Convex relaxation of mixture regression with efficient algorithms

We develop a convex relaxation of maximum a posteriori estimation of a mixture of regression models. Although our relaxation involves a semidefinite matrix variable, we reformulate the problem to eliminate the need for general semidefinite programming. In particular, we provide two reformulations that admit fast algorithms. The first is a max-min spectral reformulation exploiting quasi-Newton descent. The second is a min-min reformulation consisting of fast alternating steps of closed-form updates. We evaluate the methods against Expectation-Maximization in a real problem of motion segmentation from video data.

Use of Poisson spatiotemporal regression models for the Brazilian Amazon Forest: malaria count data

INTRODUÇÃO: A malaria é uma doença endêmica na região da Amazônia Brasileira, e a detecção de possíveis fatores de risco pode ser de grande interesse às autoridades em saúde pública. O objetivo deste artigo é investigar a associação entre variáveis ambientais e os registros anuais de malária na região amazônica usando métodos bayesianos espaço-temporais. MÉTODOS: Utilizaram-se modelos de regressão espaço-temporais de Poisson para analisar os dados anuais de contagem de casos de malária entre os anos de 1999 a 2008, considerando a presença de alguns fatores como a taxa de desflorestamento. em uma abordagem bayesiana, as inferências foram obtidas por métodos Monte Carlo em cadeias de Markov (MCMC) que simularam amostras para a distribuição conjunta a posteriori de interesse. A discriminação de diferentes modelos também foi discutida. RESULTADOS: O modelo aqui proposto sugeriu que a taxa de desflorestamento, o número de habitants por km² e o índice de desenvolvimento humano (IDH) são importantes para a predição de casos de malária. CONCLUSÕES: É possível concluir que o desenvolvimento humano, o crescimento populacional, o desflorestamento e as alterações ecológicas associadas a estes fatores estão associados ao aumento do risco de malária. Pode-se ainda concluir que o uso de modelos de regressão de Poisson que capturam o efeito temporal e espacial em um enfoque bayesiano é uma boa estratégia para modelar dados de contagem de malária.

The Poisson-exponential regression model under different latent activation schemes

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

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.

Finite mixture regression model with random effects: application to neonatal hospital length of stay

A two-component mixture regression model that allows simultaneously for heterogeneity and dependency among observations is proposed. By specifying random effects explicitly in the linear predictor of the mixture probability and the mixture components, parameter estimation is achieved by maximising the corresponding best linear unbiased prediction type log-likelihood. Approximate residual maximum likelihood estimates are obtained via an EM algorithm in the manner of generalised linear mixed model (GLMM). The method can be extended to a g-component mixture regression model with the component density from the exponential family, leading to the development of the class of finite mixture GLMM. For illustration, the method is applied to analyse neonatal length of stay (LOS). It is shown that identification of pertinent factors that influence hospital LOS can provide important information for health care planning and resource allocation. (C) 2002 Elsevier Science B.V. All rights reserved.

Modelling inpatient length of stay by a hierarchical mixture regression via the EM algorithm

The modelling of inpatient length of stay (LOS) has important implications in health care studies. Finite mixture distributions are usually used to model the heterogeneous LOS distribution, due to a certain proportion of patients sustaining-a longer stay. However, the morbidity data are collected from hospitals, observations clustered within the same hospital are often correlated. The generalized linear mixed model approach is adopted to accommodate the inherent correlation via unobservable random effects. An EM algorithm is developed to obtain residual maximum quasi-likelihood estimation. The proposed hierarchical mixture regression approach enables the identification and assessment of factors influencing the long-stay proportion and the LOS for the long-stay patient subgroup. A neonatal LOS data set is used for illustration, (C) 2003 Elsevier Science Ltd. All rights reserved.

Modelling HIV/AIDS length of stay in Portugal

Tese apresentada como requisito parcial para obtenção do grau de Doutor em Estatística e Gestão de Informação pelo Instituto Superior de Estatística e Gestão de Informação da Universidade Nova de Lisboa

Semiparametric estimation of count regression models

This paper develops a semiparametric estimation approach for mixed count regression models based on series expansion for the unknown density of the unobserved heterogeneity. We use the generalized Laguerre series expansion around a gamma baseline density to model unobserved heterogeneity in a Poisson mixture model. We establish the consistency of the estimator and present a computational strategy to implement the proposed estimation techniques in the standard count model as well as in truncated, censored, and zero-inflated count regression models. Monte Carlo evidence shows that the finite sample behavior of the estimator is quite good. The paper applies the method to a model of individual shopping behavior. © 1999 Elsevier Science S.A. All rights reserved.

