Skip to main content
SpringerLink
Log in

Designing and Analyzing Recurrent Event Data Trials

  • Chapter
  • First Online:
Biopharmaceutical Applied Statistics Symposium

Part of the book series: ICSA Book Series in Statistics ((ICSABSS))

  • 783 Accesses

Abstract

Recurrent event data analysis is common in clinical trials . Literature reviews indicate that most statistical models used for such data are often based on time to the first event or that events within a subject are considered to be independent.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
eBook
USD 16.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Similar content being viewed by others

References

  • Aalen, O. O., Borgan, Ø. & Gjessing, H. K. (2008). Survival and event history analysis: A process point of view. Springer.

    Google Scholar 

  • Altman, D. G., & Royston, P. (2000). What do we mean by validating a prognostic model? Statistics in Medicine, 19, 453–473.

    Article  Google Scholar 

  • Andersen, P. K., Abildstrom, S. Z., & Rosthøj, S. (2002). Competing risks as a multi-state model. Statistical Methods in Medical Research, 11, 203–215.

    Article  Google Scholar 

  • Andersen, P. K., Borgan, Ø., Gill, R. D., & Keiding, N. (1993). Statistical models based on counting processes. New York: Springer-Verlag.

    Book  Google Scholar 

  • Andersen, P. K., Borgan, Ø., Gill, R. D., & Keiding, N. (1997). Statistical models based on counting processes (Corrected ed.). New York: Springer.

    MATH  Google Scholar 

  • Andersen, P. K., & Gill, R. D. (1982). Cox’s regression model for counting processes: A large sample study. Annals of Statistics, 10, 1100–1120.

    Article  MathSciNet  Google Scholar 

  • Andersen P. K., & Keiding, N. (2002). Multi-state models for event history analysis. Statistical Methods in Medical Research, 11, 91.

    Google Scholar 

  • Blossfeld, H., & Rohwer, G. (1995). Techniques of event history modeling. New Jersey: Lawrence Erlbaum.

    MATH  Google Scholar 

  • Box-Steffensmeier, J. M., & De Boef, S. (2006). Repeated events survival models: The conditional Frailty model. Statistics in Medicine, 25, 3518–3533.

    Article  MathSciNet  Google Scholar 

  • Brenner, H., & Gefeller, O. (1997). Deriving more up-to-date estimates of long-term patient survival. Journal of Clinical Epidemiology, 50, 211–216.

    Article  Google Scholar 

  • Breslow, N. E. (1975). Analysis of survival data under the proportional hazards model. International Statistical Review/Revue Internationale de Statistique. 43(1), 45–57.

    Google Scholar 

  • Coleman, M. P., Forman, D., Bryant, H., Butler, J., Rachet, B., Maringe, C., Nur, U., et al. (1995–2007). Cancer survival in Australia, Canada, Denmark, Norway, Sweden, and the UK, (the International Cancer Benchmarking Partnership): An analysis of population-based cancer registry data. Lancet, 377: 127–138.

    Google Scholar 

  • Commenges, D. (1999). Multi-state models in epidemiology. Lifetime Data Analysis, 5, 315–327.

    Article  MathSciNet  Google Scholar 

  • Cook, R. J., & Lawless, J. F. (2002). Analysis of repeated events. Statistical Methods in Medical Research, 11, 141–166.

    Article  Google Scholar 

  • Cook, R. J., & Lawless, J. F. (2007). The statistical analysis of recurrent events. Springer.

    Google Scholar 

  • Courgeau, D., & Lelièvre, E. (1992). Event history analysis in demography. Oxford: Clarendon.

    Google Scholar 

  • Cox, D. R. (1972). Regression models and life-tables. Journal of the Royal Statistical Society: Series B, 34(2), 187–220.

    MathSciNet  MATH  Google Scholar 

  • Crowther, M. J. (2016). MULTISTATE: Stata module to perform multi-state survival analysis. https://ideas.repec.org/c/boc/bocode/s458207.html.

