La régression de Poisson multiniveau généralisée au sein d’un devis longitudinal : un exemple de modélisation du nombre d’arrestations de membres de gangs de rue à Montréal entre 2005 et 2007

Les données comptées (count data) possèdent des distributions ayant des caractéristiques particulières comme la non-normalité, l’hétérogénéité des variances ainsi qu’un nombre important de zéros. Il est donc nécessaire d’utiliser les modèles appropriés afin d’obtenir des résultats non biaisés. Ce mémoire compare quatre modèles d’analyse pouvant être utilisés pour les données comptées : le modèle de Poisson, le modèle binomial négatif, le modèle de Poisson avec inflation du zéro et le modèle binomial négatif avec inflation du zéro. À des fins de comparaisons, la prédiction de la proportion du zéro, la confirmation ou l’infirmation des différentes hypothèses ainsi que la prédiction des moyennes furent utilisées afin de déterminer l’adéquation des différents modèles. Pour ce faire, le nombre d’arrestations des membres de gangs de rue sur le territoire de Montréal fut utilisé pour la période de 2005 à 2007. L’échantillon est composé de 470 hommes, âgés de 18 à 59 ans. Au terme des analyses, le modèle le plus adéquat est le modèle binomial négatif puisque celui-ci produit des résultats significatifs, s’adapte bien aux données observées et produit une proportion de zéro très similaire à celle observée.

Chronic obstructive pulmonary disease in Brazil: mortality and hospitalization trends and rates, 1996-2008

SETTING: Chronic obstructive pulmonary disease (COPD) is the third leading cause of death among adults in Brazil. OBJECTIVE: To evaluate the mortality and hospitalisation trends in Brazil caused by COPD during the period 1996-2008. DESIGN: We used the health official statistics system to obtain data about mortality (1996-2008) and morbidity (1998-2008) due to COPD and all respiratory diseases (tuberculosis: codes A15-16; lung cancer: code C34, and all diseases coded from J40 to 47 in the 10th Revision of the International Classification of Diseases) as the underlying cause, in persons aged 45-74 years. We used the Joinpoint Regression Program log-linear model using Poisson regression that creates a Monte Carlo permutation test to identify points where trend lines change significantly in magnitude/direction to verify peaks and trends. RESULTS: The annual per cent change in age-adjusted death rates due to COPD declined by 2.7% in men (95%CI -3.6 to -1.8) and -2.0% (95%CI -2.9 to -1.0) in women; and due to all respiratory causes it declined by -1.7% (95%CI 2.4 to -1.0) in men and -1.1% (95%CI -1.8 to -0.3) in women. Although hospitalisation rates for COPD are declining, the hospital admission fatality rate increased in both sexes. CONCLUSION: COPD is still a leading cause of mortality in Brazil despite the observed decline in the mortality/hospitalisation rates for both sexes.

Influencia de la inmigración en la elección escolar

This empirical work studies the influence of immigrant students on individuals’ school choice in one of the most populated regions in Spain: Catalonia. It has estimated, following the Poisson model, the probability that a certain school, which immigrant students are already attending, may be chosen by natives as well as by immigrants, respectively. The information provided by the Catalonia School Department presents school characteristics of all the primary and secondary schools in Catalonia during the 2001/02 and 2002/03 school years. The results obtained support the evidence that Catalonia native families avoid schools attended by immigrants. Natives certainly prefer not to interact with immigrants. Private schools are more successful in avoiding immigrants. Finally, the main reason for non-natives’ choice is the presence of other non-natives in the same school.

