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A parametric dynamic survival model applied to breast cancer survival times

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  • K. Hemming
  • J. E. H. Shaw

Abstract

Summary. Much current analysis of cancer registry data uses the semiparametric proportional hazards Cox model. In this paper, the time‐dependent effect of various prognostic indicators on breast cancer survival times from the West Midlands Cancer Intelligence Unit are investigated. Using Bayesian methodology and Markov chain Monte Carlo estimation methods, we develop a parametric dynamic survival model which avoids the proportional hazards assumption. The model has close links to that developed by both Gamerman and Sinha and co‐workers: the log‐base‐line hazard and covariate effects are piecewise constant functions, related between intervals by a simple stochastic evolution process. Here this evolution is assigned a parametric distribution, with a variance that is further included as a hyperparameter. To avoid problems of convergence within the Gibbs sampler, we consider using a reparameterization. It is found that, for some of the prognostic indicators considered, the estimated effects change with increasing follow‐up time. In general those prognostic indicators which are thought to be representative of the most hazardous groups (late‐staged tumour and oldest age group) have a declining effect.

Suggested Citation

  • K. Hemming & J. E. H. Shaw, 2002. "A parametric dynamic survival model applied to breast cancer survival times," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 51(4), pages 421-435, October.
    • Handle: RePEc:bla:jorssc:v:51:y:2002:i:4:p:421-435
    DOI: 10.1111/1467-9876.00278
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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. 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.
    4. 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.
    5. Parfait Munezero, 2022. "Efficient particle smoothing for Bayesian inference in dynamic survival models," Computational Statistics, Springer, vol. 37(2), pages 975-994, April.

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