Fully exponential Laplace approximations for the joint modelling of survival and longitudinal data

Journal of the Royal Statistical Society. Series B: Statistical Methodology

Volumn 71, Issue 3, 2009, Pages 637-654

  Rizopoulos, Dimitris ^a   Verbeke, Geert ^b   Lesaffre, Emmanuel ^a,b  

^a ERASMUS MEDICAL CENTER   (Netherlands)

^b UNIVERSITY OF LEUVEN   (Belgium)

Author keywords

B splines; Dropout; Longitudinal models; Shared parameter model; Survival models; Time to event

Indexed keywords

EID: 66849099701     PISSN: 13697412     EISSN: 14679868     Source Type: Journal    
DOI: 10.1111/j.1467-9868.2008.00704.x     Document Type: Article

References (23)

1. Breslow, N. Clayton, D. (1993) Approximate inference in generalized linear mixed models. J. Am. Statist. Ass., 88, 9 25.
2. Cortiñas Abrahantes, J., Legrand, C., Burzykowski, T., Janssen, P., Ducrocq, V. Duchateau, L. (2007) Comparison of different estimation procedures for proportional hazards model with random effects. Computnl Statist. Data Anal., 51, 3913 3930. (Pubitemid 46501791)
3. Cox, D. Hinkley, D. (1974) Theoretical Statistics. London : Chapman and Hall.
4. De Bruijn, N. (1981) Asymptotic Methods in Analysis. New York : Dover Publications.
5. Dierckx, P. (1995) Curve and Surface Fitting with Splines. New York : Oxford University Press.
6. Follmann, D. Wu, M. (1995) An approximate generalized linear model with random effects for informative missing data. Biometrics, 51, 151 168.
7. Henderson, R., Diggle, P. Dobson, A. (2000) Joint modelling of longitudinal measurements and event time data. Biostatistics, 1, 465 480. (Pubitemid 33213549)
8. Hsieh, F., Tseng, Y.-K. Wang, J.-L. (2006) Joint modeling of survival and longitudinal data: likelihood approach revisited. Biometrics, 62, 1037 1043.
9. Kauermann, G., Xu, R. Vaida, F. (2008) Stacked Laplace-EM algorithm for duration models with time-varying and random effects. Computnl Statist. Data Anal., 52, 2514 2528.
10. Kim, D. Taylor, J. (1995) The restricted EM algorithm for maximum likelihood estimation under linear restrictions on the parameters. J. Am. Statist. Ass., 90, 708 716.
11. Lange, K. (2004) Optimization. New York : Springer.
12. Louis, T. A. (1982) Finding the observed information matrix when using the EM algorithm. J. R. Statist. Soc. B, 44, 226 233.
13. Press, W., Teukolsky, S., Vetterling, W. Flannery, B. (2007) Numerical Recipes: the Art of Scientific Computing, 3rd edn. New York : Cambridge University Press.
14. R Development Core Team (2008) R: a Language and Environment for Statistical Computing. Vienna : R Foundation for Statistical Computing.
15. Rizopoulos, D., Verbeke, G. Molenberghs, G. (2008) Shared parameter models under random effects misspecification. Biometrika, 95, 63 74.
16. Rosenberg, P. (1995) Hazard function estimation using B-splines. Biometrics, 51, 874 887.
17. Royston, P. Parmar, M. (2002) Flexible parametric proportional-hazards and proportional-odds models for censored survival data with application to prognostic modelling and estimation of treatment effects. Statist. Med., 21, 2175 2197. (Pubitemid 34830755)
18. Song, X., Davidian, M. Tsiatis, A. (2002) A semiparameteric likelihood approach to joint modeling of longitudinal and time-to-event data. Biometrics, 58, 742 753. (Pubitemid 36133752)
19. Steel, B. (1996) A modified EM algorithm for estimation in generalized mixed models. Biometrics, 52, 1295 1310.
20. Tierney, L., Kass, R. Kadane, J. (1989) Fully exponential Laplace approximations to expectations and variances of nonpositive functions. J. Am. Statist. Ass., 84, 710 716.
21. Tsiatis, A. Davidian, M. (2004) Joint modeling of longitudinal and time-to-event data: an overview. Statist. Sin., 14, 809 834. (Pubitemid 39499214)
22. Vonesh, E. (1996) A note on the use of Laplace's approximation for nonlinear mixed-effects models. Biometrika, 83, 447 452.
23. Wu, J. (1983) On the convergence properties of the EM algorithm. Ann. Statist., 11, 95 103.