Encyclopedia of GIS

2017 Edition
| Editors: Shashi Shekhar, Hui Xiong, Xun Zhou

Spatial Survival Analysis

  • Benjamin M. TaylorEmail author
Reference work entry
DOI: https://doi.org/10.1007/978-3-319-17885-1_1639

Synonyms

Definition

The statistical modeling of censored time-to-event data is the realm of survival analysis; when such data can be located in space and there is scientific interest in understanding the spatial variation in survival outcomes, a spatial survival analysis is performed. The concept of censoring is what makes survival data statistically interesting: for each observation in our dataset, we either observe the time of an event (such as death, disease progression, successful treatment, etc.) or the time or interval of time in which the observation was lost to follow-up. The observations that are lost to follow-up are the censored observations. Spatial survival analysis combines techniques from geostatistics and survival analysis to answer scientific questions like: where in space is the rate of events unusually high (or low)?

Historical Background

Survival analysis per se has a long tradition in the medical sciences, the...

This is a preview of subscription content, log in to check access.

Notes

Acknowledgements

The author is very grateful to Professor Robin Henderson for allowing him to access and use an anonymized version of the leukemia data from Henderson et al. (2002). These data were used to produce figures1–3.

References

  1. Aalen O (1978) Nonparametric inference for a family of counting processes. Ann Stat 6(4):701–726MathSciNetzbMATHCrossRefGoogle Scholar
  2. Banerjee S, Carlin BP (2002) Case studies in Bayesian statistics. Spatial semi-parametric proportional hazards models for analyzing infant mortality rates in Minnesota counties, chapter 6 Springer, New York, pp 137–151Google Scholar
  3. Banerjee S, Carlin BP (2003) Semiparametric spatio-temporal frailty modeling. Environmetrics 14(5): 523–535CrossRefGoogle Scholar
  4. Banerjee S, Carlin BP (2004) Parametric spatial cure rate models for interval-censored time-to-relapse data. Biometrics 60(1):268–275MathSciNetzbMATHCrossRefGoogle Scholar
  5. Banerjee S, Carlin BP, Gelfand AE (2014) Hierarchical modeling and analysis for spatial data, 2nd edn. Chapman and Hall/CRC, Boca RatonzbMATHGoogle Scholar
  6. Banerjee S, Dey DK (2005) Semiparametric proportional odds models for spatially correlated survival data. Lifetime Data Anal 11(2):175–191MathSciNetzbMATHCrossRefGoogle Scholar
  7. Banerjee S, Wall MM, Carlin BP (2003) Frailty modeling for spatially correlated survival data, with application to infant mortality in Minnesota. Biostatistics 4(1):123–142zbMATHCrossRefGoogle Scholar
  8. Besag J (1974) Spatial interaction and the statistical analysis of lattice systems. J R Stat Soc Ser B (Methodol) 36(2):192–236MathSciNetzbMATHGoogle Scholar
  9. Besag J, Kooperberg C (1995) On conditional and intrinsic autoregression. Biometrika 82(4):733–746MathSciNetzbMATHGoogle Scholar
  10. Besag J, York JC, Mollie A (1991) Bayesian image restoration with two applications in spatial statistics. Ann Inst Stat Math 43:22–24MathSciNetzbMATHGoogle Scholar
  11. Bhatt V, Tiwari N (2014) A spatial scan statistic for survival data based on Weibull distribution. Stat Med 33(11):1867–1876MathSciNetCrossRefGoogle Scholar
  12. Brix A, Diggle PJ (2001) Spatiotemporal prediction for log-Gaussian Cox processes. J R Stat Soc Ser B 63(4):823–841MathSciNetzbMATHCrossRefGoogle Scholar
  13. Cox DR (1972) Regression models and life-tables. J R Stat Soc Ser B 34(2):187–220MathSciNetzbMATHGoogle Scholar
  14. Cox DR, Oakes D (1984) Analysis of survival data. Chapman & Hall/CRC monographs on statistics & applied probability. CRC Press, London/New YorkGoogle Scholar
  15. Darmofal D (2009) Bayesian spatial survival models for political event processes. Am J Polit Sci 53(1):241–257CrossRefGoogle Scholar
  16. Diva U, Dey DK, Banerjee S (2008) Parametric models for spatially correlated survival data for individuals with multiple cancers. Stat Med 27(12):2127–44MathSciNetCrossRefGoogle Scholar
  17. Henderson R, Shimakura S, Gorst D (2002) Modeling spatial variation in leukemia survival data. J Am Stat Assoc 97:965–972MathSciNetzbMATHCrossRefGoogle Scholar
