Modeling Longitudinal Data, II: Standard Regression Models and Extensions

  • Pietro RavaniEmail author
  • Brendan Barrett
  • Patrick Parfrey
Part of the Methods in Molecular Biology™ book series (MIMB, volume 473)


In longitudinal studies, the relationship between exposure and disease can be measured once or multiple times while participants are monitored over time. Traditional regression techniques are used to model outcome data when each epidemiological unit is observed once. These models include generalized linear models for quantitative continuous, discrete, or qualitative outcome responses and models for time-to-event data. When data come from the same subjects or group of subjects, observations are not independent and the underlying correlation needs to be addressed in the analysis. Under these circumstances, extended models are necessary to handle complexities related to clustered data and repeated measurements of time-varying predictors or outcomes.


Generalized linear models survival analysis repeated measures multiple failure times 


  1. 1.
    1. Go, A. S., Chertow, G. M., Fan, D., McCulloch, C. E., Hsu, C. (2004) Chronic kidney disease and the risks of death, cardiovascular events, and hospitalization. N Engl J Med 351, 1296–1305.PubMedCrossRefGoogle Scholar
  2. 2.
    2. Merten, G. J., Burgess, W. P., Gray, L. V., Holleman, J. H., Roush, T. S., Kowalchuk, G. J., Bersin, R. M., Van Moore, A., Simonton, C. A. III, Rittase, R. A., Norton, H. J., Kennedy, T. P. (2004) Prevention of contrast-induced nephropathy with sodium bicarbonate: A randomized controlled trial. JAMA 291, 2328–2334.PubMedCrossRefGoogle Scholar
  3. 3.
    3. Ravani, P., Tripepi, G., Malberti, F., Testa, S., Mallamaci, F., Zoccali, C. (2005) Asymmetrical dimethylarginine predicts progression to dialysis and death in patients with chronic kidney disease: A competing risks modeling approach. J Am Soc Nephrol 16, 2449–2455.PubMedCrossRefGoogle Scholar
  4. 4.
    4. Heckbert, S. R., Post, W., Pearson, G. D., Arnett, D. K., Gomes, A. S., Jerosch-Herold, M., Hundley, W. G., Lima, J. A., Bluemke, D. A. (2006): Traditional cardiovascular risk factors in relation to left ventricular mass, volume, and systolic function by cardiac magnetic resonance imaging: The Multiethnic Study of Atherosclerosis. J Am Coll Cardiol 48, 2285–2292.PubMedCrossRefGoogle Scholar
  5. 5.
    5. Heine, G. H., Reichart, B., Ulrich, C., Kohler, H., Girndt, M. (2007) Do ultrasound renal resistance indices reflect systemic rather than renal vascular damage in chronic kidney disease? Nephrol Dial Transplant 22, 163–170.PubMedCrossRefGoogle Scholar
  6. 6.
    6. Glantz, S. A., Slinker, B. K. (2001) A Primer of Applied Regression and Analysis of Variance, 2nd ed. McGraw-Hill, New York.Google Scholar
  7. 7.
    7. Hosmer, D. W., Lemeshow, L. S. (2000) Introduction to logistic regression model, in Applied Logistic Regression, 2nd ed., John Wiley & Sons, New York, pp. 1–30.CrossRefGoogle Scholar
  8. 8.
    8. Hosmer, D. W., Lemeshow, L. S. (2000) Sample size issues when fitting logistic regression. In Applied Logistic Regression, 2nd ed. John Wiley & Sons New York, pp. 339–351.CrossRefGoogle Scholar
  9. 9.
    9. Hosmer, D. W., Lemeshow, L. S. (2000) Applied Logistic Regression, 2nd ed. John Wiley & Sons New York.CrossRefGoogle Scholar
  10. 10.
