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Clustering method for censored and collinear survival data

Author

Listed:
  • Silvia Liverani

    (Queen Mary University of London
    The British Library)

  • Lucy Leigh

    (Hunter Medical Research Institute
    University of Newcastle)

  • Irene L. Hudson

    (Royal Melbourne Institute of Technology (RMIT))

  • Julie E. Byles

    (University of Newcastle)

Abstract

In this paper we propose a Dirichlet process mixture model for censored survival data with covariates. This model is suitable in two scenarios. First, this method can be used to identify clusters determined by both the censored survival data and the predictors. Second, this method is suitable for highly correlated predictors, in cases when the usual survival models cannot be implemented because they would be unstable due to multicollinearity. The Dirichlet process mixture model links a response vector to covariate data through cluster membership and in this paper this model is extended for mixtures of Weibull distributions, which can be used to model survival times and also allow for censoring. We propose two variants of this model, one with a shape parameter common to all clusters (referred to as a global parameter) for the Weibull distributions and one with a cluster-specific shape parameter. The first satisfies the proportional hazard assumption, while the latter is very flexible, as it has the advantage of allowing estimation of the survival curve whether or not the proportional hazards assumption is satisfied. We present a simulation study and, to demonstrate the applicability of the method in practice, a real application to sleep surveys in older women from The Australian Longitudinal Study on Women’s Health. The method developed in the paper is available in the R package PReMiuM.

Suggested Citation

  • Silvia Liverani & Lucy Leigh & Irene L. Hudson & Julie E. Byles, 2021. "Clustering method for censored and collinear survival data," Computational Statistics, Springer, vol. 36(1), pages 35-60, March.
    • Handle: RePEc:spr:compst:v:36:y:2021:i:1:d:10.1007_s00180-020-01000-3
    DOI: 10.1007/s00180-020-01000-3
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    References listed on IDEAS

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    1. Chung, Yeonseung & Dunson, David B., 2009. "Nonparametric Bayes Conditional Distribution Modeling With Variable Selection," Journal of the American Statistical Association, American Statistical Association, vol. 104(488), pages 1646-1660.
    2. Dunson, David B. & Herring, Amy H. & Siega-Riz, Anna Maria, 2008. "Bayesian Inference on Changes in Response Densities Over Predictor Clusters," Journal of the American Statistical Association, American Statistical Association, vol. 103(484), pages 1508-1517.
    3. Liverani, Silvia & Hastie, David I. & Azizi, Lamiae & Papathomas, Michail & Richardson, Sylvia, 2015. "PReMiuM: An R Package for Profile Regression Mixture Models Using Dirichlet Processes," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 64(i07).
    4. W. R. Gilks & P. Wild, 1992. "Adaptive Rejection Sampling for Gibbs Sampling," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 41(2), pages 337-348, June.
    5. Bigelow, Jamie L. & Dunson, David B., 2009. "Bayesian Semiparametric Joint Models for Functional Predictors," Journal of the American Statistical Association, American Statistical Association, vol. 104(485), pages 26-36.
    Full references (including those not matched with items on IDEAS)

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