Multi-level zero-inflated Poisson regression modelling of correlated count data with excess zeros

Count data with excess zeros relative to a Poisson distribution are common in many biomedical applications. A popular approach to the analysis of such data is to use a zero-inflated Poisson (ZIP) regression model. Often, because of the hierarchical Study design or the data collection procedure, zero-inflation and lack of independence may occur simultaneously, which tender the standard ZIP model inadequate. To account for the preponderance of zero counts and the inherent correlation of observations, a class of multi-level ZIP regression model with random effects is presented. Model fitting is facilitated using an expectation-maximization algorithm, whereas variance components are estimated via residual maximum likelihood estimating equations. A score test for zero-inflation is also presented. The multi-level ZIP model is then generalized to cope with a more complex correlation structure. Application to the analysis of correlated count data from a longitudinal infant feeding study illustrates the usefulness of the approach.

Extreme temperatures and emergency department admissions for childhood asthma in Brisbane, Australia

Objectives To examine the effect of extreme temperatures on emergency department admissions (EDAs) for childhood asthma. Methods An ecological design was used in this study. A Poisson linear regression model combined with a distributed lag non-linear model was used to quantify the effect of temperature on EDAs for asthma among children aged 0–14 years in Brisbane, Australia, during January 2003–December 2009, while controlling for air pollution, relative humidity, day of the week, season and long-term trends. The model residuals were checked to identify whether there was an added effect due to heat waves or cold spells. Results There were 13 324 EDAs for childhood asthma during the study period. Both hot and cold temperatures were associated with increases in EDAs for childhood asthma, and their effects both appeared to be acute. An added effect of heat waves on EDAs for childhood asthma was observed, but no added effect of cold spells was found. Male children and children aged 0–4 years were most vulnerable to heat effects, while children aged 10–14 years were most vulnerable to cold effects. Conclusions Both hot and cold temperatures seemed to affect EDAs for childhood asthma. As climate change continues, children aged 0–4 years are at particular risk for asthma.

Associations between extreme precipitation and childhood hand, foot and mouth disease in urban and rural areas in Hefei, China

Background Understanding the relationship between extreme weather events and childhood hand, foot and mouth disease (HFMD) is important in the context of climate change. This study aimed to quantify the relationship between extreme precipitation and childhood HFMD in Hefei, China, and further, to explore whether the association varied across urban and rural areas. Methods Daily data on HFMD counts among children aged 0–14 years from 2010 January 1st to 2012 December 31st were retrieved from Hefei Center for Disease Control and Prevention. Daily data on mean temperature, relative humidity and precipitation during the same period were supplied by Hefei Bureau of Meteorology. We used a Poisson linear regression model combined with a distributed lag non-linear model to assess the association between extreme precipitation (≥ 90th precipitation) and childhood HFMD, controlling for mean temperature, humidity, day of week, and long-term trend. Results There was a statistically significant association between extreme precipitation and childhood HFMD. The effect of extreme precipitation on childhood HFMD was the greatest at six days lag, with a 5.12% (95% confident interval: 2.7–7.57%) increase of childhood HFMD for an extreme precipitation event versus no precipitation. Notably, urban children and children aged 0–4 years were particularly vulnerable to the effects of extreme precipitation. Conclusions Our findings indicate that extreme precipitation may increase the incidence of childhood HFMD in Hefei, highlighting the importance of protecting children from forthcoming extreme precipitation, particularly for those who are young and from urban areas.

Imputation en présence de données contenant des zéros

L’imputation simple est très souvent utilisée dans les enquêtes pour compenser pour la non-réponse partielle. Dans certaines situations, la variable nécessitant l’imputation prend des valeurs nulles un très grand nombre de fois. Ceci est très fréquent dans les enquêtes entreprises qui collectent les variables économiques. Dans ce mémoire, nous étudions les propriétés de deux méthodes d’imputation souvent utilisées en pratique et nous montrons qu’elles produisent des estimateurs imputés biaisés en général. Motivé par un modèle de mélange, nous proposons trois méthodes d’imputation et étudions leurs propriétés en termes de biais. Pour ces méthodes d’imputation, nous considérons un estimateur jackknife de la variance convergent vers la vraie variance, sous l’hypothèse que la fraction de sondage est négligeable. Finalement, nous effectuons une étude par simulation pour étudier la performance des estimateurs ponctuels et de variance en termes de biais et d’erreur quadratique moyenne.

