Generalized Seasonal Autoregressive Integrated Moving Average Models for Count Data with Application to Malaria Time Series with Low Case Numbers

PLoS ONE

Volumn 8, Issue 6, 2013, Pages

  Briët, Olivier J T ^a,b,c   Amerasinghe, Priyanie H ^d   Vounatsou, Penelope ^b,c  

^a INTERNATIONAL WATER MANAGEMENT INSTITUTE   (Sri Lanka)

^b SWISS TROPICAL AND PUBLIC HEALTH INSTITUTE   (Switzerland)

^c UNIVERSITY OF BASEL   (Switzerland)

^d International Water Management Institute Sub Regional Office for South Asia   (India)

Author keywords

[No Author keywords available]

Indexed keywords

ARTICLE; BAYES THEOREM; DATA ANALYSIS; GENERALIZED AUTOREGRESSIVE MOVING AVERAGE MODEL; GENERALIZED SEASONAL AUTOREGRESSIVE INTEGRATED MOVING AVERAGE MODEL; HUMAN; KERNEL METHOD; MALARIA; MATHEMATICAL ANALYSIS; PARSIMONY ANALYSIS; PREDICTION; PREVALENCE; SEASONAL VARIATION; SPATIAL AUTOCORRELATION ANALYSIS; SRI LANKA; STATISTICAL MODEL; TIME SERIES ANALYSIS;

ALGORITHMS; HUMANS; MALARIA; MODELS, STATISTICAL; PUBLIC HEALTH SURVEILLANCE; SEASONS; SRI LANKA; TIME FACTORS; WEATHER;

EID: 84878981492     PISSN: None     EISSN: 19326203     Source Type: Journal    
DOI: 10.1371/journal.pone.0065761     Document Type: Article

References (45)

