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Stochastic EM algorithms for parametric and semiparametric mixture models for right-censored lifetime data

Author

Listed:
  • Laurent Bordes

    (Univ. Pau & Pays de l’Adour)

  • Didier Chauveau

    (Univ. d’Orléans)

Abstract

Mixture models in reliability bring a useful compromise between parametric and nonparametric models, when several failure modes are suspected. The classical methods for estimation in mixture models rarely handle the additional difficulty coming from the fact that lifetime data are often censored, in a deterministic or random way. We present in this paper several iterative methods based on EM and Stochastic EM methodologies, that allow us to estimate parametric or semiparametric mixture models for randomly right censored lifetime data, provided they are identifiable. We consider different levels of completion for the (incomplete) observed data, and provide genuine or EM-like algorithms for several situations. In particular, we show that simulating the missing data coming from the mixture allows to plug a standard R package for survival data analysis in an EM algorithm’s M-step. Moreover, in censored semiparametric situations, a stochastic step is the only practical solution allowing computation of nonparametric estimates of the unknown survival function. The effectiveness of the new proposed algorithms are demonstrated in simulation studies and an actual dataset example from aeronautic industry.

Suggested Citation

  • Laurent Bordes & Didier Chauveau, 2016. "Stochastic EM algorithms for parametric and semiparametric mixture models for right-censored lifetime data," Computational Statistics, Springer, vol. 31(4), pages 1513-1538, December.
  • Handle: RePEc:spr:compst:v:31:y:2016:i:4:d:10.1007_s00180-016-0661-7
    DOI: 10.1007/s00180-016-0661-7
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    References listed on IDEAS

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    1. Dirick, Lore & Claeskens, Gerda & Baesens, Bart, 2015. "An Akaike information criterion for multiple event mixture cure models," European Journal of Operational Research, Elsevier, vol. 241(2), pages 449-457.
    2. Bordes, Laurent & Chauveau, Didier & Vandekerkhove, Pierre, 2007. "A stochastic EM algorithm for a semiparametric mixture model," Computational Statistics & Data Analysis, Elsevier, vol. 51(11), pages 5429-5443, July.
    3. Akio Suzukawa & Hideyuki Imai & Yoshiharu Sato, 2001. "Kullback-Leibler Information Consistent Estimation for Censored Data," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 53(2), pages 262-276, June.
    4. Eric Beutner & Laurent Bordes, 2011. "Estimators Based on Data‐Driven Generalized Weighted Cramér‐von Mises Distances under Censoring – with Applications to Mixture Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 38(1), pages 108-129, March.
    5. Lee, Gyemin & Scott, Clayton, 2012. "EM algorithms for multivariate Gaussian mixture models with truncated and censored data," Computational Statistics & Data Analysis, Elsevier, vol. 56(9), pages 2816-2829.
    6. Castet, Jean-Francois & Saleh, Joseph H., 2010. "Single versus mixture Weibull distributions for nonparametric satellite reliability," Reliability Engineering and System Safety, Elsevier, vol. 95(3), pages 295-300.
    7. Cao, Ricardo & Janssen, Paul & Veraverbeke, Noel, 2001. "Relative density estimation and local bandwidth selection for censored data," Computational Statistics & Data Analysis, Elsevier, vol. 36(4), pages 497-510, June.
    8. Laurent Bordes & Céline Delmas & Pierre Vandekerkhove, 2006. "Semiparametric Estimation of a Two‐component Mixture Model where One Component is known," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 33(4), pages 733-752, December.
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    Cited by:

    1. Semhar Michael & Tatjana Miljkovic & Volodymyr Melnykov, 2020. "Mixture modeling of data with multiple partial right-censoring levels," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 14(2), pages 355-378, June.
    2. Ducros, Florence & Pamphile, Patrick, 2018. "Bayesian estimation of Weibull mixture in heavily censored data setting," Reliability Engineering and System Safety, Elsevier, vol. 180(C), pages 453-462.

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