Assessing transient carryover effects in recurrent event processes, with application to chronic health conditions. (English) Zbl 1257.62102

Summary: In some settings involving recurrent events, the occurrence of one event may produce a temporary increase in the event intensity; we refer to this phenomenon as a transient carryover effect. This paper provides models and tests for carryover effects. Motivation for our work comes from events associated with chronic health conditions, and we consider two studies involving asthma attacks in children in some detail. We consider how carryover effects can be modeled and assessed, and note some difficulties in the context of heterogeneous groups of individuals. We give a simple intuitive test for no carryover effects and examine its properties. In addition, we demonstrate the need for detailed modeling in trying to deconstruct the dynamics of recurrent events.


62P10 Applications of statistics to biology and medical sciences; meta analysis
62N03 Testing in survival analysis and censored data
Full Text: DOI arXiv Euclid


[1] Andersen, P. K., Borgan, Ø., Gill, R. D. and Keiding, N. (1993). Statistical Models Based on Counting Processes . Springer, New York. · Zbl 0769.62061
[2] Ascher, H. and Feingold, H. (1984). Repairable Systems Reliability : Modeling , Inference , Misconceptions and Their Causes. Lecture Notes in Statistics 7 . Dekker, New York. · Zbl 0543.62083
[3] Baker, R. D. (1996). Some new tests of the power law process. Technometrics 38 256-265. · Zbl 0898.62121 · doi:10.2307/1270609
[4] Baker, R. D. (2001). Data-based modeling of the failure rate of repairable equipment. Lifetime Data Anal. 7 65-83. · Zbl 0998.62090 · doi:10.1023/A:1009677227030
[5] Çığşar, C. (2010). Some models and tests for carryover effects and trends in recurrent event processes. Ph.D. thesis, Univ. Waterloo, Waterloo, Ont., Canada. Available at .
[6] Çığşar, C. and Lawless, J. F. (2012). Supplement to “Assessing transient carryover effects in recurrent event processes, with application to chronic health conditions.” . · Zbl 1257.62102
[7] Cook, R. J. and Lawless, J. F. (2007). The Statistical Anlaysis of Recurrent Events . Springer, New York. · Zbl 1159.62061
[8] Cox, D. R. and Isham, V. (1980). Point Processes . Chapman & Hall, London. · Zbl 0441.60053
[9] Cox, D. R. and Lewis, P. A. W. (1966). The Statistical Analysis of Series of Events . Methuen, London. · Zbl 0148.14005
[10] Daley, D. J. and Vere-Jones, D. (2003). An Introduction to the Theory of Point Processes. Vol. I : Elementary Theory and Methods , 2nd ed. Springer, New York. · Zbl 1026.60061 · doi:10.1007/b97277
[11] Duchateau, L., Janssen, P., Kezic, I. and Fortpied, C. (2003). Evolution of recurrent asthma event rate over time in frailty models. J. R. Stat. Soc. Ser. C. Appl. Stat. 52 355-363. · Zbl 1111.62336 · doi:10.1111/1467-9876.00409
[12] Farrington, C. P. and Hocine, M. N. (2010). Within-individual dependence in self-controlled case series models for recurrent events. J. R. Stat. Soc. Ser. C. Appl. Stat. 59 457-475. · doi:10.1111/j.1467-9876.2009.00703.x
[13] Farrington, C. P. and Whitaker, H. J. (2006). Semiparametric analysis of case series data. J. R. Stat. Soc. Ser. C. Appl. Stat. 55 553-594. · Zbl 1109.62099 · doi:10.1111/j.1467-9876.2006.00554.x
[14] Farrington, C. P., Whitaker, H. J. and Hocine, M. N. (2009). Case series analysis for censored, perturbed, or curtailed post-event exposures. Biostatistics 10 3-16.
[15] Karr, A. F. (1991). Point Processes and Their Statistical Inference , 2nd ed. Probability : Pure and Applied 7 . Dekker, New York. · Zbl 0733.62088
[16] Lawless, J. F. (1987). Regression methods for Poisson process data. J. Amer. Statist. Assoc. 82 808-815. · Zbl 0657.62103 · doi:10.2307/2288790
[17] Lawless, J. F., Wigg, M. B., Tuli, S., Drake, J. and Lamberti-Pasculli, M. (2001). Analysis of repeated failures or durations, with application to shunt failures for patients with paediatric hydrocephalus. J. R. Stat. Soc. Ser. C. Appl. Stat. 50 449-465. · Zbl 1112.62344 · doi:10.1111/1467-9876.00247
[18] Lindqvist, B. H. (2006). On the statistical modeling and analysis of repairable systems. Statist. Sci. 21 532-551. · Zbl 1129.62092 · doi:10.1214/088342306000000448
[19] Ogata, Y. (1983). Likelihood analysis of point processes and its application to seismological data. Bull. Int. Statist. Inst. 50 943-961.
[20] Peña, E. A. (1998). Smooth goodness-of-fit tests for composite hypothesis in hazard based models. Ann. Statist. 26 1935-1971. · Zbl 0934.62023 · doi:10.1214/aos/1024691364
[21] Peña, E. A. (2006). Dynamic modeling and statistical analysis of event times. Statist. Sci. 21 487-500. · Zbl 1129.62088 · doi:10.1214/088342306000000349
[22] Tuli, S., Drake, J., Lawless, J. F., Wigg, M. and Lamberti-Pasculli, M. (2000). Risk factors for repeated cerebrospinal shunt failures in patients with pediatric hydrocephalus. J. Neurosurgery 92 31-38. · Zbl 1112.62344
[23] Verona, E., Petrov, D., Cserhati, E., Hofman, J., Geppe, N., Medley, H. and Hughes, S. (2003). Fluticasone propionate in asthma: A long term dose comparison study. Arch. Dis. Child. 88 503-509.
[24] Xie, M., Sun, Q. and Naus, J. (2009). A latent model to detect multiple clusters of varying sizes. Biometrics 65 1011-1020. · Zbl 1181.62185 · doi:10.1111/j.1541-0420.2009.01197.x
[25] Xu, S., Zhang, L., Nelson, J. C., Zeng, C., Mullooly, J., McClure, D. and Glanz, J. (2011). Identifying optimal risk windows for self-controlled case series studies of vaccine safety. Stat. Med. 30 742-752. · doi:10.1002/sim.4125
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.