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Space-time stick-breaking processes for small area disease cluster estimation

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Abstract

We propose a space-time stick-breaking process for the disease cluster estimation. The dependencies for spatial and temporal effects are introduced by using space-time covariate dependent kernel stick-breaking processes. We compared this model with the space-time standard random effect model by checking each model’s ability in terms of cluster detection of various shapes and sizes. This comparison was made for simulated data where the true risks were known. For the simulated data, we have observed that space-time stick-breaking process performs better in detecting medium- and high-risk clusters. For the real data, county specific low birth weight incidences for the state of South Carolina for the years 1997–2007, we have illustrated how the proposed model can be used to find grouping of counties of higher incidence rate.

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References

  • Assunção RM (2003) Space varying coefficient models for small area data. Environmetrics 14: 453–473

    Article  Google Scholar 

  • Banerjee S, Carlin B, Gelfand AE (2004) Hierarchical modeling and analysis for spatial data. Chapman and Hall, New York

    Google Scholar 

  • Bernardinelli L, Clayton D, Montomoli C (1995) Bayesian estimates of disease maps: how important are priors?. Stat Med 14: 2411–2431

    Article  PubMed  CAS  Google Scholar 

  • Best N, Richardson S, Thomas A (2005) A comparison of Bayesian spatial models for disease mapping. Stat Methods Med Res 14: 35–59

    Article  PubMed  Google Scholar 

  • Duan JA, Guindani M, Gelfand AE (2007) Generalized spatial Dirichlet process models. Biomerika 94: 809–825

    Article  Google Scholar 

  • Dunson DB, Park JH (2008) Kernel stick-breaking processes. Biomerika 95: 307–323

    Article  Google Scholar 

  • Fang J, Madhavan S, Alderman MH (1999) Low birthweight: race and maternal nativity-impact of community income. Pediatrics 103: E5

    Article  PubMed  CAS  Google Scholar 

  • Ferguson TS (1983) Bayesian density estimation by mixtures of normal distributions. In: Rizvi MH, Rustagi JS, Siegmund D (eds) Recent advances in statistics. Academic Press, New York, pp 287–302

    Google Scholar 

  • Fernandez C, Green PJ (2002) Modelling spatially correlated data via mixtures: a Bayesian approach. J R Stat Soc Ser B 64: 805–826

    Article  Google Scholar 

  • Gelfand AE, Ghosh SK (1998) Model choice: a minimum posterior predictive loss. Biometrika 85: 1–11

    Article  Google Scholar 

  • Gelfand AE, Kottas A, MacEachern SN (2005) Bayesian nonparametric spatial modeling with Dirichlet process mixing. J Am Stat Assoc 100: 1021–1035

    Article  CAS  Google Scholar 

  • Gelfand AE, Vounatsou P (2003) Proper multivariate conditional autoregressive models for spatial data analysis. Biostatistics 4: 11–25

    Article  PubMed  Google Scholar 

  • Gelman A, Carlin JB, Stern HS, Rubin DB (2004) Bayesian data analysis. Chapmann Hall, Boca Raton

    Google Scholar 

  • Goldenberg RL, Culhane JF (2007) Low birth weight in the United States. Am J Clin Nutr 85:584S–590S

    Google Scholar 

  • Grady S (2006) Racial disparities in low birthweight and the contribution of residential segregation: a multilevel analysis. Soc Sci Med 63: 3013–3029

    Article  PubMed  Google Scholar 

  • Green J, Richardson S (2002) Hidden Markov models and disease mapping. J Am Stat Assoc 97: 1055–1070

    Article  Google Scholar 

  • Green PJ, Richardson S (2001) Modelling heterogeneity with and without the Dirichlet process. Scand J Stat 28: 355–375

    Article  Google Scholar 

  • Griffin JE, Steel MF (2006) Order-based dependent Dirichlet processes. J Am Stat Assoc 101: 179–194

    Article  CAS  Google Scholar 

  • Hennig C (2000) Identifiability of models for clusterwise linear regression. J Classif 17: 273–296

    Article  Google Scholar 

  • Hossain MM, Lawson AB (2010) Space-time Bayesian small area disease risk models: development and evaluation with a focus on cluster detection. Environ Ecol Stat 17: 73–95

    Article  PubMed  Google Scholar 

  • Ishwaran H, James LF (2001) Gibbs sampling methods for stick-breaking priors. J Am Stat Assoc 96: 161–173

