Abstract
In this chapter, we introduce a new regression model for recurrent event data, in which the time of each recurrence is associated to one or multiple latent causes and no information is provided about the cause responsible for the event occurrence. This model is characterized by a fully parametric rate function and it is based on the exponential-Poisson distribution. The time of each recurrence is then given by the minimum lifetime value among all latent causes. Inference aspects of the proposed model are discussed via Bayesian inference by using Markov Chain Monte Carlo (MCMC) method. A simulation study investigates the frequentist properties of the posterior estimators for different sample sizes. A real-data application demonstrates the use of the proposed model.
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Notes
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The data can be found on http://www.umass.edu/statdata/statdata/data
References
Aalen, O.O., Borgan, O., Gjessing, H.K.: Survival and Event History Analysis: A Process Point of View. Springer, New York (2008)
Andersen, P.K., Borgan, O., Gill, R.D., Keiding, N.: Statistical Models Based on Counting Processes. Springer, New York (1993)
Andersen, P.K., Gill, R.D.: Cox’s regression model for counting processes: a large sample study. Ann. Stat. 10, 1100–1120 (1982)
Chib, S., Greenberg, E.: Understanding the Metropolis–Hastings algorithm. Am. Stat. 49, 327–335 (1995)
Cook, R.J., Lawless, J.F.: The statistical analysis of recurrent events. Springer, New York (2007)
Gelman, A., Rubin, D.B.: Inference from iterative simulation using multiple sequences. Stat. Sci. 4, 457–472 (1992)
Hosmer, D.W., Lemeshow, S., May, S.: Applied Survival Analysis: Regression Modeling of Time to Event Data. Wiley, New York (2008)
Huang, C.Y., Luo, X., Follmann, D.A.: A model checking method for the proportional hazards model with recurrent gap time data. Biostatistics 12, 535–547 (2011)
Ibrahim, J.G., Chen, M.H., Sinha, D.: Bayesian Survival Analysis. Springer, New York (2005)
Kalbfleisch, J.D., Prentice, R.L.: The Statistical Analysis of Failure Time Data. Wiley, New Jersey (2002)
Kus, C.: A new lifetime distribution. Comput. Stat. Data Anal. 51, 4497–4509 (2007)
Lawless, J.F.: Statistical Models and Methods for Lifetime Data. Wiley, New Jersey (2003)
Lawless, J.F., Nadeau, C.: Some simple robust methods for the analysis of recurrent events. Technometrics pp. 158–168 (1995)
Paulino, C.D.M., Turkman, M.A.A., Murteira, B.: Estatistica Bayesiana. Fundacao Calouste, Gulbenkian (2003)
Pena, E.A., Slate, E.H., Gonzalez, J.R.: Semiparametric inference for a general class of models for recurrent events. J. Stat. Plan. Inference 137(6), 1727–1747 (2007)
Prentice, R.L., Williams, B.J., Peterson, A.V.: On the regression analysis of multivariate failure time data. Biometrika 68, 373–379 (1981)
R Development Core Team: R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna (2013)
Rubinstein, R.Y., Kroese, D.P.: Simulation and the Monte Carlo Method. Wiley-Interscience, New Jersey (2008)
Xu, Y., Cheung, Y.B., Lam, K.F., Milligan, P.: Estimation and interpretation of incidence rate difference for recurrent events when the estimation model is misspecified. Biometrical Journal 54, 750–765 (2012)
Zhao, X., Zhou, X.: Modeling gap times between recurrent events by marginal rate function. Comput. Stat. Data Anal. 56, 370–383 (2012)
Zhao, X.B., Zhou, X., Wang, J.L.: Semiparametric model for recurrent event data with excess zeros and informative censoring. J. Stat. Plan. Inference 142(1), 289–300 (2012)
Acknowledgements
This work was partially funded by the Brazilian institutions FAPESP, CAPES, and CNPq.
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Macera, M., Louzada, F., Cancho, V. (2015). The Exponential-Poisson Regression Model for Recurrent Events: A Bayesian Approach. In: Polpo, A., Louzada, F., Rifo, L., Stern, J., Lauretto, M. (eds) Interdisciplinary Bayesian Statistics. Springer Proceedings in Mathematics & Statistics, vol 118. Springer, Cham. https://doi.org/10.1007/978-3-319-12454-4_29
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