Impacto da cárie precoce severa na infância na qualidade de vida relacionada à saúde bucal de pré-escolares sob privação social

Early childhood caries, especially in its severe form, which is characterized by an acute and aggressive nature, can have negative impacts on thequality of life of a child, due to effects such as difficulty in chewing, decreased appetite, weight loss, insomnia, changes in behavior and a decreased performance in school, among others. Moreover, the quality of life of the child`s family can also be affected, as the pain and discomfort caused by this type of caries result in loss of working days of parents, spending on dental treatments, changes in sleep patterns and stress. The aim of this study was to evaluate the impact of severe early childhood caries in the Oral Health-Related Quality of Life (OHRQoL) of public daycares`s preschool children through the Escala de Impacto da Saúde Bucal na Primeira Infância, a Brazilian version of the Early Childhood Oral Health Impact Scale (ECOHIS). A single calibrated examiner (kappa=1.0) evaluated, through the dmfs index, the oral health of 116 children aged between 3 and 5, which were included in one of three study groups: "caries-free", "not-severe early childhood caries" and "severe early childhood caries". The parents responded to ECOHIS, to assess their perception regarding the OHRQoL of their children, and a questionnaire on socioeconomic conditions. The OHRQoL was measured through the total scores and domains of ECOHIS. Descriptive analysis, Mann-Whitney test, Kruskal-Wallis test, chi-square test and Poisson multiple regression with robust variance were used. Among the children observed, 38.8% were caries-free, 27.6% showed not-severe early childhood caries and 33.6% showed severe early childhood caries. Regarding the total score of ECOHIS, severe early childhood caries had a greater negative impact on OHRQoL, compared to caries-free and not-severe early childhood caries groups (p <0.001). Regarding the child subscale, there was significant difference between the "severe early childhood caries" group and the other groups in all domains, except for theone of self-image / social interaction. In the family subscale domains, there was statistical significance between the severe early childhood caries and the caries-free groups in all domains (p <0.001), whereas between the "severe early childhood caries and not-severe early childhood caries groups there was a statistically significant difference only in the domain of parental anguish (p <0.001). Multivariate analysis showed that early childhood caries and the parent`s age were significantly associated to OHRQoL (p <0.05), independently of the other variables in the model. The presence of severe early childhood caries resulted in greater negative impact on OHRQoL (AdjPR= 6.016; 95%CI = 3.12 11.56; p<0.001), while older parents reported better OHRQoL (AdjPR = 0.603; 95%CI = 0.428 - 0.850; p = 0.004). The presence of severe early childhood caries had a negative impact on OHRQoL of preschool children and their families.

Desigualdades sociais na prevalência de doenças crônicas no Brasil, PNAD-2003

Os inquéritos de saúde de base populacional constituem o principal instrumento utilizado para conhecer a prevalência de doenças crônicas, de restrições de atividades e de uso de serviços de saúde. Com base nos dados da PNAD-2003, foram estimadas as prevalências das 12 doenças crônicas pesquisadas, segundo sexo, idade, cor, escolaridade, macrorregião de residência e situação urbana ou rural do domicílio. Foram analisados a presença de limitações e o uso de serviços de saúde segundo a presença de doença crônica. Utilizando regressão de Poisson, foram estimadas as razões de prevalências ajustadas por idade, sexo, macrorregião de residência e tipo de respondente. A prevalência de pelo menos uma doença crônica aumentou com a idade, foi maior entre mulheres, indígenas, pessoas com menor escolaridade, cidadãos detentores de plano de saúde, migrantes de outros estados, residentes em áreas urbanas e moradores da região Sul. A presença de doença crônica provocou aumento de limitação de atividades e da demanda por serviços de saúde. As condições mais prevalentes foram: doença de coluna, hipertensão, artrite e depressão. Foi detectada significativa desigualdade social no padrão das doenças crônicas, segundo gênero, cor/raça, nível de escolaridade, região de residência e situação do domicílio.