Modeling Repeated Time-to-event Health Conditions with Discontinuous Risk Intervals

 

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Summary

Objectives: Researchers have often used rather simple approaches to analyze repeated time-to-event health conditions that either examine time to the first event or treat multiple events as independent. More sophisticated models have been developed, although previous applications have focused largely on such outcomes having continuous risk intervals. Limitations of applying these models include their difficulty in implementation without careful attention to forming the data structures.

Methods: We first review time-to-event models for repeated events that are extensions of the Cox model and frailty models. Next, we develop a way to efficiently set up the data structures with discontinuous risk intervals for such models, which are more appropriate for many applications than the continuous alternatives. Finally, we apply these models to a real dataset to investigate the effect of gender on functional disability in a cohort of older persons. For comparison, we demonstrate modeling time to the first event.

Results: The GEE Poisson, the Cox counting process, and the frailty models provided similar parameter estimates of gender effect on functional disability, that is, women had increased risk of bathing disability and other disability (disability in walking, dressing, or transferring) as compared to men. These results, especially for other disabilities, were quite different from those provided by an analysis of the first-event outcomes. However, the effect of gender was no longer significant in the counting process model fully adjusted for covariates.

Conclusion: Modeling time to only the first event may not be adequate. After properly setting up the data structures, repeated event models that account for the correlation between multiple events within subjects can be easily implemented with common statistical software packages.