    10. Dupont, W. D. (2002) Introduction to Poisson regression: Inferences on morbidity and mortality rates, in A Simple Introduction to the Analysis of Complex Data. Cambridge University Press, Cambridge, MA, pp. 269–294.Google Scholar
  11. 11.
    11. Kleinbaum, D. G., Kupper, L. L., Muller, K. E., Nizam, A. (1997) Poisson regression analysis, in Applied Regression Analysis and Multivariable Methods. Duxbury Press, Belmont, CA, pp. 687–710.Google Scholar
  12. 12.
    12. Hosmer, D. W., Lemeshow, L. S. (1999) Applied Survival Analysis, Regression Modelling of Time to Event Data. John Wiley & Sons, New York.Google Scholar
  13. 13.
    13. Kleinbaum, D. G. (2005) Survival Analysis, a Self-Learning Text. Springer-Verlag, New York.Google Scholar
  14. 14.
    14. Cox, D. R. (1972) Regression models and life-tables. J Royal Stat Soc, Series B, 34, 187–220.Google Scholar
  15. 15.
    15. Bland, M., Altman, D. G. (1986) Statistical methods for assessing agreement between two methods of clinical measurements. Lancet 1, 307–310.PubMedCrossRefGoogle Scholar
  16. 16.
    16. Lin, D. Y., Wei, L. J. (1989) The robust inference for the Cox proportional hazards model. J Amer Stat Assoc 84, 1074–1078.CrossRefGoogle Scholar
  17. 17.
    17. White, H. (1982) Maximum likelihood estimation of misspecifed models. Econometrica 50, 1–25.CrossRefGoogle Scholar
  18. 18.
    18. Zeger, S. L., Liang, K.-Y. (1986) Longitudinal data analysis for discrete and continuous outcomes. Biometrics 42, 121–130.PubMedCrossRefGoogle Scholar
  19. 19.
    19. Therneau, T. M., Grambisch, P. M. (2000) Multiple events per subject and frailty models, in Modeling Survival Data: Extending the Cox Model. Springer-Verlag, New York, pp. 159–260.Google Scholar
  20. 20.
    20. Lee, E. W., Wei, L. J., Amato, D. (1992) Cox-type regression analysis for large number of small groups of correlated failure time observations, in Survival Analysis, State of the Art. Kluwer Academic Publishers, Dodrecht, the Netherlands, pp. 237–247.Google Scholar
  21. 21.
    21. Ravani, P., Tripepi, G., Malberti, F., et al. (2005) Asymmetrical dimethylarginine predicts progression to dialysis and death in patients with chronic kidney disease: A competing risks modeling approach. J Am Soc Neph 16, 2449–2455.CrossRefGoogle Scholar
  22. 22.
    22. Lunn, M., McNeil, D. (1995) Applying Cox regression to competing risks. Biometrics 51, 524–532.PubMedCrossRefGoogle Scholar
  23. 23.
    23. Wei, L. J., Lin, D. Y., Weissfeld, L. (1989) Regression analysis of multivariate incomplete failure time data by modeling marginal distributions. J Amer Stat Assoc 84, 1065–1073.CrossRefGoogle Scholar
  24. 24.
    24. Andersen, P. K., Gill, R. D. (1982) Cox's regression model for counting processes: A large sample study. Ann Stat 10, 1100–1120.CrossRefGoogle Scholar
  25. 25.
    25. Prentice, R. L., Williams, B. J., Peterson, A. V. (1981) On the regression analysis of multivariate failure time data. Biometrika 68, 373–379.CrossRefGoogle Scholar
  26. 26.
    26. Eknoyan, G., Beck, G. J., Cheung, A. K., Daugirdas, J. T., Greene, T., Kusek, J. W., Allon, M., Bailey, J., Delmez, J. A., Depner, T. A., Dwyer, J. T., Levey, A. S., Levin, N. W., Milford, E., Ornt, D. B., Rocco, M. V., Schulman, G., Schwab, S. J., Teehan, B. P., Toto, R., Hemodialysis (HEMO) Study Group. (2002) Effect of dialysis dose and membrane flux in maintenance hemodialysis. N Engl J Med 347 (25), 2010–2019.PubMedCrossRefGoogle Scholar
