Joint analysis of correlated repeated measures and recurrent events processes in the presence of death, with application to a study on acquired immune deficiency syndrome

Journal of the Royal Statistical Society. Series C: Applied Statistics

Volumn 58, Issue 1, 2009, Pages 65-81

  Liu, Lei ^a   Huang, Xuelin ^b  

^a UNIVERSITY OF VIRGINIA   (United States)

^b UNIVERSITY OF TEXAS   (United States)

Author keywords

Frailty model; Informative censoring; Longitudinal data analysis; Mixed effects model; Proportional hazards model

Indexed keywords

EID: 58149163015     PISSN: 00359254     EISSN: 14679876     Source Type: Journal    
DOI: 10.1111/j.1467-9876.2008.00641.x     Document Type: Article

References (48)

1. Abramowitz, M. Stegun, I. (1972) Handbook of Mathematical Functions. New York : Dover Publications.
2. Abrams, D. I., Goldman, A. I., Launer, C., Korvick, J. A., Neaton, J. D., Crane, L. R., Grodesky, M., Wakefield, S., Muth, K., Kornegay, S., Cohn, D. L., Harris, A., Luskin-Hawk, R., Markowitz, N., Sampson, J. H., Thompson, M. Deyton, L. (1994) A comparative trial of Didanosine or Zalcitabine after treatment with Zidovudine in patients with human immunodeficiency virus infection. New Engl. J. Med., 330, 657 662.
3. Andersen, P. K. Gill, R. D. (1982) Cox's regression model for counting processes: a large sample study. Ann. Statist., 10, 1100 1120.
4. Cox, D. R. (1972) Regression models and life-tables (with discussion). J. R. Statist. Soc. B, 34, 187 220.
5. Dempster, A. P., Laird, N. M. Rubin, D. B. (1977) Maximum likelihood from incomplete data via the EM algorithm (with discussion). J. R. Statist. Soc. B, 39, 1 38.
6. Diggle, P. Kenward, M. G. (1994) Informative drop-out in longitudinal data analysis (with discussion). Appl. Statist., 43, 49 93.
7. Faucett, C. L. Thomas, D. C. (1996) Simultaneously modelling censored survival data and repeatedly measured covariates: a Gibbs sampling approach. Statist. Med., 15, 1663 1685.
8. Feng, S., Wolfe, R. A. Port, P. K. (2005) Frailty survival model analysis of the National Deceased Donor Kidney Transplant Dataset using Poisson variance structures. J. Am. Statist. Ass., 100, 728 735.
9. Golub, G. H. Welsch, J. H. (1969) Calculation of Gaussian quadrature rules. Math. Computn, 23, 221 230.
10. Guo, X. Carlin, B. P. (2004) Separate and joint modeling of longitudinal and event time data using standard computer packages. Am. Statistn, 58, 16 24.
11. Guo, W. S., Ratcliffe, S. J. Ten Have, T. T. (2004) A random pattern-mixture model for longitudinal data with dropouts. J. Am. Statist. Ass., 99, 929 937.
12. Henderson, R., Diggle, P. Dobson, A. (2000) Joint modelling of longitudinal measurements and event time data. Biostatistics, 1, 465 480.
13. Henderson, R. Oman, P. (1999) Effect of frailty on marginal regression estimates in survival analysis. J. R. Statist. Soc. B, 61, 367 379.
14. Hogan, J. Laird, N. (1997a) Mixture models for the joint distribution of repeated measures and event times. Statist. Med., 16, 239 257.
15. Hogan, J. Laird, N. (1997b) Model-based approaches to analysing incomplete longitudinal and failure time data. Statist. Med., 16, 259 272.
16. Hogan, J. Laird, N. (1998) Increasing efficiency from censored survival data by using random effects to model longitudinal covariates. Statist. Meth. Med. Res., 7, 28 48.
17. Hsieh, F., Tseng, Y.-K. Wang, J.-L. (2006) Joint modeling of survival and longitudinal data: likelihood approach revisited. Biometrics, 62, 1037 1043.
18. Huang, X. Liu, L. (2007) A joint frailty model for survival time and gap times between recurrent events. Biometrics, 63, 389 397.
19. Huang, C.-Y. Wang, M. C. (2004) Joint modeling and estimation for recurrent event processes and failure time data. J. Am. Statist. Ass., 99, 1153 1165.
20. Huang, Y. Wang, M. C. (2003) Frequency of recurrent events at failure time: modeling and inference. J. Am. Statist. Ass., 98, 663 670.
21. Kalbfleisch, J. D. Prentice, R. (2002) The Statistical Analysis of Failure Time Data, 2nd edn. New York : Wiley.