  • Dean, C. B., & Balshaw, R. (1997). Efficiency lost by analyzing counts rather than event times in Poisson and overdispersed Poisson regression models. Journal of the American Statistical Association, 92, 1387–1398.

    Article  MathSciNet  Google Scholar 

  • Duchateau, L., & Janssen, P. (2008). The Frailty model. Springer.

    Google Scholar 

  • Efron, B. (1974). The efficiency of Cox’s likelihood function for censored data. Journal of the American Statistical Association., 72(359), 557–565.

    Article  MathSciNet  Google Scholar 

  • Ette, E. I., Godfrey, C. J., Ogenstad, S., & Williams, P. (2002). Analysis of simulated clinical trials. In Simulation for designing clinical trials: A pharmacokinetic-pharmacodynamic modeling perspective. Marcel-Dekker, IBSN: 0-8247-0862-8.

    Google Scholar 

  • Fine, J. P., & Gray, R. J. (1999). A proportional hazards model for the subdistribution of a competing risk. Journal of the American Statistical Association, 94, 496–509.

    Article  MathSciNet  Google Scholar 

  • Fuchs, H. J., Borowitz, D. S., Christiansen, D. H., Morris, E. M., Nash, M. L., Ramsey, B. W., Rosenstein, B. J. et al. (1994). Effect of aerosolized recombinant human DNase on exacerbations of respiratory symptoms and on pulmonary function in patients with cystic fibrosis. The Pulmozyme Study Group. New England Journal of Medicine, 331(10):637–42.

    Google Scholar 

  • Gamel, J. W., & Vogel, R. L. (2001). Non-parametric comparison of relative versus cause-specific survival in Surveillance, Epidemiology and End Results (SEER) programme breast cancer patients. Statistical Methods in Medical Research, 10, 339–352.

    Article  Google Scholar 

  • Ghosh, D., & Lin, D. Y. (2000). Nonparametric analysis of recurrent events and death. Biometrics, 56(2), 554–562.

    Article  MathSciNet  Google Scholar 

  • Glynn, R. J., & Buring, J. E. (1996). Ways of measuring rates of recurrent events. British Medical Journal, 312, 364–367.

    Article  Google Scholar 

  • Guo, Z., Gill, T. M., & Allore, H. G. (2008). Modeling repeated time-to-event health conditions with discontinuous risk intervals. Methods of Information in Medicine, 47, 107–116.

    Google Scholar 

  • Gutierrez, R. G. (2002). Parametric frailty and shared frailty survival models. Stata Journal, 2, 22–44.

    Google Scholar 

  • Hilbe, J. M. (2007). Negative binomial regression. Cambridge University Press.

    Google Scholar 

  • Hougaard, P. (1984). Life table methods for heterogeneous populations: Distributions describing the heterogeneity. Biometrika, 71, 75–83.

    Article  MathSciNet  Google Scholar 

  • Hougaard, P. (1986a). A class of multivariate failure time distributions. Biometrika, 73, 671–678.

    MathSciNet  MATH  Google Scholar 

  • Hougaard, P. (1986b). Survival models for heterogeneous populations derived from stable distributions. Biometrika, 73, 397–96.

    Google Scholar 

  • Hougaard, P. (1995). Frailty models for survival data. Lifetime Data Analysis, 1, 255–273.

    Article  Google Scholar 

  • Hougaard, P. (1999). Multi-state models: A review. Lifetime Data Analysis, 5, 239–264.

    Article  MathSciNet  Google Scholar 

  • Hougaard, P. (2000). Analysis of multivariate survival data. New York: Springer.

    Book  Google Scholar 

  • Hsu, L., Gorfine, M., & Malone, K. (2007). On robustness of marginal regression coefficient estimates and hazard functions in multivariate survival analysis of family data when the frailty distribution is mis-specified. Statistics in Medicine, 26, 4657–4678.