1. Gomez-Elipe A, Otero A, van Herp M, guirre-Jaime A, (2007) Forecasting malaria incidence based on monthly case reports and environmental factors in Karuzi, Burundi, 1997-2003. Malar J 6: 129.
2. Briët OJT, Vounatsou P, Gunawardena DM, Galappaththy GNL, Amerasinghe PH (2008) Models for short term malaria prediction in Sri Lanka. Malar J 7.
3. Wangdi K, Singhasivanon P, Silawan T, Lawpoolsri S, White NJ, et al. (2010) Development of temporal modelling for forecasting and prediction of malaria infections using time-series and ARIMAX analyses: a case study in endemic districts of Bhutan. Malar J 9: 251 doi: -10.1186/1475-2875-9-251.
4. Stefani A, Hanf M, Nacher M, Girod R, Carme B, (2011) Environmental, entomological, socioeconomic and behavioural risk factors for malaria attacks in Amerindian children of Camopi, French Guiana. Malar J 10: 246 doi: -10.1186/1475-2875-10-246.
5. Zinszer K, Verma AD, Charland K, Brewer TF, Brownstein JS, et al. (2012) A scoping review of malaria forecasting: past work and future directions. BMJ Open 2: e001992.
6. Hu W, Tong S, Mengersen K, Connell D, (2007) Weather variability and the incidence of cryptosporidiosis: comparison of time series poisson regression and SARIMA models. Ann Epidemiol 17: 679-688.
7. Hu W, Clements A, Williams G, Tong S, (2010) Dengue fever and El Nino/Southern Oscillation in Queensland, Australia: a time series predictive model. Occup Environ Med 67: 307-311.
8. Briët OJT, Vounatsou P, Gunawardena DM, Galappaththy GN, Amerasinghe PH, (2008) Temporal correlation between malaria and rainfall in Sri Lanka. Malar J 7: 77 doi: 10.1186/1475-2875-7-77.
9. Konradsen F, Amerasinghe FP, van der Hoek W, Amerasinghe PH (2000) Malaria in Sri Lanka: Current knowledge on transmission and control. Colombo: International Water Management Institute.
10. Briët OJT, Galappaththy GN, Amerasinghe PH, Konradsen F (2006) Malaria in Sri Lanka: one year post-tsunami. Malaria Journal 5.
11. World Health Organization (2012) World malaria report: 2012.
12. King G, (1988) Statistical models for political science event counts: Bias in conventional procedures and evidence for the exponential Poisson regression model. American Journal of Political Science 32: 838-863.
13. Teklehaimanot HD, Schwartz J, Teklehaimanot A, Lipsitch M, (2004) Weather-based prediction of Plasmodium falciparum malaria in epidemic-prone regions of Ethiopia II. Weather-based prediction systems perform comparably to early detection systems in identifying times for interventions. Malar J 19: 44.
14. Ravines RR, Schmidt AM, Migon HS, (2006) Revisiting distributed lag models through a Bayesian perspective. Applied Stochastic Models in Business & Industry 22: 193-210.
15. Nobre AA, Schmidt AM, Lopes HF, (2005) Spatio-temporal models for mapping the incidence of malaria in Pará. Environmetrics 16: 291-304.
16. Benjamin MA, Rigby RA, Stasinopoulos DM, (2003) Generalized Autoregressive Moving Average Models. Journal of the American Statistical association 98: 214-223.
17. West M. and Harrison J. (1997) Bayesian forecasting and dynamic models. New York: Springer-Verlag. 680 p.
18. Gamerman D, (1998) Markov chain Monte Carlo for dynamic generalized linear models. Biometrika 85: 215-227.
19. Cox DR, (1981) Statistical analysis of time series: some recent developments. Scandinavian Journal of Statistics 8: 93-115.
20. Jackman S (1998) Time series models for discrete data: solutions to a problem with quantitative studies of international conflict. 1-37.
21. Czado C, Kolbe A, (2007) Model-based quantification of the volatility of options at transaction level with extended count regression models. Applied Stochastic Models in Business and Industry 23: 1-21.
22. Davis RA, Dunsmuir WTM, Streett SB, (2003) Observation-driven models for Poisson counts. Biometrika 90: 777-790.
23. Jung RC, Kukuk M, Liesenfeld R, (2006) Time series of count data: modeling, estimation and diagnostics. Computational Statistics & Data Analysis 51: 2350-2364.
24. Zeger SL, Qaqish B, (1988) Markov regression models for time series: a quasi-likelihood approach. Biometrics 44: 1019-1031.
25. Grunwald G, Hyndman R, Tedesco L, Tweedie R, (2000) Non-Gaussian conditional linear AR(1) models. Australian & New Zealand Journal of Statistics 42: 479-495.
26. Heinen A. (2003) Modelling time series count data: An autoregressive conditional Poisson model. Louvain-la-Neuve: Université catholique de Louvain, Center for Operations Research and Econometrics (CORE). 37 p.
27. Morina D, Puig P, Rios J, Vilella A, Trilla A, (2011) A statistical model for hospital admissions caused by seasonal diseases. Stat Med 30: 3125-3136.
28. McKenzie E, (1988) Some ARMA models for dependent sequences of Poisson count. Advances in Applied Probability 20: 822-835.
29. Alzaid AA, Al-Osh MA, (1993) Some autoregressive moving average processes with generalized Poisson marginal distributions. Annals of the Institute of Statistical Mathematics 45: 223-232.
30. Jung RC, Tremayne AR, (2006) Binomial thinning models for integer time series. Statistical Modelling 6: 81-96.
31. Zeger SL, (1988) A regression model for time series of counts. Biometrika 75: 621-629.
32. Kleinschmidt I, Sharp B, Mueller I, Vounatsou P, (2002) Rise in malaria incidence rates in South Africa: a small-area spatial analysis of variation in time trends. Am J Epidemiol 155: 257-264.
33. Bernardinelli L, Clayton D, Pascutto C, Montomoli C, Ghislandi M, et al. (1995) Bayesian analysis of space-time variation in disease risk. Stat Med 14: 2433-2443.
34. Mabaso ML, Vounatsou P, Midzi S, Da Silva J, Smith T, (2006) Spatio-temporal analysis of the role of climate in inter-annual variation of malaria incidence in Zimbabwe. Int J Health Geogr 5: 20.
35. Knorr-Held L, Besag J, (1998) Modelling risk from a disease in time and space. Stat Med 17: 2045-2060.
36. Waller LA, Carlin BP, Xia H, Gelfand AE, (1997) Hierarchical spatio-temporal mapping of disease rates. Journal of the American Statistical association 92: 607-617.
37. Jones MC, (1987) Randomly choosing parameters from the stationary and invertibility region of autoregressive-moving average models. Applied Statistics 36: 134-138.
38. Plummer M (2003) JAGS: A Program for Analysis of Bayesian Graphical Models Using Gibbs Sampling. Proceedings of the 3rd International Workshop on Distributed Statistical Computing (DSC 2003).
39. Box GEP, Cox DR, (1964) An analysis of transformations. Journal of the Royal Statistical Society: Series B 26: 211-252.
40. Chatfield Chris (2004) The analysis of time series: an introduction. Boca Raton: Chapman & Hall/CRC. 333 p.
41. Said SE, Dickey DA, (1984) Testing for unit roots in autoregressive-moving average models of unknown order. Biometrika 74: 599-607.
42. Brooks SP, Gelman A, (1998) Alternative methods for monitoring convergence of iterative simulations. Journal of Computational and Graphical Statistics 7: 434-455.
43. Dunn PK, Smyth GK, (1996) Randomized quantile residuals. Journal of Computational and Graphical Statistics 5: 236-244.
44. Ljung GM, Box GEP, (1978) On a measure of lack of fit in time series models. Biometrika 65: 297-303.
45. Chen Y-T, (2002) On the robustness of Ljung-Box and McLeod-Li Q tests: a simulation study. Economics Bulletin 3: 1-10.