A review of Cox's model extensions for multiple events

  • Ana Maria Abreu Departamento de Matemática, Faculdade de Ciências Exatas e da Engenharia, Universidade da Madeira, 9020-105 Funchal, Portugal
  • Ivo Sousa-Ferreira Centro de Estatística e Aplicações, Faculdade de Ciências, Universidade de Lisboa, 1749-016 Lisboa, Portugal
Keywords: extensions of Cox's model, multiple events, Survival Analysis


In longitudinal studies, it is usual that a given subject can experience several failures. To analyse multiple failure-time data, we reviewed some extensions of Cox's regression model, which were proposed by: Prentice, Williams and Peterson (PWP); Andersen and Gill (AG); Wei, Lin e Weissfeld (WLW); and Lee, Wei and Amato (LWA). Our main goal is to underline the differences between these extensions, through a brief but careful description, providing also some guidance on how to choose the proper model for each situation. The guidelines presented in this work revealed to be a useful pointer to easily choose the most suitable model. Secondarily, we used the survsim and the survival R packages to illustrate the practical implementation of these models.


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[1] D. Cox, “Partial likelihood,” Biometrika, 1975, 62(2): 269-276.
[2] D. Cox, “Regression Models and Life-Tables,” Journal of the Royal Statistical Society. Series B (Methodological), 1972, 34(2): 187-220.
[3] P. Kelly e L.-Y. Lim, “Survival analysis for recurrent event data: an application to childhood infectious diseases,” Statistics in Medicine, 2000, 19(1): 13-33.
[4] I. Sousa-Ferreira e A. Abreu, “Hybrid model for recurrent event data,” em Matrices, Statistics and Big Data: Proceedings of the 25th International Workshop on Matrices and Statistics (IWMS'2016, Funchal, Madeira. Portugal, 6-9 June 2016), S. Ahmed, F. Carvalho e S. Puntanen, Edits., Springer, 2019, in press.
[5] R. Prentice, B. Williams e A. Peterson, “On the Regression Analysis of Multivariate Failure Time Data,” Biometrika, 1981, 68(2): 373-379.
[6] P. Andersen e R. Gill, “Cox's Regression Model for Counting Processes: A Large Sample Study,” The Annals of Statistics, 1982, 10(4): 1100-1120.
[7] L. Wei, D. Lin e L. Weissfeld, “Regression Analysis of Multivariate Incomplete Failure Time Data by Modeling Marginal Distributions,” Journal of the American Statistical Association, 1989, 84(408): 1065-1073.
[8] E. Lee, L. Wei e D. Amato, “Cox-Type Regression Analysis for Large Numbers of Small Groups of Correlated Failure Time Observations,” em Survival Analysis: State of the Art, J. Klein e P. Goel, Edits., Dordrecht, Springer Netherlands, 1992, 237-247.
[9] D. Lin e L. Wei, “The Robust Inference for the Cox Proportional Hazards Model,” Journal of the American Statistical Association, 1989, 84(408): 1074-1078.
[10] J. Castañeda e B. Gerritse, “Appraisal of Several Methods to Model Time to Multiple Events per Subject: Modelling Time to Hospitalizations and Death,” Revista Colombiana de Estadística, 2010, 33(1): 43-61.
[11] I. Ferreira, Modelos para Acontecimentos Múltiplos, Funchal, Portugal: (Master's dissertation). Faculdade de Ciências Exatas e da Engenharia, Universidade da Madeira, 2016.
[12] T. Therneau e P. Grambsch, Modeling Survival Data: Extending the Cox Model, New York: Springer Science & Business Media, 2000.
[13] T. Therneau e S. Hamilton, “rhDNase as an example of recurrent event analysis,” Statistics in Medicine, 1997, 16(18): 2029-2047.
[14] R Development Core Team, R: A Language and Environment for Statistical Computing, Vienna, Austria: R Foundation for Statistical Computing (ISBN: 3-900051-07-0), 2018.
[15] J. Box-Steffensmeier e S. De Boef, “Repeated events survival models: the conditional frailty model,” Statistics in Medicine, 2006, 25(20): 3518-3533.
[16] J. Cai e D. Schaubel, “Analysis of Recurrent Event Data,” em Handbook of Statistics: Advances in Survival Analysis, vol. 23, N. Balakrishnan e C. Rao, Edits., North Holland, Elsevier, 2003, 603-623.
[17] R. Cook e J. Lawless, “Analysis of repeated events,” Statistical Methods in Medical Research, 2002, 11(2): 141-166.
[18] L. Wei e D. Glidden, “An overview of statistical methods for multiple failure time data in clinical trials,” Statistics in Medicine, 1997, 16(8): 833-839.
[19] E. Kaplan e P. Meier, “Nonparametric Estimation from Incomplete Observations,” Journal of the American Statistical Association, 1958, 53(282): 457-481.
[20] L. Amorim e J. Cai, “Modelling recurrent events: a tutorial for analysis in epidemiology,” International Journal of Epidemiology, 2015, 44(1): 324-333.
[21] D. Moriña e A. Navarro, “The R package survsim for the simulation of simple and complex survival data,” Journal of Statistical Software, 2014, 59(2): 1-20.
[22] D. Moriña e A. Navarro, survsim: Simulation of simple and complex survival data, (R package version 1.1.5), 2018.
[23] T. Therneau, survival: A package for survival analysis in S, R package version 2.43-3, 2018.
[24] C. Metcalfe e S. Thompson, “Wei, Lin and Weissfeld's marginal analysis of multivariate failure time data: should it be applied to a recurrent events outcome?,” Statistical Methods in Medical Research, 2007, 16(2): 103-122.
[25] D. Lin, “Cox regression analysis of multivariate failure time data: The marginal approach,” Statistics in Medicine, 1994, 13(21): 2233-2247.
How to Cite
Abreu, A. M., & Sousa-Ferreira, I. (2019). A review of Cox’s model extensions for multiple events. IJRDO - Journal of Applied Science (ISSN: 2455-6653), 5(2), 47-62. Retrieved from https://ijrdo.org/index.php/as/article/view/2677