https://doi.org/10.1002/env.2501, which has been published in final form at https://doi.org/10.1002/env.2501. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Use of Self-Archived VersionsMotivated by studies of wildfire seasonality, we propose a nonhomogeneous hidden Markov random field to model the spatial distribution of georeferenced fire occurrences during the year, by representing occurrence times as circular data. The model is based on a mixture of Kato–Jones circular densities, whose parameters vary across space according to a latent nonhomogeneous Potts model, modulated by georeferenced covariates. It allows us to segment fire occurrences according to a finite number of latent classes that represent the conditional distributions of the data under specific periods of the year, simultaneously accounting for unobserved heterogeneity and spatial autocorrelation. Further, it parsimoniously accommodates specific features of wildfire occurrence data such as multimodality, skewness, and kurtosis. Due to the numerical intractability of the likelihood function, estimation of the parameters is based on composite likelihood methods. It reduces to a computationally efficient expectation–maximization algorithm that iteratively alternates the maximization of a weighted composite likelihood function with weights updating. The proposal is illustrated in a study of wildfire occurrences in the Iberian Peninsula during a decadeJose Ameijeiras‐Alonso and Rosa M. Crujeiras gratefully acknowledge the support of Project MTM2016‐76969‐P (Spanish State Research Agency, AEI), co‐funded by the European Regional Development Fund (ERDF), IAP network from Belgian Science Policy. Part of the research was carried out by Jose Ameijeiras‐Alonso during his visit to University of Roma Tre, supported by Grants BES‐2014‐071006 and EEBB‐I‐17‐12716 from the Spanish Ministry of Economy, Industry and Competitiveness. Francesco Lagona is supported by the 2015 PRIN supported project “Environmental processes and human activities: capturing their interactions via statistical methods”, funded by the Italian Ministry of Education, University and Scientific ResearchNO

Allopathic versus Homeopathic Strategies and the Recurrence of Prescriptions: Results from a Pharmacoeconomic Study in Italy

This is a pharmaeconomic study to assess the impact of different, cost-specific pharmacological strategies on the recurrence rate of prescriptions in the treatment of cold symptoms. Data were obtained from a prospective cohort study reporting individual prescriptions histories of subjects experiencing cold symptoms, obtained by a stratified random sample of 316 subjects, clustered into 139 Italian families, followed up for 40 months. Costs of homeopathic and allopathic treatments were recorded within each prescription. A Cox proportional hazards model with random effects was exploited to regress time elapsed between subsequent prescriptions over the relative difference between homeopathic- and allopathic-related costs, adjusting for age and gender and accounting for unobserved individual heterogeneity. Relative risks of event (prescription) re-occurrence have been estimated. The recurrence rate of prescriptions raise when allopathic strategies are preferred to homeopathic alternatives. No significant differences were observed between gender groups, while age was marginally significant. Inter-subjects heterogeneity was not significant