    Article  Google Scholar 

  • Ishwaran H, Zarepour M (2002) Exact and approximate sum representations for the Dirichlet process. Can J Stat 30: 269–283

    Article  Google Scholar 

  • Janevic T, Stein CR, Savitz DA, Kaufman JS, Mason SM, Herring AH (2010) Neighborhood deprivation and adverse birth outcomes among diverse ethnic groups. Ann Epidemiol 20: 445–451

    Article  PubMed  CAS  Google Scholar 

  • Knorr-Held L (2000) Bayesian modelling of inseparable space-time variation in disease risk. Stat Med 19: 2555–2567

    Article  PubMed  CAS  Google Scholar 

  • Knorr-Held L, Besag J (1998) Modelling risk from a disease in time and space. Stat Med 17: 2045–2060

    Article  PubMed  CAS  Google Scholar 

  • Kottas A, Duan JA, Gelfand AE (2007) Modeling disease incidence data with spatial and spatial-temporal Dirichlet process mixtures. Biom J 49: 1–14

    Google Scholar 

  • Lambert PC, Sutton AJ, Burton PR, Abrams KR, Jones DR (2005) How vague is vague? A simulation impact of the use of vague prior distributions in MCMC using winbugs. Stat Med 24: 2401–2428

    Article  PubMed  Google Scholar 

  • Lawson AB, Song HR, Cai B, Hossain MM, Huang K (2010) Space-time latent component modeling of geo-referenced health data. Stat Med 29: 2012–2027

    Article  PubMed  Google Scholar 

  • Lo AY (1984) On a class of Bayesian nonparametric estimates: I. Density estimates. Ann Stat 12: 351–357

    Article  Google Scholar 

  • Ohlssen DI, Sharples LD, Spiegelhalter DJ (2007) Flexible random-effects models using Bayesian semi-parametric models: application to institutional comparisons. Stat Med 26: 2088–2112

    Article  PubMed  CAS  Google Scholar 

  • Pearl M, Braveman P, Abrams B (2001) The ralationship of neighborhood socioeconomic characteristics to birthweight among 5 ethnic groups in California. Am J Public Health 91: 1808–1814

    Article  PubMed  CAS  Google Scholar 

  • Reich BJ, Fuentes M (2007) A multivariate semiparametric Bayesian spatial modeling framework for hurricane surface wind fields. Ann Appl Stat 1: 249–264

    Article  Google Scholar 

  • Richardson S, Thomas A, Best N, Elliott P (2004) Interpreting posterior relative risk estimates in disease-mapping studies. Environ Health Perspect 112: 1016–1025

    Article  PubMed  Google Scholar 

  • Sethuraman J (1994) A constructive definition of Dirichlet priors. Stat Sin 4: 639–650

    Google Scholar 

  • Spiegelhalter D, Thomas A, Best N, Lunn D (2003) WinBUGS user manual [1.4.]. MRC Biostatistics Unit, Institute of Public Health, Cambridge

  • Waller LA, Carlin BP, Xia H, Gelfand AE (1997) Hierarchical spatio-temporal mapping of disease rates. J Am Stat Assoc 92: S.607–S.617

    Article  Google Scholar 

  • Xia H, Carlin BP (1998) Spatio-temporal models with errors in covariates: mapping Ohio lung cancer mortality. Stat Med 17: 2025–2043

    Article  PubMed  CAS  Google Scholar 

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Authors and Affiliations

  1. Division of Biostatistics and Epidemiology, Cincinnati Children’s Hospital Medical Center, Cincinnati, Ohio

    Md. Monir Hossain

  2. Division of Biostatistics, Bioinformatics and Epidemiology, Medical University of South Carolina, Charleston, SC, USA

    Andrew B. Lawson & Jungsoon Choi

  3. Department of Epidemiology and Biostatistics, University of South Carolina, Columbia, SC, USA

    Bo Cai & Jihong Liu

  4. Department of Community and Family Health, University of South Florida, Tampa, FL, USA

    Russell S. Kirby

Authors
  1. Md. Monir Hossain
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  2. Andrew B. Lawson
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  3. Bo Cai
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  4. Jungsoon Choi
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  5. Jihong Liu
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  6. Russell S. Kirby
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Correspondence to Md. Monir Hossain.

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Hossain, M.M., Lawson, A.B., Cai, B. et al. Space-time stick-breaking processes for small area disease cluster estimation. Environ Ecol Stat 20, 91–107 (2013). https://doi.org/10.1007/s10651-012-0209-0

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  • DOI: https://doi.org/10.1007/s10651-012-0209-0

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