  27. 27.
    Ravani P, Tripepi G, Pecchini P, Mallamaci F, Malberti F, Zoccali C (2008) Urotensin II is an inverse predictor of death and fatal cardiovascular events in chronic kidney disease. Kidney Int 73, 95–101PubMedCrossRefGoogle Scholar
  28. 28.
    28. Huang, X., Wolfe, R. A. (2002) A frailty model for informative censoring. Biometrics 58, 510–520.PubMedCrossRefGoogle Scholar
  29. 29.
    Box-Steffensmeier, J. M., De Boef, S. (2005) Repeated events survival models: The conditional frailty model. Stat Med (Epub ahead of print)Google Scholar
  30. 30.
    30. Liu, L., Wolfe, R. A., Huang, X. (2004) Shared frailty models for recurrent events and a terminal event. Biometrics 60, 747–756.PubMedCrossRefGoogle Scholar
  31. 31.
    31. Mahe, C., Chevret, S. (2001) Analysis of recurrent failure times data: Should the baseline hazard be stratified? Stat Med 20, 3807–3815.PubMedCrossRefGoogle Scholar
  32. 32.
    32. Hougaard, P. (1995) Frailty models for survival data. Lifetime Data Anal 1,255–273.PubMedCrossRefGoogle Scholar
  33. 33.
    33. Pickles, A., Crouchley, R. (1995) A comparison of frailty models for multivariate survival data. Stat Med 14 (13), 1447–1461.PubMedCrossRefGoogle Scholar
  34. 34.
    34. Dittrich, E., Puttinger, H., Schillinger, M., Lang, I., Stefenelli, T., Horl, W. H., Vychytil, A. (2006) Effect of radio contrast media on residual renal function in peritoneal dialysis patients—a prospective study. Nephrol Dial Transplant 21(5), 1334–1339.PubMedCrossRefGoogle Scholar
  35. 35.
    35. van Vilsteren, M. C., de Greef, M. H., Huisman, R. M. (2005) The effects of a low-to-moderate intensity pre-conditioning exercise programme linked with exercise counselling for sedentary haemodialysis patients in the Netherlands: results of a randomized clinical trial. Nephrol Dial Transplant 20(1), 141–146.PubMedCrossRefGoogle Scholar
  36. 36.
    36. Weijnen, T. J., van Hamersvelt, H. W., Just, P. M., Struijk, D. G., Tjandra, Y. I., ter Wee, P. M., de Charro, F. T. (2003) Economic impact of extended time on peritoneal dialysis as a result of using polyglucose: The application of a Markov chain model to forecast changes in the development of the ESRD programme over time. Nephrol Dial Transplant18(2), 390–396.PubMedCrossRefGoogle Scholar
  37. 37.
    37. Espinosa, M., Martn-Malo, A., Ojeda, R., Santamara, R., Soriano, S., Aguera, M., Aljama, P. (2004) Marked reduction in the prevalence of hepatitis C virus infection in hemodialysis patients: Causes and consequences. Amer J Kidney Dis 43 (4), 685–689.CrossRefGoogle Scholar
  38. 38.
    Ravani P, Parfrey P, Murphy S, Gadag V, Barrett B (2008) Clinical research of kidney diseases IV: Standard regression models. Nephrol Dial Transplant 23, 475–82PubMedCrossRefGoogle Scholar
  39. 39.
    Ravani P, Parfrey P, Gadag V, Malberti F, Barrett B (2008) Clinical research of kidney diseases V: extended analytic models. Nephrol Dial Transplant 23, 1484–92PubMedCrossRefGoogle Scholar

Copyright information

© Humana Press, a part of Springer Science+Business Media, LLC 2008

Authors and Affiliations

  • Pietro Ravani
    • 1
    Email author
  • Brendan Barrett
    • 2
  • Patrick Parfrey
    • 2
  1. 1.Divisione di NeprologiaAzienda InstitutiCremonaItaly
  2. 2.Department of MedicineMemorial University of NewfoundlandCanada

Personalised recommendations