On the posterior distribution of the number of components in a finite mixture

The posterior distribution of the number of components k in a finite mixture satisfies a set of inequality constraints. The result holds irrespective of the parametric form of the mixture components and under assumptions on the prior distribution weaker than those routinely made in the literature on Bayesian analysis of finite mixtures. The inequality constraints can be used to perform an ``internal'' consistency check of MCMC estimates of the posterior distribution of k and to provide improved estimates which are required to satisfy the constraints. Bounds on the posterior probability of k components are derived using the constraints. Implications on prior distribution specification and on the adequacy of the posterior distribution of k as a tool for selecting an adequate number of components in the mixture are also explored.Comment: Published at http://dx.doi.org/10.1214/009053604000000788 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Retrospective sampling in MCMC with an application to COM-Poisson regression

The normalization constant in the distribution of a discrete random variable may not be available in closed form; in such cases, the calculation of the likelihood can be computationally expensive. Approximations of the likelihood or approximate Bayesian computation methods can be used; but the resulting Markov chain Monte Carlo (MCMC) algorithm may not sample from the target of interest. In certain situations, one can efficiently compute lower and upper bounds on the likelihood. As a result, the target density and the acceptance probability of the Metropolis–Hastings algorithm can be bounded. We propose an efficient and exact MCMC algorithm based on the idea of retrospective sampling. This procedure can be applied to a number of discrete distributions, one of which is the Conway–Maxwell–Poisson distribution. In practice, the bounds on the acceptance probability do not need to be particularly tight in order to accept or reject a move. We demonstrate this method using data on the emergency hospital admissions in Scotland in 2010, where the main interest lies in the estimation of the variability of admissions, as it is considered as a proxy for health inequalities

An online application for the classification and evidence evaluation of forensic glass fragments

We present an easy-to-use and freely accessible online application for the analysis of forensic glass fragments. The application is browser based and takes as input .csv or .txt files containing measurements from glass fragments obtained using a scanning electron microscope with an energy-dispersive X-ray (SEM-EDX) spectrometer. The application was developed to (i) classify glass fragments into use-type categories (classification), and (ii) compute the evidential strength of two sets of fragments under competing propositions (evidence evaluation). Detailed examples of how to use the application for both tasks are given, which highlight its user-friendly interface. The suitability of the statistical methods used by the application was checked using simulation studies, and improvements upon previous methods were found in both tasks

A population-based study on myelodysplastic syndromes in the Lazio Region (Italy), medical miscoding and 11-year mortality follow-up. The Gruppo Romano-Laziale Mielodisplasie experience of retrospective multicentric registry

Data on Myelodysplastic Syndromes (MDS) are difficult to collect by cancer registries because of the lack of reporting and the use of different classifications of the disease. In the Lazio Region, data from patients with a confirmed diagnosis of MDS, treated by a hematology center, have been collected since 2002 by the Gruppo Romano-Laziale Mielodisplasie (GROM-L) registry, the second MDS registry existing in Italy. This study aimed at evaluating MDS medical miscoding during hospitalizations, and patients' survival. For these purposes, we selected 644 MDS patients enrolled in the GROM-L registry. This cohort was linked with two regional health information systems: the Hospital Information System (HIS) and the Mortality Information System (MIS) in the 2002-2012 period. Of the 442 patients who were hospitalized at least once during the study period, 92% had up to 12 hospitalizations. 28.5% of patients had no hospitalization episodes scored like MDS, code 238.7 of the International Classification of Disease, Ninth Revision, Clinical Modification (ICD-9-CM). The rate of death during a median follow-up of 46 months (range 0.9-130) was 45.5%. Acute myeloid leukemia (AML) was the first cause of mortality, interestingly a relevant portion of deaths is due to cerebro-cardiovascular events and second tumors. This study highlights that MDS diagnosis and treatment, which require considerable healthcare resources, tend to be under-documented in the HIS archive. Thus we need to improve the HIS to better identify information on MDS hospitalizations and outcome. Moreover, we underline the importance of comorbidity in MDS patients' survival

Efficient Bayesian inference for COM-Poisson regression models

COM-Poisson regression is an increasingly popular model for count data. Its main advantage is that it permits to model separately the mean and the variance of the counts, thus allowing the same covariate to affect in different ways the average level and the variability of the response variable. A key limiting factor to the use of the COM-Poisson distribution is the calculation of the normalisation constant: its accurate evaluation can be time-consuming and is not always feasible. We circumvent this problem, in the context of estimating a Bayesian COM-Poisson regression, by resorting to the exchange algorithm, an MCMC method applicable to situations where the sampling model (likelihood) can only be computed up to a normalisation constant. The algorithm requires to draw from the sampling model, which in the case of the COM-Poisson distribution can be done efficiently using rejection sampling. We illustrate the method and the benefits of using a Bayesian COM-Poisson regression model, through a simulation and two real-world data sets with different levels of dispersion

COVID-19 Severity in Multiple Sclerosis: Putting Data Into Context

Background and objectives: It is unclear how multiple sclerosis (MS) affects the severity of COVID-19. The aim of this study is to compare COVID-19-related outcomes collected in an Italian cohort of patients with MS with the outcomes expected in the age- and sex-matched Italian population. Methods: Hospitalization, intensive care unit (ICU) admission, and death after COVID-19 diagnosis of 1,362 patients with MS were compared with the age- and sex-matched Italian population in a retrospective observational case-cohort study with population-based control. The observed vs the expected events were compared in the whole MS cohort and in different subgroups (higher risk: Expanded Disability Status Scale [EDSS] score > 3 or at least 1 comorbidity, lower risk: EDSS score ≤ 3 and no comorbidities) by the χ2 test, and the risk excess was quantified by risk ratios (RRs). Results: The risk of severe events was about twice the risk in the age- and sex-matched Italian population: RR = 2.12 for hospitalization (p < 0.001), RR = 2.19 for ICU admission (p < 0.001), and RR = 2.43 for death (p < 0.001). The excess of risk was confined to the higher-risk group (n = 553). In lower-risk patients (n = 809), the rate of events was close to that of the Italian age- and sex-matched population (RR = 1.12 for hospitalization, RR = 1.52 for ICU admission, and RR = 1.19 for death). In the lower-risk group, an increased hospitalization risk was detected in patients on anti-CD20 (RR = 3.03, p = 0.005), whereas a decrease was detected in patients on interferon (0 observed vs 4 expected events, p = 0.04). Discussion: Overall, the MS cohort had a risk of severe events that is twice the risk than the age- and sex-matched Italian population. This excess of risk is mainly explained by the EDSS score and comorbidities, whereas a residual increase of hospitalization risk was observed in patients on anti-CD20 therapies and a decrease in people on interferon