Short-term forecasting of daily COVID-19 cases in Brazil by using the Holt’s model

Introduction: We evaluated the performance of the Holt’s model to forecast the daily COVID-19 reported cases in Brazil and three Brazilian states. Methods: We chose the date of the first COVID-19 case to April 25, 2020, as the training period, and April 26 to May 3, 2020, as the test period. Results: The Holt’s model performed well in forecasting the cases in Brazil and in São Paulo and Minas Gerais states, but the forecasts were underestimated in Rio de Janeiro state. Conclusions: The Holt’s model can be an adequate shortterm forecasting method if their assumptions are adequately verified and validated by experts

Using a Bayesian change-point statistical model with autoregressive terms to study the monthly number of dispensed asthma medications by public health services

In this paper, it is proposed a Bayesian analysis of a time series in the presence of a random change-point and autoregressive terms. The development of this model was motivated by a data set related to the monthly number of asthma medications dispensed by the public health services of Ribeirão Preto, Southeast Brazil, from 1999 to 2011. A pronounced increase trend has been observed from 1999 to a specific change-point, with a posterior decrease until the end of the series. In order to obtain estimates for the parameters of interest, a Bayesian Markov Chain Monte Carlo (MCMC) simulation procedure using the Gibbs sampler algorithm was developed. The Bayesian model with autoregressive terms of order 1 fits well to the data, allowing to estimate the change-point at July 2007, and probably reflecting the results of the new health policies and previously adopted programs directed toward patients with asthma. The results imply that the present model is useful to analyse the monthly number of dispensed asthma medications and it can be used to describe a broad range of epidemiological time series data where a change-point is present.Peer Reviewe

ESTIMAÇÃO DOS PARÂMETROS DA DISTRIBUIÇÃO BETA-BINOMIAL: UMA APLICAÇÃO USANDO O SOFTWARE SAS

In this paper we describe the parameter estimation of the beta-binomial distribution using the procedure NLMIXED of the SAS software. The beta-binomial distribution is a discrete mixture distribution which can capture overdispersion in the data. The estimation of parameters of the beta-binomial distribution can lead to computational problems, since it does not belong to the exponential family and there are not explicit solutions for the maximum likelihood estimation. Using a real dataset, we show that the SAS software can be satisfactorily used for the estimation of the parameters. We also consider the possibility of including a covariate in the model. The SAS codes used in this paper are given in an Appendix.http://dx.doi.org/10.5902/2179460X17512Neste artigo nós descrevemos a estimação dos parâmetros da distribuição beta-binomial usando o procedimento NLMIXED do software SAS. A distribuição beta-binomial é uma distribuição de misturas discreta capaz de capturar a superdispersão dos dados. A estimação dos parâmetros de uma distribuição beta-binomial pode oferecer problemas computacionais, dado que ela não pertence a uma família exponencial e não há soluções explícitas para o método da máxima verossimilhança. Usando dados reais, nós mostramos que o software SAS pode ser satisfatoriamente usado para a estimação dos parâmetros. Nós também consideramos a possibilidade de incluir uma covariável no modelo. As linhas de comando SAS usadas neste artigo não disponibilizadas em um anexo

Modelagem Bayesiana do risco de infecção tuberculosa para estudos com perdas de seguimento

OBJECTIVE: To develop a statistical model based on Bayesian methods to estimate the risk of tuberculosis infection in studies including individuals lost to follow-up, and to compare it with a classic deterministic model. METHODS: The proposed stochastic model is based on a Gibbs sampling algorithm that uses information of lost to follow-up at the end of a longitudinal study. For simulating the unknown number of reactors at the end of the study and lost to follow-up, but not reactors at time 0, a latent variable was introduced in the new model. An exercise of application of both models in the comparison of the estimates of interest was presented. RESULTS: The point estimates obtained from both models are near identical; however, the Bayesian model allowed the estimation of credible intervals as measures of precision of the estimated parameters. CONCLUSIONS: The Bayesian model can be valuable in longitudinal studies with low adherence to follow-up.OBJETIVO: Desarrollar un modelo estadístico en basado en métodos Bayesianos para estimar el riesgo de infección tuberculosa en estudios con pérdidas de seguimiento, comparándolo con un modelo clásico deterministico. MÉTODOS: El modelo estocástico propuesto se basa en un algoritmo de muestreadotes de Gibbs, utilizando las informaciones de pérdidas de seguimiento al final de un estudio longitudinal. Para simular el número desconocido de individuos reactores al final del estudio y pérdidas de seguimiento, pero no reactores en el tiempo inicial, una variable latente fue introducida en el nuevo modelo. Se presenta un ejercicio de aplicación de ambos modelos para comparación de las estimaciones generadas. RESULTADOS: Las estimaciones puntuales suministradas por ambos modelos son próximas, pero el modelo Bayesiano presentó la ventaja de traer los intervalos de credibilidad como medidas de variabilidad muestral de los parámetros estimados. CONCLUSIONES: El modelo Bayesiano puede ser útil en estudios longitudinales con baja adhesión al seguimiento.OBJETIVO: Desenvolver um modelo estatístico baseado em métodos Bayesianos para estimar o risco de infecção tuberculosa em estudos com perdas de seguimento, comparando-o com um modelo clássico determinístico. MÉTODOS: O modelo estocástico proposto é baseado em um algoritmo de amostradores de Gibbs, utilizando as informações de perdas de seguimento ao final de um estudo longitudinal. Para simular o número desconhecido de indivíduos reatores ao final do estudo e perdas de seguimento, mas não reatores no tempo inicial, uma variável latente foi introduzida no novo modelo. Apresenta-se um exercício de aplicação de ambos os modelos para comparação das estimativas geradas. RESULTADOS: As estimativas pontuais fornecidas por ambos os modelos são próximas, mas o modelo Bayesiano apresentou a vantagem de trazer os intervalos de credibilidade como medidas da variabilidade amostral dos parâmetros estimados. CONCLUSÕES: O modelo Bayesiano pode ser útil em estudos longitudinais com baixa adesão ao seguimento

