Lifetime Data Analysis

, Volume 23, Issue 3, pp 495–515 | Cite as

Generalized accelerated failure time spatial frailty model for arbitrarily censored data

  • Haiming Zhou
  • Timothy Hanson
  • Jiajia Zhang


Flexible incorporation of both geographical patterning and risk effects in cancer survival models is becoming increasingly important, due in part to the recent availability of large cancer registries. Most spatial survival models stochastically order survival curves from different subpopulations. However, it is common for survival curves from two subpopulations to cross in epidemiological cancer studies and thus interpretable standard survival models can not be used without some modification. Common fixes are the inclusion of time-varying regression effects in the proportional hazards model or fully nonparametric modeling, either of which destroys any easy interpretability from the fitted model. To address this issue, we develop a generalized accelerated failure time model which allows stratification on continuous or categorical covariates, as well as providing per-variable tests for whether stratification is necessary via novel approximate Bayes factors. The model is interpretable in terms of how median survival changes and is able to capture crossing survival curves in the presence of spatial correlation. A detailed Markov chain Monte Carlo algorithm is presented for posterior inference and a freely available function frailtyGAFT is provided to fit the model in the R package spBayesSurv. We apply our approach to a subset of the prostate cancer data gathered for Louisiana by the surveillance, epidemiology, and end results program of the National Cancer Institute.


Interval-censored data Heteroscedastic survival Linear dependent tailfree process Spatial data Stratified AFT model 



This work was supported by NCI grant 5R03CA176739. The authors would like to thank the editor, the associate editor, and the two referees for their valuable comments, which led to great improvements to the paper.

Supplementary material

10985_2016_9361_MOESM1_ESM.pdf (1.1 mb)
Supplementary material 1 (pdf 1122 KB)


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Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.Division of StatisticsNorthern Illinois UniversityDeKalbUSA
  2. 2.Department of StatisticsUniversity of South CarolinaColumbiaUSA
  3. 3.Department of Epidemiology and BiostatisticsUniversity of South CarolinaColumbiaUSA

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