Antonello Maruotti

A mixed non-homogeneous hidden Markov model for categorical data, with application to alcohol consumption

Hidden Markov models (HMMs) are frequently used to analyse longitudinal data, where the same set of subjects is repeatedly observed over time. In this context, several sources of heterogeneity may arise at individual and/or time level, which affect the hidden process, that is, the transition probabilities between the hidden states. In this paper, we propose the use of a finite mixture of non-homogeneous HMMs (NH-HMMs) to face the heterogeneity problem. The non-homogeneity of the model allows us to take into account observed sources of heterogeneity by means of a proper set of covariates, time and/or individual dependent, explaining the variations in the transition probabilities. Moreover, we handle the unobserved sources of heterogeneity at the individual level, due to, for example, omitted covariates, by introducing a random term with a discrete distribution. The resulting model is a finite mixture of NH-HMM that can be used to classify individuals according to their dynamic behaviour or to estimate a mixed NH-HMM without any assumption regarding the distribution of the random term following the non-parametric maximum likelihood approach. We test the effectiveness of the proposal through a simulation study and an application to real data on alcohol abuse.

Cardiovascular mortality and chronotropic incompetence in systolic heart failure: the importance of a reappraisal of current cut-off criteria.

An independent role for the exercise‐induced heart rate (HR) response—and specifically the chronotropic incompetence (CI)—in the prognosis of heart failure (HF) is still debated. The multicentre study reported here sought to investigate the prognostic values of HR and CI variables on cardiovascular mortality in a large cohort of systolic HF patients.

Deceptive meaning of oxygen uptake measured at the anaerobic threshold in patients with systolic heart failure and atrial fibrillation

Background Oxygen uptake at the anaerobic threshold (VO2AT), a submaximal exercise-derived variable, independent of patients’ motivation, is a marker of outcome in heart failure (HF). However, previous evidence of VO2AT values paradoxically higher in HF patients with permanent atrial fibrillation (AF) than in those with sinus rhythm (SR) raised uncertainties. Design We tested the prognostic role of VO2AT in a large cohort of systolic HF patients, focusing on possible differences between SR and AF. Methods Altogether 2976 HF patients (2578 with SR and 398 with AF) were prospectively followed. Besides a clinical examination, each patient underwent a maximal cardiopulmonary exercise test (CPET). Results The follow-up was analysed for up to 1500 days. Cardiovascular death or urgent cardiac transplantation occurred in 303 patients (250 (9.6%) patients with SR and 53 (13.3%) patients with AF, p = 0.023). In the entire population, multivariate analysis including peak oxygen uptake (VO2) showed a prognostic capacity (C-index) similar to that obtained including VO2AT (0.76 vs 0.72). Also, left ventricular ejection fraction, ventilation vs carbon dioxide production slope, β-blocker and digoxin therapy proved to be significant prognostic indexes. The receiver-operating characteristic (ROC) curves analysis showed that the best predictive VO2AT cut-off for the SR group was 11.7 ml/kg/min, while it was 12.8 ml/kg/min for the AF group. Conclusions VO2AT, a submaximal CPET-derived parameter, is reliable for long-term cardiovascular mortality prognostication in stable systolic HF. However, different VO2AT cut-off values between SR and AF HF patients should be adopted.

How individual characteristics affect university students drop-out: a semiparametric mixed-effects model for an Italian case study

University drop-out is a topic of increasing concern in Italy as well as in other countries. In empirical analysis, university drop-out is generally measured by means of a binary variable indicating the drop-out versus retention. In this paper, we argue that the withdrawal decision is one of the possible outcomes of a set of four alternatives: retention in the same faculty, drop out, change of faculty within the same university, and change of institution. We examine individual-level data collected by the administrative offices of “Sapienza” University of Rome, which cover 117 072 students enrolling full-time for a 3-year degree in the academic years from 2001/2002 to 2006/2007. Relying on a non-parametric maximum likelihood approach in a finite mixture context, we introduce a multinomial latent effects model with endogeneity that accounts for both heterogeneity and omitted covariates. Our estimation results show that the decisions to change faculty or university have their own peculiarities, thus we suggest that caution should be used in interpreting results obtained without modeling all the relevant alternatives that students face.

Bayesian hidden Markov modelling using circular-linear general projected normal distribution

We introduce a multivariate hidden Markov model to jointly cluster time-series observations with different support, that is, circular and linear. Relying on the general projected normal distribution, our approach allows for bimodal and/or skewed cluster-specific distributions for the circular variable. Furthermore, we relax the independence assumption between the circular and linear components observed at the same time. Such an assumption is generally used to alleviate the computational burden involved in the parameter estimation step, but it is hard to justify in empirical applications. We carry out a simulation study using different data-generation schemes to investigate model behavior, focusing on well recovering the hidden structure. Finally, the model is used to fit a real data example on a bivariate time series of wind speed and direction. Copyright

Clustering Multivariate Longitudinal Observations: The Contaminated Gaussian Hidden Markov Model