Aplicação da equação de Paisson-Boltzmann com condição de contorno para regulação carga-potencial a sistemas polieletrolíticos

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

An assessment of the economic impact of climate change on the health sector In Jamaica

Climate change is a naturally occurring phenomenon in which the earth‘s climate goes through cycles of warming and cooling; these changes usually take place incrementally over millennia. Over the past century, there has been an anomalous increase in global temperature, giving rise to accelerated climate change. It is widely accepted that greenhouse gas emissions from human activities such as industries have contributed significantly to the increase in global temperatures. The existence and survival of all living organisms is predicated on the ability of the environment in which they live not only to provide conditions for their basic needs but also conditions suitable for growth and reproduction. Unabated climate change threatens the existence of biophysical and ecological systems on a planetary scale. The present study aims to examine the economic impact of climate change on health in Jamaica over the period 2011-2050. To this end, three disease conditions with known climate sensitivity and importance to Jamaican public health were modelled. These were: dengue fever, leptospirosis and gastroenteritis in children under age 5. Historical prevalence data on these diseases were obtained from the Ministry of Health Jamaica, the Caribbean Epidemiology Centre, the Climate Studies Group Mona, University of the West Indies Mona campus, and the Meteorological Service of Jamaica. Data obtained spanned a twelve-year period of 1995-2007. Monthly data were obtained for dengue and gastroenteritis, while for leptospirosis, the annual number of cases for 1995-2005 was utilized. The two SRES emission scenarios chosen were A2 and B2 using the European Centre Hamburg Model (ECHAM) global climate model to predict climate variables for these scenarios. A business as usual (BAU) scenario was developed using historical disease data for the period 2000-2009 (dengue fever and gastroenteritis) and 1995-2005 (leptospirosis) as the reference decades for the respective diseases. The BAU scenario examined the occurrence of the diseases in the absence of climate change. It assumed that the disease trend would remain unchanged over the projected period and the number of cases of disease for each decade would be the same as the reference decade. The model used in the present study utilized predictive empirical statistical modelling to extrapolate the climate/disease relationship in time, to estimate the number of climate change-related cases under future climate change scenarios. The study used a Poisson regression model that considered seasonality and lag effects to determine the best-fit model in relation to the diseases under consideration. Zhang and others (2008), in their review of climate change and the transmission of vector-borne diseases, found that: ―Besides climatic variables, few of them have included other factors that can affect the transmission of vector-borne disease….‖ (Zhang 2008) Water, sanitation and health expenditure are key determinants of health. In the draft of the second communication to IPCC, Jamaica noted the vulnerability of public health to climate change, including sanitation and access to water (MSJ/UNDP, 2009). Sanitation, which in its broadest context includes the removal of waste (excreta, solid, or other hazardous waste), is a predictor of vector-borne diseases (e.g. dengue fever), diarrhoeal diseases (such as gastroenteritis) and zoonoses (such as leptospirosis). In conceptualizing the model, an attempt was made to include non-climate predictors of these climate-sensitive diseases. The importance of sanitation and water access to the control of dengue, gastroenteritis and leptospirosis were included in the Poisson regression model. The Poisson regression model obtained was then used to predict the number of disease cases into the future (2011-2050) for each emission scenario. After projecting the number of cases, the cost associated with each scenario was calculated using four cost components. 1. Treatment cost morbidity estimate. The treatment cost for the number of cases was calculated using reference values found in the literature for each condition. The figures were derived from studies of the cost of treatment and represent ambulatory and non-fatal hospitalized care for dengue fever and gastroenteritis. Due to the paucity of published literature on the health care cost associated with leptospirosis, only the cost of diagnosis and antibiotic therapy were included in the calculation. 2. Mortality estimates. Mortality estimates are recorded as case fatality rates. Where local data were available, these were utilized. Where these were unavailable, appropriate reference values from the literature were used. 3. Productivity loss. Productivity loss was calculated using a human capital approach, by multiplying the expected number of productive days lost by the caregiver and/or the infected person, by GDP per capita per day (US$ 14) at 2008 GDP using 2008 US$ exchange rates. 4. No-option cost. The no-option cost refers to adaptation strategies for the control of dengue fever which are ongoing and already a part of the core functions of the Vector Control Division of the Ministry of Health, Jamaica. An estimated US$ 2.1 million is utilized each year in conducting activities to prevent the post-hurricane spread of vector borne diseases and diarrhoea. The cost includes public education, fogging, laboratory support, larvicidal activities and surveillance. This no-option cost was converted to per capita estimates, using population estimates for Jamaica up to 2050 obtained from the Statistical Institute of Jamaica (STATIN, 2006) and the assumption of one expected major hurricane per decade. During the decade 2000-2009, Jamaica had an average inflation of 10.4% (CIA Fact book, last updated May 2011). This average decadal inflation rate was applied to the no-option cost, which was inflated by 10% for each successive decade to adjust for changes in inflation over time.

