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

• J.A M. de Queiroz ^[1] ; D.C. Aragon ^[2] ; L.M. de Mello ^[2] ; I.T.S. Previdelli ^[1] ; E.Z. Martinez ^[2]
  1. [1] Universidade Estadual de Maringá

     Universidade Estadual de Maringá

     Brasil

     
  2. [2] Universidade de São Paulo

     Universidade de São Paulo

     Brasil

     
• Localización: Sort: Statistics and Operations Research Transactions, ISSN 1696-2281, Vol. 42, Nº. 1, 2018, págs. 3-26
• Idioma: inglés
• Enlaces
  • Texto completo (pdf)
• Resumen

  • n 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.

• Referencias bibliográficas
  • Achcar, J.A. and Loibel, S. (1998). Constant hazard models with a change-point: a Bayesian analysis using Markov Chain Monte Carlo methods....
  • Achcar, J.A., Rodrigues, E.R., Paulino, C.D. and Soares, P. (2010). Non-homogeneous Poisson models with a change-point: an application to...
  • Achcar, J.A., Rodrigues, E.R. and Tzintzun, G. (2011). Using non-homogeneous Poisson models with multiple change-points to estimate the number...
  • Achcar, J.A., Martinez, E.Z., Ruffino-Netto, A., Paulino, C.D. and Soares P. (2008). A statistical model investigating the prevalence of tuberculosis...
  • Barry, D. and Hartigan, J.A. (1993). A Bayesian analysis for change point problems. Journal of the American Statistical Association, 88, 309–319.
  • Bittar, O.J.N.V., Mendes, J.D.V. and Magalhães, A. (2011). Rede Hospitalar no Estado de São Paulo: Mapear para Regular. São Paulo: Secretaria...
  • Botega, A. and Santos, M.R. (2007). Descentralização das ações de assistência farmacêutica asma e rinite. In: Cerci-Neto, A. (org.)...
  • Casella, G. and George, E.I. (1992). Explaining the Gibbs sampler. The American Statistician, 46, 167–174.
  • Carlin, B.P. and Louis, T.A. (1996). Bayes and Empirical Bayes Methods for Data Analysis. New York:
  • Chapman and Hall. Carlin, B.P., Gelfand, A.E. and Smith, A.F.M. (1992). Hierarchical Bayesian analysis of change-point problems. Journal of...
  • Chen, M.H., Shao, Q.M. and Ibrahim, J.G. (2000). Monte Carlo Methods in Bayesian Computation. New York: Springer.
  • Chen, C.H., Xirasagar, S. and Lin, H.C. (2006). Seasonality in adult asthma admissions, air pollutant levels, and climate: a population-based...
  • Chib, S. (1998). Estimation and comparison of multiple change-point models. Journal of Econometrics, 86, 221–241.
  • Dey, D.K. and Purkayastha, S. (1997). Bayesian approach to change-point problems. Communications in Statistics Theory and Methods, 26, 2035–2047.
  • Fearnhead, P. (2006). Exact and efficient Bayesian inference for multiple changepoint problems. Statistics and Computing, 16, 203–213.
  • Geisser, S. and Eddy, W. (1979). A predictive approach to model selection. Journal of the American Statistical Association, 74, 153–160.
  • Gelfand, A.E., Dey, D.K. and Chang, H. (1992). Model determination using predictive distributions with implementation via sampling-based methods....
  • Ghosh, P. and Vaida, F. (2007). Random change point modelling of HIV immunologic responses. Statistics in Medicine, 26, 2074–2087.
  • Hackl, P. (2012). Statistical Analysis and Forecasting of Economic Structural Change. New York: Springer.
  • Ivey, M.A., Simeon, D.T. and Monteil, M.A. (2003). Climatic variables are associated with seasonal acute asthma admissions to accident and...
  • Jensen, U. and Lautkebohmert, C. (2007). Change-Point Models. In: Ruggeri, F., Kenett, R. and Faltin, W. Encyclopedia of Statistics in Quality...
  • Jornet-Sanz, M., Corberán-Vallet, A., Santonja, F. and Villanueva, R. (2017). A Bayesian stochastic SIRS model with a vaccination strategy...
  • Lee, T.S. (2010). Change-point problems: bibliography and review. Journal of Statistical Theory and Practice, 4, 643–662.
  • Lavielle, M. and Lebarbier, E. (2001). An application of MCMC methods for the multiple change-points problem. Signal Process, 81, 39–53.
  • Lunn, D.J., Thomas, A., Best, N. and Spiegelhalter D. (2000). WinBUGS a Bayesian modelling framework: concepts, structure, and extensibility....
  • Motazedian, S., Ghaffarpasand, F., Mojtahedi, K. and Asadi N. (2010). Terbutaline versus salbutamol for suppression of preterm labor: a randomized...
  • Ntzoufras, I. (2009). Bayesian Modeling using WinBUGS. Hoboken: Wiley.
  • Peterson, M.G., Gaeta, T.J., Birkhahn, R.H., Fernández, J.L. and Mancuso, C.A. (2012). History of symptom triggers in patients presenting...
  • Sociedade Brasileira de Pneumologia e Tisiologia. (2012). Diretrizes da Sociedade Brasileira de Pneumologia e Tisiologia para o Manejo da...
  • Spiegelhalter, D.J., Best, N.G., Carlin, B.P. and Linde, A. (2014). The deviance information criterion: 12 years on. Journal of the Royal...
  • Thomazelli, L.M., Vieira, S., Leal, A.L., Sousa, T.S., Oliveira, D.B., Golono, M.A., Gillio, A.E., Stwien, K. E., Erdman, D.D. and Durigon,...
  • Zeger, S.L., Irizarry, R. and Peng, R.D. (2006). On time series analysis of public health and biomedical data. Annual Review of Public Health,...