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Generalized accelerated failure time spatial frailty model for arbitrarily censored data

Author

Listed:
  • Haiming Zhou

    (Northern Illinois University)

  • Timothy Hanson

    (University of South Carolina)

  • Jiajia Zhang

    (University of South Carolina)

Abstract

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.

Suggested Citation

  • Haiming Zhou & Timothy Hanson & Jiajia Zhang, 2017. "Generalized accelerated failure time spatial frailty model for arbitrarily censored data," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 23(3), pages 495-515, July.
    • Handle: RePEc:spr:lifeda:v:23:y:2017:i:3:d:10.1007_s10985-016-9361-4
    DOI: 10.1007/s10985-016-9361-4
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    References listed on IDEAS

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    1. Timothy E. Hanson & Athanasios Kottas & Adam J. Branscum, 2008. "Modelling stochastic order in the analysis of receiver operating characteristic data: Bayesian non‐parametric approaches," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 57(2), pages 207-225, April.
    2. Portnoy S., 2003. "Censored Regression Quantiles," Journal of the American Statistical Association, American Statistical Association, vol. 98, pages 1001-1012, January.
    3. Jiajia Zhang & Andrew B. Lawson, 2011. "Bayesian parametric accelerated failure time spatial model and its application to prostate cancer," Journal of Applied Statistics, Taylor & Francis Journals, vol. 38(3), pages 591-603, November.
    4. Koenker, Roger, 2008. "Censored Quantile Regression Redux," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 27(i06).
    5. Yi Li & Louise Ryan, 2002. "Modeling Spatial Survival Data Using Semiparametric Frailty Models," Biometrics, The International Biometric Society, vol. 58(2), pages 287-297, June.
    6. Luping Zhao & Timothy E. Hanson, 2011. "Spatially Dependent Polya Tree Modeling for Survival Data," Biometrics, The International Biometric Society, vol. 67(2), pages 391-403, June.
    7. Maria De Iorio & Wesley O. Johnson & Peter Müller & Gary L. Rosner, 2009. "Bayesian Nonparametric Nonproportional Hazards Survival Modeling," Biometrics, The International Biometric Society, vol. 65(3), pages 762-771, September.
    8. A. Jara & T. E. Hanson, 2011. "A class of mixtures of dependent tail-free processes," Biometrika, Biometrika Trust, vol. 98(3), pages 553-566.
    9. Hennerfeind, Andrea & Brezger, Andreas & Fahrmeir, Ludwig, 2006. "Geoadditive Survival Models," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 1065-1075, September.
    10. Brent R. Logan & John P. Klein & Mei‐Jie Zhang, 2008. "Comparing Treatments in the Presence of Crossing Survival Curves: An Application to Bone Marrow Transplantation," Biometrics, The International Biometric Society, vol. 64(3), pages 733-740, September.
    11. Hanson, Timothy E., 2006. "Inference for Mixtures of Finite Polya Tree Models," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 1548-1565, December.
    12. Luping Zhao & Timothy E. Hanson & Bradley P. Carlin, 2009. "Mixtures of Polya trees for flexible spatial frailty survival modelling," Biometrika, Biometrika Trust, vol. 96(2), pages 263-276.
    13. Kottas A. & Gelfand A.E., 2001. "Bayesian Semiparametric Median Regression Modeling," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 1458-1468, December.
    14. Henderson R. & Shimakura S. & Gorst D., 2002. "Modeling Spatial Variation in Leukemia Survival Data," Journal of the American Statistical Association, American Statistical Association, vol. 97, pages 965-972, December.
    15. Stephen Walker & Bani K. Mallick, 1999. "A Bayesian Semiparametric Accelerated Failure Time Model," Biometrics, The International Biometric Society, vol. 55(2), pages 477-483, June.
    16. Sy Han Chiou & Sangwook Kang & Jun Yan, 2015. "Semiparametric Accelerated Failure Time Modeling for Clustered Failure Times From Stratified Sampling," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(510), pages 621-629, June.
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    1. Jiajia Zhang & Timothy Hanson & Haiming Zhou, 2019. "Bayes factors for choosing among six common survival models," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 25(2), pages 361-379, April.
    2. Piyali Basak & Antonio Linero & Debajyoti Sinha & Stuart Lipsitz, 2022. "Semiparametric analysis of clustered interval‐censored survival data using soft Bayesian additive regression trees (SBART)," Biometrics, The International Biometric Society, vol. 78(3), pages 880-893, September.

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