    Article  MathSciNet  Google Scholar 

  • Jahn-Eimermacher, A., Ingel, K., Ozga, A. K., Preussler, S., & Binder, H. (2015). Simulating recurrent event data with hazard functions defined on a total time scale. BMC Medical Research Methodology, 15, 16.

    Article  Google Scholar 

  • Kachitvichyanukul, V. (1982). Computer generation of poisson, binomial, and hypergeometric random variables. Ph.D. thesis, Purdue University.

    Google Scholar 

  • Kelly, P. J., & Lim, L. L. (2000). Survival analysis for recurrent event data: An application to child-hood infectious diseases. Statistics in Medicine, 19, 13–33.

    Article  Google Scholar 

  • Kemp, A. W., & Kemp, C. D. (1990). A composition-search algorithm for low-parameter Poisson generation. Journal of Statistical Computation and Simulation, 35, 239–244.

    Article  MathSciNet  Google Scholar 

  • Kemp, C. D., & Kemp, A. W. (1991). Poisson random variate generation. Applied Statistics, 40, 143–158.

    Article  Google Scholar 

  • Lambert, P. C., & Royston, P. (2009). Further development of flexible parametric models for survival analysis. Stata Journal, 9, 265–290.

    Google Scholar 

  • Li, Q., & Lagakos, S. (1997). Use of the Wei-Lin-Weissfeld method for the analysis of a recurring and terminating event. Statistics in Medicine, 16, 925–940.

    Article  Google Scholar 

  • Lin, D. Y. (1994). Cox regression analysis of multivariate failure time data: The marginal approach. Statistics in Medicine, 13, 2233–2247.

    Article  Google Scholar 

  • Lin, D. Y., & Wei, L. J. (1989). The robust inference for the Cox proportional hazards model. Journal of the American Statistical Association, 84, 1074–1078.

    Article  MathSciNet  Google Scholar 

  • Lunn, M., & McNeil, D. (1995). Applying Cox regression to competing risks. Biometrics, 51, 524–532.

    Article  Google Scholar 

  • Marso, S. P., Daniels, G. H., Brown-Frandsen, K., Kristensen, P., Kristensen, P., Mann, J. F. E., et al. (2016). Liraglutide and cardiovascular outcomes in type 2 diabetes. New England Journal of Medicine, 375, 311–322.

    Article  Google Scholar 

  • Metcalfe, C., & Thompson, S. G. (2006). The importance of varying the event generation process in simulation studies of statistical methods for recurrent events. Statistics in Medicine, 25, 165–179.

    Article  MathSciNet  Google Scholar 

  • Metcalfe, C., & Thompson, S. G. (2007). Wei, Lin and Weissfeld’s marginal analysis of multivariate failure time data: Should it be applied to recurrent events outcome? Statistical Methods in Medical Research, 16, 103–122.

    Article  MathSciNet  Google Scholar 

  • Møller, H., Sandin, F., Bray, F., Klint, A., Linklater, K. M., Purushotham, A., et al. (2010). Breast cancer survival in England, Norway and Sweden: A population-based comparison. International Journal of Cancer, 127, 2630–2638.

    Article  Google Scholar 

  • Prentice, R. L., Williams, B. J., & Peterson, A. V. (1981). On the regression analysis of multivariate failure time data. Biometrika, 68, 373–379.

    Article  MathSciNet  Google Scholar 

  • Royston, P., & Lambert, P.C. (2011). Flexible parametric survival analysis using Stata: Beyond the Cox model. Stata-Press.

    Google Scholar 

  • Royston, P., & Parmar, M. K. B. (2002). Flexible parametric proportional-hazards and proportional-odds models for censored survival data, with application to prognostic modelling and estimation of treatment effects. Statistics in Medicine, 21, 2175–2197.

    Article  Google Scholar 

  • Sagara, I., Giorgi, R., Doumbo, O. K., Piarroux, R., & Gaudart, J. (2014). Modelling recurrent events: Comparison of statistical models with continuous and discontinuous risk intervals on recurrent malaria episodes data. Malaria Journal, 13, 293.