22. Lancaster, A. Intrator, O. (1998) Panel data with survival: hospitalization of HIV-positive patients. J. Am. Statist. Ass., 93, 46 53.
23. Lawless, J. F. Zhan, M. (1998) Analysis of interval-grouped recurrent event data using piecewise constant rate function. Can. J. Statist., 26, 549 565.
24. Littell, R. C., Milliken, G. A., Stroup, W. W., Wolfinger, R. D. Schabernberger, O. (2006) SAS for Mixed Model, 2nd edn. Cary : SAS Institute.
25. Little, R. Rubin, D. B. (2002) Statistical Analysis with Missing Data, 2nd edn. New York : Wiley.
26. Liu, L. Huang, X. (2008) The use of Gaussian quadrature for estimation in frailty proportional hazards models. Statist. Med., 27, 2665 2683.
27. Liu, L., Huang, X. O'Quigley, J. (2008) Analysis of longitudinal data in the presence of informative observational times and a dependent terminal event, with application to medical cost data. Biometrics, to be published, doi :.
28. Liu, L., Wolfe, R. A. Huang, X. (2004) Shared frailty models for recurrent events and a terminal event. Biometrics, 60, 747 756.
29. Liu, L. Yu, Z. (2008) A likelihood reformulation method in non-normal random effects models. Statist. Med., 27, 3105 3124.
30. Liu, Q. Pierce, D. A. (1994) A note on Gauss-Hermite quadrature. Biometrika, 81, 624 629.
31. Molenberghs, G. Verbeke, G. (2005) Models for Discrete Longitudinal Data. New York : Springer.
32. Neaton, J. D., Wentworth, D. N., Rhame, F., Hogan, C., Abrams, D. I. Deyton, L. (1994) Considerations in choice of a clinical endpoint for AIDS clinical trials. Statist. Med., 13, 2107 2125.
33. Nelson, K. P., Lipsitz, S. R., Fitzmaurice, G. M., Ibrahim, J., Parzen, M. Strawderman, R. (2006) Use of the probability integral transformation to fit nonlinear mixed-effects models with nonnormal random effects. J. Computnl Graph. Statist., 15, 39 57.
34. Pinheiro, J. C. Bates, D. M. (1995) Approximations to the log-likelihood function in the non-linear mixed-effects models. J. Computnl Graph. Statist., 4, 12 35.
35. Ratcliffe, S. J., Guo, W. Ten Have, T. R. (2004) Joint modeling of longitudinal and survival data via a common frailty. Biometrics, 60, 892 899.
36. Stram, D. O. Lee, J. W. (1994) Variance components testing in the longitudinal mixed effects model. Biometrics, 50, 1171 1177 correction, 51 (1995), 1196.
37. Therneau, T. M. Grambsch P. M. (2000) Modeling Survival Data: extending the Cox Model. New York : Springer.
38. Tsiatis, A. A. Davidian, M. (2001) A semiparametric estimator for the proportional hazards model with longitudinal covariates measured with error. Biometrika, 88, 447 458.
39. Tsiatis, A. A. Davidian, M. (2004) Joint modeling of longitudinal and time-to-event data: an overview. Statist. Sin., 14, 809 834.
40. Verbeke, G. Molenberghs, G. (2000) Linear Mixed Models for Longitudinal Data. New York : Springer.
41. Vonesh, E. F., Greene, T. Schluchter, M. D. (2006) Shared parameter models for the joint analysis of longitudinal data and event times. Statist. Med., 25, 143 163.
42. Wang, M., Qin, J. Chiang, C. (2001) Analyzing recurrent event data with informative censoring. J. Am. Statist. Ass., 96, 1057 1065.
43. Wei, L. J., Lin, D. Y. Weissfeld, L. (1989) Regression analysis of multivariate incomplete failure time data by modeling marginal distributions. J. Am. Statist. Ass., 84, 1065 1073.
44. Wulfsohn, M. S. Tsiatis, A. A. (1997) A joint model for survival and longitudinal data measured with error. Biometrics, 53, 330 339.
45. Xu, J. Zeger, S. L. (2001) Joint analysis of longitudinal data comprising repeated measures and times to events. Appl. Statist., 50, 375 387.
46. Yu, M. G., Law, N. J., Taylor, J. M. G. Sandler, H. M. (2004) Joint longitudinal-survival-cure models and their application to prostate cancer Statist. Sin., 14, 835 862.
47. Zeng, D. Lin, D. Y. (2007a) Semiparametric transformation models with random effects for recurrent events. J. Am. Statist. Ass., 102, 167 180.
48. Zeng, D. Lin, D. Y. (2007b) Maximum likelihood estimation in semiparametric regression models with censored data (with discussion). J. R. Statist. Soc. B, 69, 507 564.