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Bayesian Threshold Regression Model with Random Effects for Recurrent Events

Author

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  • P. Economou

    (University of Patras)

  • S. Malefaki

    (University of Patras)

  • C. Caroni

    (National Technical University of Athens)

Abstract

It is of practical importance to extend time-to-event models in order to be applicable in situations with recurrent events on the same individual or machine. The model proposed here extends in this direction a threshold regression model with random individual effects, in which event times are modeled as realizations of the first hitting times of an underlying Wiener process, leading to Inverse Gaussian distributions of times between events. In our approach, the parameters of the distribution of an event time may depend on features of the process (such as number of previous events and total elapsed time) as well as on measured, possibly time varying, covariates and the individuals’ random effects. A Bayesian approach is adopted for model estimation using an improved MCMC algorithm, which guarantees a proper choice of proposal distribution at any step of the hybrid Gibbs sampler when this is required. Model fitting is investigated using simulated data and the model is applied to a set of real data on drug users who made repeated contacts with treatment services.

Suggested Citation

  • P. Economou & S. Malefaki & C. Caroni, 2015. "Bayesian Threshold Regression Model with Random Effects for Recurrent Events," Methodology and Computing in Applied Probability, Springer, vol. 17(4), pages 871-898, December.
    • Handle: RePEc:spr:metcap:v:17:y:2015:i:4:d:10.1007_s11009-015-9445-8
    DOI: 10.1007/s11009-015-9445-8
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    References listed on IDEAS

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    1. Xiang, Liming & Yau, Kelvin K.W. & Tse, S.K. & Lee, Andy H., 2007. "Influence diagnostics for random effect survival models: Application to a recurrent infection study for kidney patients on portable dialysis," Computational Statistics & Data Analysis, Elsevier, vol. 51(12), pages 5977-5993, August.
    2. William Griffiths, 2002. "A Gibbs’ Sampler for the Parameters of a Truncated Multivariate Normal Distribution," Department of Economics - Working Papers Series 856, The University of Melbourne.
    3. Abrahantes, Jose Cortinas & Legrand, Catherine & Burzykowski, Tomasz & Janssen, Paul & Ducrocq, Vincent & Duchateau, Luc, 2007. "Comparison of different estimation procedures for proportional hazards model with random effects," Computational Statistics & Data Analysis, Elsevier, vol. 51(8), pages 3913-3930, May.
    4. Horrace, William C., 2005. "Some results on the multivariate truncated normal distribution," Journal of Multivariate Analysis, Elsevier, vol. 94(1), pages 209-221, May.
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    Cited by:

    1. Jonathan A. Race & Michael L. Pennell, 2021. "Semi-parametric survival analysis via Dirichlet process mixtures of the First Hitting Time model," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 27(1), pages 177-194, January.

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