• References

• 1 Twisk JWR, Smidt N, de Vente W. Applied analysis of recurrent events: a practical overview. J Epidemiol Community Health 2005; 59: 706-710.
  CrossrefPubMedGoogle Scholar
• 2 Therneau TM, Grambsch PM. Modeling survival data: extending the Cox model. New York:: Springer; 2000
  Google Scholar
• 3 Wei LJ, Glidden DV. An overview of statistical methods for multiple failure time data in clinical trials. Stat Med 1997; 16: 833-839.
  CrossrefPubMedGoogle Scholar
• 4 Therneau TM, Hamilton SA. rhDNase as an example of recurrent event analysis. Stat Med 1997; 16: 2029-2047.
  CrossrefPubMedGoogle Scholar
• 5 Aalen OO, Husebye E. Statistical analysis of repeated events forming renewal processes. Stat Med 1991; 10: 1227-1240.
  CrossrefPubMedGoogle Scholar
• 6 Kelly PJ, Lim LL. Survival analysis for recurrent event data: an application to childhood infectious disease. Stat Med 2000; 19: 13-33.
  CrossrefPubMedGoogle Scholar
• 7 Clayton D. Some approaches to the analysis of recurrent event data. Stat Methods Med Res 1994; 3: 244-262.
  CrossrefPubMedGoogle Scholar
• 8 Lin DY. Cox regression analysis of multivariate failure time data. Stat Med 1994; 13: 2233-2247.
  CrossrefPubMedGoogle Scholar
• 9 Cook RJ, Lawless JF. Analysis of Repeated Events. Stat Methods Med Res 2002; 11: 141-166.
  CrossrefPubMedGoogle Scholar
• 10 Gill TM, Guo Z, Allore HG. The epidemiology of bathing disability among older persons. J Am Geriatr Soc 2006; 54: 1524-1530.
  CrossrefPubMedGoogle Scholar
• 11 Gill TM, Allore HG, Hardy SE, Guo Z. The dynamic nature of mobility disability in older persons. J Am Geriatr Soc 2006; 54: 248-254.
  CrossrefPubMedGoogle Scholar
• 12 Hardy SE, Allore HG, Guo Z, Dubin JA, Gill TM. The effect of prior disability history on subsequent functional transitions. J Gerontol A Biol Sci Med Sci 2006; 61A: 272-277.
  PubMedGoogle Scholar
• 13 Fleiss JL, Levin B, Cho Paik M. Statistical Methods for Rates and Proportions. 3nd ed. New York: John Wiley & Sons; 2003
  Google Scholar
• 14 Liang KY, Zeger SL. Longitudinal data analysis using generalized linear models. Biometrika 1986; 73: 13-22.
  CrossrefPubMedGoogle Scholar
• 15 Hosmer DWJ, Lemeshow S. Applied survival analysis. Regression modeling of time to event data. New York, NY: John Wiley & Sons; 1999
  Google Scholar
• 16 Cox DR. Regression models and life-tables. J R Stat Soc 1972; B34: 86-94.
  PubMedGoogle Scholar
• 17 Andersen PK, Gill RD. Cox’s regression model for counting processes: a large sample study. Ann Stat 1982; 10: 1100-1120.
  CrossrefPubMedGoogle Scholar
• 18 Prentice RL, Williams BJ, Peterson AV. On the regression analysis of multivariate failure time data. Biometrika 1981; 68: 373-379.
  CrossrefPubMedGoogle Scholar
• 19 Lin DY, Wei LJ. The robust inference for the proportional hazards model. J Am Stat Soc 1989; 84: 1074-1078.
  PubMedGoogle Scholar
• 20 Gill TM, Desai MM, Gahbauer EA, Holford TR, Williams CS. Restricted activity among community- living older persons: incidence, precipitants, and health care utilization. Ann Intern Med 2001; 135: 313-321.
  CrossrefPubMedGoogle Scholar
• 21 Gill TM, Allore HG, Holford TR, Guo Z. Hospitalization, restricted activity, and the development of disability among old persons. JAMA 2004; 292: 2115-2124.
  CrossrefPubMedGoogle Scholar
• 22 Fleming TR, Harrington DP. Counting processes and survival analysis. New York: Wiley; 1991
  Google Scholar
• 23 Andersen PK, Borgan Ø, Gill RD, Keiding N. Statistical models based on counting processes. New York: Springer; 1993
  Google Scholar
• 24 Folstein MF, Folstein SE, McHugh PR. “Minimental state.” A practical method for grading the cognitive state of patients for the clinician. J Psychiatr Res 1975; 12: 189-198.
  CrossrefPubMedGoogle Scholar
• 25 Guralnik JM, Ferrucci L, Pieper CF, Leveille SG, Markides KS, Ostir GV, Studenski S, Berkman LF, Wallace RB. Lower extremity function and subsequent disability: consistency across studies, predictive models, and value of gait speed alone compared with the short physical performance battery. J Gerontol Med Sci 2000; 55A: M221-M231.
  PubMedGoogle Scholar
• 26 Radloff LS. The CES-D Scale: A self report depression scale for research in the general population. Appl Psychol Meas 1977; 1: 385-401.
  CrossrefPubMedGoogle Scholar
• 27 Box-Steffensmeier JM, Zorn C. Duration models for repeated events. JOP 2002; 64: 1069-1094.
  CrossrefPubMedGoogle Scholar
• 28 Boher J, Cook RJ. Implications of model misspecification in robust tests for recurrent events. Lifetime Data Anal 2006; 12: 69-95.
  CrossrefPubMedGoogle Scholar
• 29 Jiang ST, Landers TL, Rhoads TR. Proportional intensity models robustness with overhaul intervals. Qual Reliab Engng Int 2006; 22: 251-263.
  CrossrefPubMedGoogle Scholar
• 30 Laird N, Olivier D. Covariance Analysis of Censored Survival Data Using Log-Linear Analysis Techniques. J Am Stat Soc 1981; 76: 231-240.
  PubMedGoogle Scholar
• 31 Wei LJ, Lin DY, Weissfeld L. Regression analysis of multivariate incomplete failure time data by modeling marginal distributions. J Am Stat Soc 1989; 84: 1065-1073.
  PubMedGoogle Scholar
• 32 SAS/STAT 9.1 User’s Guide. Cary, NC: SAS Institute; 2004
  PubMed
• 33 S-PLUS 6 for Windows Guide to Statistics Volume 2. Seattle, WA: Insightful Corporation; 2001.
  PubMed