Temporal Trends of Asthma Mortality Rates in Brazil from 1980 to 2010

Objective. Mortality from asthma has varied among countries during the last several decades. This study aimed to identify temporal trends of asthma mortality in Brazil from 1980 to 2010. Method. We analyzed 6840 deaths of patients aged 5-34 years that occurred in Brazil with the underlying cause of asthma. We applied a log-linear model using Poisson regression to verify peaks and trends. We also calculated the point estimation and 95% confidence interval (CI 95%) of the annual percent change (APC) of the mortality rates, and the average annual percent change (AAPC) for 2001-2010. Results. A decline was observed from 1980 to 1992 [APC = -3.4 (-5.0 to -1.8)], followed by a nonsignificant rise until 1996 [APC = 6.8 (-1.4 to 15.6)], and a new downward trend from 1997 to 2010 [APC = -2.7 (-3.9 to -1.6)]. The APCs varied according to age strata: 5-14 years from 1980 to 2010 [-0.3 (-1.1 to 0.5)]; 15-24 years from 1980 to 1991 [-2.1 (-5.0 to 0.9)], from 1992 to 1996 [6.8 (-6.7 to 22.2)], and from 1997 to 2010 [-3.9 (-5.7 to -2.0)]; 24-25 years from 1980 to 1992 [-2.5 (-4.6 to -0.3)], from 1993 to 1995 [12.0 (-21.1 to 59.1)], and from 1996-2010 [-1.7 (-3.0 to -0.4)]. AAPC from 2001 to 2010 was -1.7 (-3.0 to -0.4); the decline for this period was significant for patients over 15 years old, women, and those living in the Southeast region. Conclusion. Asthma mortality rates in Brazil have been declining since the late 1990s.

Advances in Dynamic Modeling and Computation for Count Data

A class of multi-process models is developed for collections of time indexed count data. Autocorrelation in counts is achieved with dynamic models for the natural parameter of the binomial distribution. In addition to modeling binomial time series, the framework includes dynamic models for multinomial and Poisson time series. Markov chain Monte Carlo (MCMC) and Po ́lya-Gamma data augmentation (Polson et al., 2013) are critical for fitting multi-process models of counts. To facilitate computation when the counts are high, a Gaussian approximation to the P ́olya- Gamma random variable is developed.

Three applied analyses are presented to explore the utility and versatility of the framework. The first analysis develops a model for complex dynamic behavior of themes in collections of text documents. Documents are modeled as a “bag of words”, and the multinomial distribution is used to characterize uncertainty in the vocabulary terms appearing in each document. State-space models for the natural parameters of the multinomial distribution induce autocorrelation in themes and their proportional representation in the corpus over time.

The second analysis develops a dynamic mixed membership model for Poisson counts. The model is applied to a collection of time series which record neuron level firing patterns in rhesus monkeys. The monkey is exposed to two sounds simultaneously, and Gaussian processes are used to smoothly model the time-varying rate at which the neuron’s firing pattern fluctuates between features associated with each sound in isolation.

The third analysis presents a switching dynamic generalized linear model for the time-varying home run totals of professional baseball players. The model endows each player with an age specific latent natural ability class and a performance enhancing drug (PED) use indicator. As players age, they randomly transition through a sequence of ability classes in a manner consistent with traditional aging patterns. When the performance of the player significantly deviates from the expected aging pattern, he is identified as a player whose performance is consistent with PED use.

All three models provide a mechanism for sharing information across related series locally in time. The models are fit with variations on the P ́olya-Gamma Gibbs sampler, MCMC convergence diagnostics are developed, and reproducible inference is emphasized throughout the dissertation.

