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Statistical Analysis of Bivariate Recurrent Event Data with Incomplete Observation Gaps

  • Kim, Yang-Jin (Department of Statistics, Sookmyung Women's University)
  • Received : 2013.03.05
  • Accepted : 2013.06.13
  • Published : 2013.07.31

Abstract

Subjects can experience two types of recurrent events in a longitudinal study. In addition, there may exist intermittent dropouts that results in repeated observation gaps during which no recurrent events are observed. Therefore, theses periods are regarded as non-risk status. In this paper, we consider a special case where information on the observation gap is incomplete, that is, the termination time of observation gap is not available while the starting time is known. For a statistical inference, incomplete termination time is incorporated in terms of interval-censored data and estimated with two approaches. A shared frailty effect is also employed for the association between two recurrent events. An EM algorithm is applied to recover unknown termination times as well as frailty effect. We apply the suggested method to young drivers' convictions data with several suspensions.

Acknowledgement

Supported by : Sookmyung Women's University

References

  1. Cai, J. and Schaubel, D. E. (2004). Marginal means/rates models for multiple type recurrent event types, Lifetime Data Analysis, 10, 121-138. https://doi.org/10.1023/B:LIDA.0000030199.23383.45
  2. Cook, R. J., Lawless, J. F. and Lee, K. A. (2010). A copula-based mixed Poisson model for bivariate recurrent events under event-dependent censoring, Statistics in Medicine, 29, 694-707.
  3. Cook, R., Zeng, L. and Lee, K. (2008). A multistate model for bivariate interval-censored failure time data, Biometrics, 64, 1100-1109. https://doi.org/10.1111/j.1541-0420.2007.00978.x
  4. Duchateau, L., Jassen, P., Kezic, I. and Fortpied, C. (2003). Evolution of recurrent asthma event rate over time in frailty models, Journal of the Royal Statistical Society, Series C (Applied Statistics), 52, 355-363. https://doi.org/10.1111/1467-9876.00409
  5. Finkelstein, D. M. (1986). A proportional hazards model for interval-censored failure time data, Biometrics, 42, 845-854. https://doi.org/10.2307/2530698
  6. Foucher, Y., Giral, M., Soulillou, J.-F. and Daures, J.-P. (2007). A semi-Markov model for multistate and interval-censored data with multiple terminal events. Application in renal transplantation, Statistics in Medicine, 26, 5381-5393. https://doi.org/10.1002/sim.3100
  7. Goetghebeur, E. and Ryan, L. (2000). Semiparametric regression analysis of interval-censored data, Biometrics, 56, 1139-1144. https://doi.org/10.1111/j.0006-341X.2000.01139.x
  8. Kim, Y. and Jhun, M. (2008). Analysis of recurrent event data with incomplete observation gaps, Statistics in Medicine, 27, 1075-1085. https://doi.org/10.1002/sim.2994
  9. Lawless, J. F. and Nadeau, J. C. (1995). Some simple robust methods for the analysis of recurrent events, Technometrics, 37, 158-168. https://doi.org/10.1080/00401706.1995.10484300
  10. Lawless, J. F. and Zhan, M. (1998). Analysis of interval-grouped recurrent event data using piecewise constant rate functions, Canadian Journal of Statistics, 26, 549-565. https://doi.org/10.2307/3315717
  11. Lindsey, J. and Ryan, L. (1998). Methods for interval censored data. Tutorial in biostatistics, Statistics in Medicine, 17, 219-138. https://doi.org/10.1002/(SICI)1097-0258(19980130)17:2<219::AID-SIM735>3.0.CO;2-O
  12. Liu, L., Wolfe, R. A. and Huang, X. (2004). Shared frailty models for recurrent events and a terminal event, Biometrics, 60, 747-756. https://doi.org/10.1111/j.0006-341X.2004.00225.x
  13. Pan, W. (2000). Multiple imputation approach to Cox regression with interval censored data, Biometrics, 56, 199-203. https://doi.org/10.1111/j.0006-341X.2000.00199.x
  14. Sun, J., Kim, Y., Hewett, J., Johnson, J. C., Farmer, J. and Gibler, M. (2001). Evaluation of traffic injury prevention programs using counting process approaches, Statistics in Medicine, 96, 469-475.
  15. Therneau, T. M. and Hamilton, S. C. (1997). rhDNase as an example of recurrent event analysis, Statistics in Medicine, 16, 2029-2047. https://doi.org/10.1002/(SICI)1097-0258(19970930)16:18<2029::AID-SIM637>3.0.CO;2-H
  16. Turnbull, B. W. (1976). The empirical distribution function with arbitrarily grouped censored and truncated data, Journal of the Royal Statistical Society: Series B (Statistical Methodology), 38, 290-295.
  17. Zhao, Q. and Sun, J. (2006). Semiparametric and nonparametric estimation of recurrent event with observation gaps, Computational Statistics & Data Analysis, 51, 1924-1933. https://doi.org/10.1016/j.csda.2005.12.006