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Bayesian accelerated failure time models based on penalized mixtures of Gaussians: regularization and variable selection

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  • Susanne Konrath
  • Ludwig Fahrmeir
  • Thomas Kneib

Abstract

In many biostatistical applications concerned with the analysis of duration times and especially those including high-dimensional genetic information, the following three extensions of classical accelerated failure time (AFT) models are required: (1) a flexible, nonparametric estimate of the survival time distribution, (2) a structured additive predictor including linear as well as nonlinear effects of continuous covariates and possibly further types of effects such as random or spatial effects, and (3) regularization and variable selection of high-dimensional effect vectors. Although a lot of research has dealt with these features separately, the development of AFT models combining them in a unified framework has not been considered yet. We present a Bayesian approach for modeling and inference in such flexible AFT models, incorporating a penalized Gaussian mixture error distribution, a structured additive predictor with Bayesian P-splines as a main ingredient, and Bayesian versions of ridge and LASSO as well as a spike and slab priors to enforce sparseness. Priors for regression coefficients are conditionally Gaussian, facilitating Markov chain Monte Carlo inference. The proposed model class is extensively tested in simulation studies and applied in the analysis of acute myeloid leukemia survival times considering microarray information as well as clinical covariates as prognostic factors. Copyright Springer-Verlag Berlin Heidelberg 2015

Suggested Citation

  • Susanne Konrath & Ludwig Fahrmeir & Thomas Kneib, 2015. "Bayesian accelerated failure time models based on penalized mixtures of Gaussians: regularization and variable selection," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 99(3), pages 259-280, July.
    • Handle: RePEc:spr:alstar:v:99:y:2015:i:3:p:259-280
    DOI: 10.1007/s10182-014-0240-6
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    References listed on IDEAS

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    1. Lee Anthony & Caron Francois & Doucet Arnaud & Holmes Chris, 2012. "Bayesian Sparsity-Path-Analysis of Genetic Association Signal using Generalized t Priors," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 11(2), pages 1-31, January.
    2. Thomas Kneib & Ludwig Fahrmeir, 2007. "A Mixed Model Approach for Geoadditive Hazard Regression," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 34(1), pages 207-228, March.
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    5. Komarek, Arnost & Lesaffre, Emmanuel, 2008. "Bayesian Accelerated Failure Time Model With Multivariate Doubly Interval-Censored Data and Flexible Distributional Assumptions," Journal of the American Statistical Association, American Statistical Association, vol. 103, pages 523-533, June.
    6. 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.
    7. Brezger, Andreas & Lang, Stefan, 2006. "Generalized structured additive regression based on Bayesian P-splines," Computational Statistics & Data Analysis, Elsevier, vol. 50(4), pages 967-991, February.
    8. Fahrmeir, Ludwig & Kneib, Thomas, 2011. "Bayesian Smoothing and Regression for Longitudinal, Spatial and Event History Data," OUP Catalogue, Oxford University Press, number 9780199533022.
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    Cited by:

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