Extended truncated Tweedie-Poisson model

It has been argued that by truncating the sample space of the negative binomial and of the inverse Gaussian-Poisson mixture models at zero, one is allowed to extend the parameter space of the model. Here that is proved to be the case for the more general three parameter Tweedie-Poisson mixture model. It is also proved that the distributions in the extended part of the parameter space are not the zero truncation of mixed poisson distributions and that, other than for the negative binomial, they are not mixtures of zero truncated Poisson distributions either. By extending the parameter space one can improve the fit when the frequency of one is larger and the right tail is heavier than is allowed by the unextended model. Considering the extended model also allows one to use the basic maximum likelihood based inference tools when parameter estimates fall in the extended part of the parameter space, and hence when the m.l.e. does not exist under the unextended model. This extended truncated Tweedie-Poisson model is proved to be useful in the analysis of words and species frequency count data.

Randomized observation periods for the compound Poisson risk model: Dividends

In the framework of the classical compound Poisson process in collective risk theory, we study a modification of the horizontal dividend barrier strategy by introducing random observation times at which dividends can be paid and ruin can be observed. This model contains both the continuous-time and the discrete-time risk model as a limit and represents a certain type of bridge between them which still enables the explicit calculation of moments of total discounted dividend payments until ruin. Numerical illustrations for several sets of parameters are given and the effect of random observation times on the performance of the dividend strategy is studied.

Estimating the number of ozone peaks in Mexico City using a non-homogeneous Poisson model

In this paper, we consider the problem of estimating the number of times an air quality standard is exceeded in a given period of time. A non-homogeneous Poisson model is proposed to analyse this issue. The rate at which the Poisson events occur is given by a rate function lambda(t), t >= 0. This rate function also depends on some parameters that need to be estimated. Two forms of lambda(t), t >= 0 are considered. One of them is of the Weibull form and the other is of the exponentiated-Weibull form. The parameters estimation is made using a Bayesian formulation based on the Gibbs sampling algorithm. The assignation of the prior distributions for the parameters is made in two stages. In the first stage, non-informative prior distributions are considered. Using the information provided by the first stage, more informative prior distributions are used in the second one. The theoretical development is applied to data provided by the monitoring network of Mexico City. The rate function that best fit the data varies according to the region of the city and/or threshold that is considered. In some cases the best fit is the Weibull form and in other cases the best option is the exponentiated-Weibull. Copyright (C) 2007 John Wiley & Sons, Ltd.

The Poisson-exponential regression model under different latent activation schemes

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

The Conway-Maxwell-Poisson-generalized gamma regression model with long-term survivors

In this paper, we proposed a flexible cure rate survival model by assuming the number of competing causes of the event of interest following the Conway-Maxwell distribution and the time for the event to follow the generalized gamma distribution. This distribution can be used to model survival data when the hazard rate function is increasing, decreasing, bathtub and unimodal-shaped including some distributions commonly used in lifetime analysis as particular cases. Some appropriate matrices are derived in order to evaluate local influence on the estimates of the parameters by considering different perturbations, and some global influence measurements are also investigated. Finally, data set from the medical area is analysed.

A non-homogeneous poisson model with spatial anisotropy applied to ozone data from Mexico City

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

A Bayesian analysis of the Conway-Maxwell-Poisson cure rate model

The purpose of this paper is to develop a Bayesian analysis for the right-censored survival data when immune or cured individuals may be present in the population from which the data is taken. In our approach the number of competing causes of the event of interest follows the Conway-Maxwell-Poisson distribution which generalizes the Poisson distribution. Markov chain Monte Carlo (MCMC) methods are used to develop a Bayesian procedure for the proposed model. Also, some discussions on the model selection and an illustration with a real data set are considered.

The Poisson-exponential regression model under different latent activation schemes

In this paper, a new family of survival distributions is presented. It is derived by considering that the latent number of failure causes follows a Poisson distribution and the time for these causes to be activated follows an exponential distribution. Three different activation schemes are also considered. Moreover, we propose the inclusion of covariates in the model formulation in order to study their effect on the expected value of the number of causes and on the failure rate function. Inferential procedure based on the maximum likelihood method is discussed and evaluated via simulation. The developed methodology is illustrated on a real data set on ovarian cancer.