Using a Bayesian change-point statistical model with autoregressive terms to study the monthly number of dispensed asthma medications by public health services

In this paper, it is proposed a Bayesian analysis of a time series in the presence of a random change-point and autoregressive terms. The development of this model was motivated by a data set related to the monthly number of asthma medications dispensed by the public health services of Ribeirão Preto, Southeast Brazil, from 1999 to 2011. A pronounced increase trend has been observed from 1999 to a specific change-point, with a posterior decrease until the end of the series. In order to obtain estimates for the parameters of interest, a Bayesian Markov Chain Monte Carlo (MCMC) simulation procedure using the Gibbs sampler algorithm was developed. The Bayesian model with autoregressive terms of order 1 fits well to the data, allowing to estimate the change-point at July 2007, and probably reflecting the results of the new health policies and previously adopted programs directed toward patients with asthma. The results imply that the present model is useful to analyse the monthly number of dispensed asthma medications and it can be used to describe a broad range of epidemiological time series data where a change-point is present

Impact of children with complex chronic conditions on costs in a tertiary referral hospital

OBJECTIVES To investigate the impact of complex chronic conditions on the use of healthcare resources and hospitalization costs in a pediatric ward of a public tertiary referral university hospital in Brazil. METHODS This is a longitudinal study with retrospective data collection. Overall, three one-year periods, separated by five-year intervals (2006, 2011, and 2016), were evaluated. Hospital costs were calculated in three systematic samples of 100 patients each, consisting of patients with and without complex chronic conditions in proportion to their participation in the studied year. RESULTS Over the studied period, the hospital received 2,372 admissions from 2,172 patients. The proportion of hospitalized patients with complex chronic conditions increased from 13.3% in 2006 to 16.9% in 2016 as a result of a greater proportion of neurologically impaired children, which rose from 6.6% to 11.6% of the total number of patients in the same period. Patients’ complexity also progressively increased, which greatly impacted the use of healthcare resources and costs, increasing by 11.6% from 2006 (R$1,300,879.20) to 2011 (R$1,452,359.71) and 9.4% from 2011 to 2016 (R$1,589,457.95). CONCLUSIONS Hospitalizations of pediatric patients with complex chronic conditions increased from 2006 to 2016 in a Brazilian tertiary referral university hospital, associated with an important impact on hospital costs. Policies to reduce these costs in Brazil are greatly needed

Uma Abordagem Bayesiana na Análise de Dados Longitudinais Obtidos por Amostragem com Reposição

O objetivo deste estudo é mostrar a aplicabilidade de um modelo Bayesiano, proposto para a análise de um conjunto de dados médicos longitudinais com uma estrutura não usual. Um único indivíduo pode vir a participar da pesquisa mais de uma vez e, a cada participação, dados clínicos e laboratoriais podem classificá-lo em um dentre quatro grupos de interesse. Tal experimento foi assim delineado por utilizar uma população restrita (pacientes submetidos a transplante de medula óssea). Observa-se que o modelo proposto mostrou-se uma importante ferramenta para a análise destes dados

Using a Bayesian change-point statistical model with autoregressive terms to study the monthly number of dispensed asthma medications by public health services

In this paper, it is proposed a Bayesian analysis of a time series in the presence of a random change-point and autoregressive terms. The development of this model was motivated by a data set related to the monthly number of asthma medications dispensed by the public health services of Ribeirao Preto, Southeast Brazil, from 1999 to 2011. A pronounced increase trend has been observed from 1999 to a specific change-point, with a posterior decrease until the end of the series. In order to obtain estimates for the parameters of interest, a Bayesian Markov Chain Monte Carlo (MCMC) simulation procedure using the Gibbs sampler algorithm was developed. The Bayesian model with autoregressive terms of order 1 fits well to the data, allowing to estimate the change-point at July 2007, and probably reflecting the results of the new health policies and previously adopted programs directed toward patients with asthma. The results imply that the present model is useful to analyse the monthly number of dispensed asthma medications and it can be used to describe a broad range of epidemiological time series data where a change-point is present