  18. Hennerfeind A, Brezger A, Fahrmeir L (2006) Geoadditive survival models. J Am Stat Assoc 101(475): 1065–1075MathSciNetzbMATHCrossRefGoogle Scholar
  19. Huang L, Kulldorff M, Gregorio D (2007) A spatial scan statistic for survival data. Biometrics 63(1):109–118MathSciNetzbMATHCrossRefGoogle Scholar
  20. Jerrett M, Burnett RT, Ma R, Arden Pope III C, Krewski D, Newbold KB, Thurston G, Shi Y, Finkelstein N, Calle EE, et al (2005) Spatial analysis of air pollution and mortality in Los Angeles. Epidemiology 16(6):727–736CrossRefGoogle Scholar
  21. Kaplan EL, Meier P (1958) Nonparametric estimation from incomplete observations. J Am Stat Assoc 53(282):457–481MathSciNetzbMATHCrossRefGoogle Scholar
  22. Klein JP, Ibrahim JG, Scheike TH, van Houwelingen JC, Van Houwelingen HC (2013) Handbook of survival analysis. Chapman and Hall/CRC handbooks of modern statistical methods series. Taylor & Francis Group, Boca RatonzbMATHGoogle Scholar
  23. Klein JP, Moeschberger ML (2003) Survival analysis: techniques for censored and truncated data. Statistics for biology and health. Springer, New YorkzbMATHGoogle Scholar
  24. Krige D (1951) A statistical approach to some basic mine valuation problems on the witwatersrand. J Chem Metall Mining Soc S Afr 52:119–139Google Scholar
  25. Li Y, Lin X (2006) Semiparametric normal transformation models for spatially correlated survival data. J Am Stat Assoc 101(474):591–603MathSciNetzbMATHCrossRefGoogle Scholar
  26. Li Y, Ryan L (2002) Modeling spatial survival data using semiparametric frailty models. Biometrics 58(2): 287–297MathSciNetzbMATHCrossRefGoogle Scholar
  27. Lindgren F, Rue H, Lindström J (2011) An explicit link between Gaussian fields and Gaussian Markov random fields: the stochastic partial differential equation approach. J R Stat Soc Ser B 73(4):423–498MathSciNetzbMATHCrossRefGoogle Scholar
  28. Nelson W (1969) Hazard plotting for incomplete failure data. J Qual Technol 1:27–52Google Scholar
  29. Paik J, Ying Z (2012) A composite likelihood approach for spatially correlated survival data. Comput Stat Data Anal 56(1):209–216MathSciNetzbMATHCrossRefGoogle Scholar
  30. Pickles AR, Crouchley R (1994) Generalizations and applications of frailty models for survival and event data. Stat Methods Med Res 3:263–278CrossRefGoogle Scholar
  31. Royston P, Parmar MK (2002) Flexible parametric proportional-hazards and proportional-odds models for censored survival data, with application to prognostic modelling and estimation of treatment effects. Stat Med 21(15):2175–2197CrossRefGoogle Scholar
  32. Rue H, Martino S, Chopin N (2009) Approximate Bayesian inference for latent Gaussian models by using integrated nested Laplace approximations. J R Stat Soc Ser B 71(2):319–392MathSciNetzbMATHCrossRefGoogle Scholar
  33. Taylor BM (2015) Auxiliary variable Markov chain Monte Carlo for spatial survival and geostatistical models. Available from http://arxiv.org/abs/ISO1.01665http://arxiv.org/abs/ISO1.01665
  34. Taylor BM, Rowlingson BS (2014, to appear) spatsurv: an R package for Bayesian inference with spatial survival models. J Stat SoftwGoogle Scholar
  35. Tonda T, Satoh K, Otani K, Sato Y, Maruyama H, Kawakami H, Tashiro S, Hoshi M, Ohtaki M (2012) Investigation on circular asymmetry of geographical distribution in cancer mortality of Hiroshima atomic bomb survivors based on risk maps: analysis of spatial survival data. Radiat Environ Biophys 51(2):133–141CrossRefGoogle Scholar
  36. Wall MM (2004) A close look at the spatial structure implied by the CAR and SAR models. J Stat Plan Inf 121:311–324MathSciNetzbMATHCrossRefGoogle Scholar
  37. Wienke A (2010) Frailty models in survival analysis. Chapman & Hall/CRC biostatistics series. CRC Press, Boca RatonCrossRefGoogle Scholar
  38. Zhang J, Lawson AB (2011) Bayesian parametric accelerated failure time spatial model and its application to prostate cancer. J Appl Stat 38(2):591–603MathSciNetCrossRefGoogle Scholar
  39. Zhao L, Hanson TE (2011) Spatially dependent Polya tree modeling for survival data. Biometrics 67(2):391–403MathSciNetzbMATHCrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Faculty of Health and MedicineLancaster UniversityLancasterUK