    Article  Google Scholar 

  • Stukel, T. A. (1993). Comparison of methods for the analysis of longitudinal interval count data. Statistics in Medicine, 12, 1339–1351.

    Article  Google Scholar 

  • Thall, P. F. (1988). Mixed Poisson likelihood regression models for longitudinal interval count data. Biometrics, 44, 197–209.

    Article  MathSciNet  Google Scholar 

  • Therneau, T. M. (1997). Extending the Cox model. In Proceedings of the First Seattle Symposium in Biostatistics. New York: Springer.

    Google Scholar 

  • Therneau, T. M., & Grambsch, P. M. (2000). Modeling survival data. New York: Springer.

    MATH  Google Scholar 

  • Therneau, T. M., & Hamilton, S. A. (1997). rhDNase as an example of recurrent event analysis. Statistics in Medicine Banner, 16, 2029–2047.

    Article  Google Scholar 

  • Thomsen, J. L., & Parner, E.T. (2006). Methods for analysing recurrent events in health care data. Examples from admissions in Ebeltoft Health Promotion project. Family Practice, 23, 407–413.

    Google Scholar 

  • Tsiatis, A. A. (2005). Competing risks. In P. Armitage & T. Colton (Eds.), Encyclopedia of Biostatistics (2nd ed., pp. 1025–1035). Hoboken, NJ: Wiley.

    Google Scholar 

  • Vaupel, J. W., Manton, K., & Stallard, E. (1979). The impact of heterogeneity in individual frailty on the dynamics of mortality. Demography, 16, 439–454.

    Article  Google Scholar 

  • Wei, L. J., Lin, D. Y., & Weissfeld, L. (1989). Regression analysis of multivariate incomplete failure time data by modeling marginal distributions. Journal of the American Statistical Association., 84, 1065–1073.

    Article  MathSciNet  Google Scholar 

  • Westfall, P. H., Dmitrienko, A., DeSouza, C., & Tomoiaga, A. (2010). Clinical trials simulation: A publicly available, grid-enabled, GUI-Driven SAS® system. SAS Global Forum 2010, Paper 180–2010.

    Google Scholar 

  • Westfall, P. H., Tsai, K., Ogenstad, S., Tomoiaga, A., Moseley, S., & Lu, Y. (2008). Clinical trials simulation: A statistical approach. Journal of Biopharmaceutical Statistics, 18(4), 611–630.

    Article  MathSciNet  Google Scholar 

  • Wienke, A., Holm, H., Skytthe, A., & Yashin, A. (2001). The heritability of mortality due to heart diseases: A correlated Frailty model applied to Danish twins. Twin Research, 4(4), 266–274.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Statogen Consulting LLC, 1600 Woodfield Creek Drive #215, Wake Forest, NC, 27587, USA

    Stephan Ogenstad

Authors
  1. Stephan Ogenstad
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Stephan Ogenstad .

Editor information

Editors and Affiliations

  1. Jiann-Ping Hsu College of Public Health, Georgia Southern University, Statesboro, Georgia, USA

    Karl E. Peace

  2. School of Social Work & Gillings School of Global Public Health, University of North Carolina, Chapel Hill, North Carolina, USA

    Ding-Geng Chen

  3. Boston University, Cambridge, Massachusetts, USA

    Sandeep Menon

Rights and permissions

Reprints and permissions

Copyright information

© 2018 Springer Nature Singapore Pte Ltd.

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Ogenstad, S. (2018). Designing and Analyzing Recurrent Event Data Trials. In: Peace, K., Chen, DG., Menon, S. (eds) Biopharmaceutical Applied Statistics Symposium . ICSA Book Series in Statistics. Springer, Singapore. https://doi.org/10.1007/978-981-10-7829-3_5

Download citation

Publish with us

Policies and ethics

Search

Navigation