Count data time series models based on Double Poisson distribution

Dados de s´eries temporais s~ao originados a partir de estudos em que se reportam, por exemplo, taxas de mortalidade, n´umero de hospitaliza¸c~oes, de infec¸c~oes por alguma doen¸ca ou outro evento de interesse, em per´?odos definidos (dia, semana, m^es ou ano), objetivando-se observar tend^encias, sazonalidades ou fatores associados. Dados de contagem s~ao aqueles representados pelas vari´aveis quantitativas discretas, ou seja, observa¸c~oes que assumem valores inteiros, no intervalo {0, 1, 2, 3, ...}, por exemplo, o n´umero de filhos de casais residentes em um bairro. Diante dessa particularidade, ferramentas estat´?sticas adequadas devem ser utilizadas, e modelos baseados na distribui¸c~ao de Poisson apresentam-se como op¸c~oes mais indicadas do que os baseados nos m´etodos propostos por Box e Jenkins (2008), usualmente utilizados para an´alise de dados cont´?nuos, mas empregados para dados discretos, ap´os transforma¸c~oes logar´?tmicas. Uma limita¸c~ao da distribui¸c~ao de Poisson ´e que ela assume m´edia e vari^ancia iguais, sendo um obst´aculo nos casos em que h´a superdispers~ao (vari^ancia maior que a m´edia) ou subdispers~ao (vari^ancia menor que a m´edia). Diante disso, a distribui¸c~ao Poisson Dupla, proposta por Efron (1986), surge como alternativa, pois permite se estimarem os par^ametros de m´edia e vari^ancia, nos casos em que a vari^ancia dos dados ´e menor, igual ou maior que a m´edia, fornecendo grande flexibilidade aos modelos. Este trabalho teve como objetivo principal o desenvolvimento de modelos Bayesianos de s´eries temporais para dados de contagem, utilizando-se distribui¸c~oes de probabilidade para vari´aveis discretas, tais como de Poisson e Poisson Dupla. Al´em disso, foi introduzido um modelo baseado na distribui¸c~ao Poisson Dupla para dados de contagem com excesso de zeros. Os resultados obtidos pelo ajuste dos modelos de s´eries temporais baseados na distribui¸c~ao Poisson Dupla foram comparados com aqueles obtidos por meio do uso da distribui¸c~ao de Poisson. Como aplica¸c~oes principais, foram apresentados resultados obtidos pelo ajuste de modelos para dados de registros de acidentes com picadas de cobras, no Estado de S~ao Paulo, e picadas de escorpi~oes, na cidade de Ribeir~ao Preto, SP, entre os anos de 2007 e 2014. Com rela¸c~ao a esta ´ultima aplica¸c~ao, foram consideradas covari´aveis referentes a dados clim´aticos, como temperaturas m´aximas e m´?nimas m´edias mensais e precipita¸c~ao. Nas situa¸c~oes em que a vari^ancia era diferente da m´edia, modelos baseados na distribui¸c~ao Poisson Dupla mostraram melhor ajuste aos dados, quando comparados aos modelos de Poisson.Time series data are derived from studies in which there are reported mortality, number of hospitalizations infections by disease or other event of interest per day, week, month or year, in order to observe trends, seasonality or associated factors. Count data are represented by discrete quantitative variables, i.e. observations that take integer values in the range {0, 1, 2, 3, ...}. In view of this particular characteristic, such data must be analyzed by adequate statistical tools and the Poisson distribution is an option for modeling, being more suitable than models based on methods proposed by Box and Jenkins (2008), usually applied for continuous data, but used in the modeling of discrete data after logarithmic transformation. A limitation of the Poisson distribution is that it assumes equal mean and variance being an obstacle in cases which there are data overdispersion (variance higher than mean) or underdispersion (variance lower than mean). Therefore the Double Poisson distribution, proposed by Efron (1986), is an alternative because it allows to estimate the mean and variance parameters in cases wich variance of the data is lower, equal, or higher than mean providing great flexibility to the models. This work aims to develop time series models for count data, under Bayesian approach using probability distributions for discrete variables such as Poisson and Double Poisson. Furthermore it will be introduced a zero-inflated Double Poisson model to excess zeros counting data. The results obtained by adjusting the time series models based on Double Poisson distribution are compared with those obtained by considering the Poisson distribution. As main applications modeling of snake bites reports in the State of S~ao Paulo and scorpion stings in the city of Ribeir~ao Preto considering covariates as maximum and minimum average monthly temperatures and rainfall among the years 2007 and 2014 will be presented. Regression models based on double Poisson distribution showed a better fit to the data, when compared to Poisson models