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Dynamic Bayesian Models for Survival Data

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  • Dani Gamerman

Abstract

Dynamic models are proposed for the study of survival data with explanatory variables whose effects change through time. The parameters modelling these effects are allowed to vary between time intervals and a system equation provides the stochastic link for adjacent values. Sequential analysis is used, based on a factorization of the likelihood over the time intervals. The updating equations are obtained via the dynamic generalized modelling approach of West, Harrison and Migon. Predictive features for follow‐up studies and analysis of new observations are obtained and some numerical applications are provided.

Suggested Citation

  • Dani Gamerman, 1991. "Dynamic Bayesian Models for Survival Data," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 40(1), pages 63-79, March.
    • Handle: RePEc:bla:jorssc:v:40:y:1991:i:1:p:63-79
    DOI: 10.2307/2347905
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    Cited by:

    1. Godolphin, E.J. & Triantafyllopoulos, Kostas, 2006. "Decomposition of time series models in state-space form," Computational Statistics & Data Analysis, Elsevier, vol. 50(9), pages 2232-2246, May.
    2. Pavel Čížek & Jinghua Lei & Jenny E. Ligthart, 2017. "Do Neighbours Influence Value-Added-Tax Introduction? A Spatial Duration Analysis," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 79(1), pages 25-54, February.
    3. K J Wilson & M Farrow, 2010. "Bayes linear kinematics in the analysis of failure rates and failure time distributions," Journal of Risk and Reliability, , vol. 224(4), pages 309-321, December.
    4. Kostas Triantafyllopoulos, 2009. "Inference of Dynamic Generalized Linear Models: On‐Line Computation and Appraisal," International Statistical Review, International Statistical Institute, vol. 77(3), pages 430-450, December.
    5. Cizek, P. & Lei, J. & Ligthart, J.E., 2012. "The Determinants of VAT Introduction : A Spatial Duration Analysis," Discussion Paper 2012-071, Tilburg University, Center for Economic Research.
    6. Gebrenegus Ghilagaber, 2018. "Environmental recidivism in Sweden: distributional shape and effects of sanctions on duration of compliance," Quality & Quantity: International Journal of Methodology, Springer, vol. 52(2), pages 869-882, March.
    7. Bhattacharjee, Arnab & Bhattacharjee, Madhuchhanda, 2007. "Bayesian Analysis of Hazard Regression Models under Order Restrictions on Covariate Effects and Ageing," MPRA Paper 3938, University Library of Munich, Germany.
    8. Dani Gamerman & Thiago Rezende Santos & Glaura C. Franco, 2013. "A Non-Gaussian Family Of State-Space Models With Exact Marginal Likelihood," Journal of Time Series Analysis, Wiley Blackwell, vol. 34(6), pages 625-645, November.
    9. Luca La Rocca, 2008. "Bayesian Non‐Parametric Estimation of Smooth Hazard Rates for Seismic Hazard Assessment," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 35(3), pages 524-539, September.
    10. Hideo Kozumi, 2000. "Bayesian Analysis of Discrete Survival Data with a Hidden Markov Chain," Biometrics, The International Biometric Society, vol. 56(4), pages 1002-1006, December.
    11. Parfait Munezero, 2022. "Efficient particle smoothing for Bayesian inference in dynamic survival models," Computational Statistics, Springer, vol. 37(2), pages 975-994, April.
    12. Gouno Evans & Guérineau Lise, 2015. "Failure Rate Estimation in a Dynamic Environment," Stochastics and Quality Control, De Gruyter, vol. 30(1), pages 1-8, June.
    13. Michael L. Pennell & David B. Dunson, 2006. "Bayesian Semiparametric Dynamic Frailty Models for Multiple Event Time Data," Biometrics, The International Biometric Society, vol. 62(4), pages 1044-1052, December.
    14. Peter Congdon, 2009. "Life Expectancies for Small Areas: A Bayesian Random Effects Methodology," International Statistical Review, International Statistical Institute, vol. 77(2), pages 222-240, August.
    15. Jonathan L. French & Joseph G. Ibrahim, 2002. "Bayesian Methods for a Three–State Model for Rodent Carcinogenicity Studies," Biometrics, The International Biometric Society, vol. 58(4), pages 906-916, December.
    16. T. R. Santos, 2018. "A Bayesian GED-Gamma stochastic volatility model for return data: a marginal likelihood approach," Papers 1809.01489, arXiv.org.
    17. Ian W. McKeague & Mourad Tighiouart, 2000. "Bayesian Estimators for Conditional Hazard Functions," Biometrics, The International Biometric Society, vol. 56(4), pages 1007-1015, December.
    18. David B. Dunson & Patricia Chulada & Samuel J. Arbes Jr, 2003. "Bayesian Modeling of Time-Varying and Waning Exposure Effects," Biometrics, The International Biometric Society, vol. 59(1), pages 83-91, March.
    19. Madhuja Mallick & Nalini Ravishanker, 2006. "Additive Positive Stable Frailty Models," Methodology and Computing in Applied Probability, Springer, vol. 8(4), pages 541-558, December.
    20. Zuqiang Qiou & Nalini Ravishanker & Dipak K. Dey, 1999. "Multivariate Survival Analysis with Positive Stable Frailties," Biometrics, The International Biometric Society, vol. 55(2), pages 637-644, June.

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