The Gaussian hidden Markov model (HMM) is widely considered for the analysis of heterogenous continuous multivariate longitudinal data. To robustify this approach with respect to possible elliptical heavy-tailed departures from normality, due to the presence of outliers, spurious points, or noise (collectively referred to as bad points herein), the contaminated Gaussian HMM is here introduced. The contaminated Gaussian distribution represents an elliptical generalization of the Gaussian distribution and allows for automatic detection of bad points in the same natural way as observations are typically assigned to the latent states in the HMM context. Once the model is fitted, each observation has a posterior probability of belonging to a particular state and, inside each state, of being a bad point or not. In addition to the parameters of the classical Gaussian HMM, for each state we have two more parameters, both with a specific and useful interpretation: one controls the proportion of bad points and one specifies their degree of atypicality. A sufficient condition for the identifiability of the model is given, an expectation-conditional maximization algorithm is outlined for parameter estimation and various operational issues are discussed. Using a large-scale simulation study, but also an illustrative artificial dataset, we demonstrate the effectiveness of the proposed model in comparison with HMMs of different elliptical distributions, and we also evaluate the performance of some well-known information criteria in selecting the true number of latent states. The model is finally used to fit data on criminal activities in Italian provinces. Supplementary materials for this article are available online

Cardiopulmonary exercise test and sudden cardiac death risk in hypertrophic cardiomyopathy

Background In hypertrophic cardiomyopathy (HCM), most of the factors associated with the risk of sudden cardiac death (SCD) are also involved in the pathophysiology of exercise limitation. The present multicentre study investigated possible ability of cardiopulmonary exercise test in improving contemporary strategies for SCD risk stratification. Methods A total of 623 consecutive outpatients with HCM, from five tertiary Italian HCM centres, were recruited and prospectively followed, between September 2007 and April 2015. The study composite end point was SCD, aborted SCD and appropriate implantable cardioverter defibrillator (ICD) interventions. Results During a median follow-up of 3.7 years (25th–75th centile: 2.2–5.1 years), 25 patients reached the end point at 5 years (3 SCD, 4 aborted SCD, 18 appropriate ICD interventions). At multivariate analysis, ventilation versus carbon dioxide relation during exercise (VE/VCO2 slope) remains independently associated to the study end point either when challenged with the 2011 American College of Cardiology Foundation/American Heart Association guidelines-derived score (C index 0.748) or with the 2014 European Society of Cardiology guidelines-derived score (C index 0.750). A VE/VCO2 slope cut-off value of 31 showed the best accuracy in predicting the SCD end point within the entire HCM study cohort (sensitivity 64%, specificity 72%, area under the curve 0.72). Conclusions Our data suggest that the VE/VCO2 slope might improve SCD risk stratification, particularly in those HCM categories classified at low-intermediate SCD risk according to contemporary guidelines. There is a need for further larger studies, possibly on independent cohorts, to confirm our preliminary findings.

A hidden Markov approach to the analysis of space–time environmental data with linear and circular components

The analysis of bivariate space–time series with linear and circular components is complicated by (1) multiple correlations, across time, space and between variables, (2) different supports on which the variables are observed, the real line and the circle, and (3) the periodic nature of circular data. We describe a multivariate hidden Markov model that includes these features of the data within a single framework. The model integrates a circular von Mises Markov field and a Gaussian Markov field, with parameters that evolve in time according to a latent (hidden) Markov chain. It allows to describe the data by means of a finite number of time-varying latent regimes, associated with easily interpretable components of large-scale and small-scale spatial variation. It can be estimated by a computationally feasible expectation–maximization algorithm. In a case study of sea currents in the Northern Adriatic Sea, it provides a parsimonious representation of the sea surface in terms of alternating environmental states.

A finite mixture model for multivariate counts under endogenous selectivity

We describe a selection model for multivariate counts, where association between the primary outcomes and the endogenous selection source is modeled through outcome-specific latent effects which are assumed to be dependent across equations. Parametric specifications of this model already exist in the literature; in this paper, we show how model parameters can be estimated in a finite mixture context. This approach helps us to consider overdispersed counts, while allowing for multivariate association and endogeneity of the selection variable. In this context, attention is focused both on bias in estimated effects when exogeneity of selection (treatment) variable is assumed, as well as on consistent estimation of the association between the random effects in the primary and in the treatment effect models, when the latter is assumed endogeneous. The model behavior is investigated through a large scale simulation experiment. An empirical example on health care utilization data is provided.

A two-part mixed-effects pattern-mixture model to handle zero-inflation and incompleteness in a longitudinal setting.

Two-part regression models are frequently used to analyze longitudinal count data with excess zeros, where the same set of subjects is repeatedly observed over time. In this context, several sources of heterogeneity may arise at individual level that affect the observed process. Further, longitudinal studies often suffer from missing values: individuals dropout of the study before its completion, and thus present incomplete data records. In this paper, we propose a finite mixture of hurdle models to face the heterogeneity problem, which is handled by introducing random effects with a discrete distribution; a pattern-mixture approach is specified to deal with non-ignorable missing values. This approach helps us to consider overdispersed counts, while allowing for association between the two parts of the model, and for non-ignorable dropouts. The effectiveness of the proposal is tested through a simulation study. Finally, an application to real data on skin cancer is provided.