Bayesian proportional hazards model with time-varying regression coefficients: A penalized Poisson regression approach

Statistics in Medicine

Volumn 24, Issue 24, 2005, Pages 3977-3989

  Lambert, Philippe ^a   Eilers, Paul H C ^b  

^a UNIVERSITÉ CATHOLIQUE DE LOUVAIN   (Belgium)

^b LEIDEN UNIVERSITY   (Netherlands)

Author keywords

Markov chain Monte Carlo methods; Metropolis adjusted Langevin algorithm; P splines; Proportional hazards

Indexed keywords

ADVANCED CANCER; ALGORITHM; ARTICLE; BAYES THEOREM; CANCER PATIENT; CANCER RISK; CLINICAL STUDY; CONTROLLED STUDY; CORRELATION COEFFICIENT; COVARIANCE; FEMALE; HUMAN; LOGLINEAR MODEL; MAJOR CLINICAL STUDY; OVARY CANCER; PARAMETRIC TEST; POISSON DISTRIBUTION; PROPORTIONAL HAZARDS MODEL; REGRESSION ANALYSIS; RISK ASSESSMENT; STATISTICAL ANALYSIS; SURVIVAL RATE; SURVIVAL TIME;

BAYES THEOREM; HUMANS; POISSON DISTRIBUTION; PROPORTIONAL HAZARDS MODELS; REGRESSION ANALYSIS; SURVIVAL ANALYSIS; TIME FACTORS;

EID: 30944433781     PISSN: 02776715     EISSN: 10970258     Source Type: Journal    
DOI: 10.1002/sim.2396     Document Type: Article

References (24)

1. Efron B. Logistic regression, survival analysis, and the kaplan-meier curve. Journal of the American Statistical Association 1988; 83:414-425.
2. Tutz G, Binder H. Flexible modelling of discrete failure time including time-varying smooth effects. Statistics in Medicine 2004; 23:2445-2461.
3. Kauermann G. Penalized spline smoothing in multivariable survival models with varying coefficients. Computational Statistics and Data Analysis 2005; 49:169-186.
4. Eilers PHC, Marx BD. Flexible smoothing with B-splines and penalties (with discussion). Statistical Science 1996; 11:89-121.
5. Berry SM, Carroll RJ, Ruppert D. Bayesian smoothing and regression splines for measurement error problems. Journal of the American Statistical Association 2002; 97:160-169.
6. Lang S, Brezger A. Bayesian P-splines. Journal of Computational and Graphical Statistics 2004; 13:183-212.
7. Lambert P. Archimedean copula estimation using Bayesian splines smoothing techniques. Discussion Paper 05-27, Institut de Statistique, Université catholique de Louvain, Louvain-la-Neuve, Belgium, 2005. http://www.stat.ucl.ac.be/ISpub/ISdp.html
8. Fahrmeir L, Kneib T, Lang S. Penalized structured additive regression for space-time data: a Bayesian perspective. Statistica Sinica 2004; 14:715-745.
9. Fahrmeir L. Recent advances in semiparametric Bayesian function estimation. Discussion Paper 137, Ludwig Maximilians University Munich, 1998. http://www.stat.uni-muenchen.de/sfb386/papers/dp1998.html
10. Denison D, Smith AFM, Mallick BK. Bayesian Methods for Nonlinear Classification and Regression. Wiley: New York, 2002.
11. Biller C. Adaptive Bayesian regression splines in semiparametric generalized linear models. Journal of Computational Statistics and Data Analysis 2000; 12:122-140.
12. Gamerman D. Efficient sampling from the posterior distribution in generalized linear models. Statistics and Computing 1997; 7:57-68.
13. Brezger A, Lang S. Generalized structured additive regression based on Bayesian P-splines. Journal of Computational Statistics and Data Analysis 2005, in press.
14. London D. Graduation: The Revision of Estimates. ACTEX Publications: Winsted, CT, 1985.
15. Gilks WR, Richardson S, Spiegelhalter DJ. Markov Chain Monte Carlo in Practice. Chapman & Hall/CRC: London, Boca Raton, FL, 1996.
16. Roberts GO, Tweedie RL. Exponential convergence of Langevin distributions and their discrete approximations. Bernoulli 1996; 24:341-363.
17. Roberts GO, Rosenthal JS. Optimal scaling of discrete approximations to Langevin diffusions. Journal of the Royal Statistical Society, Series B 1998; 60:225-268.
18. Verweij PJM, van Houwelingen HC. Cross-validation in survival analysis. Statistics in Medicine 1993; 12: 2305-2314.
19. Gelman A, Carlin JB, Stern HS, Rubin DB. Bayesian Data Analysis. Chapman & Hall/CRC: London, Boca Raton, FL, 2003.
20. Verweij PJM, van Houwelingen HC. Time-dependent effects of fixed covariates in Cox regression. Biometrics 1995; 51:1550-1556.
21. van Houwelingen HC, Eilers PHC. Non-proportional hazards models in survival analysis. Compstat 2000 Proceedings, Utrecht, The Netherlands, 21-25 August 2000.
22. Hennerfeind A, Brezger A, Fahrmeir L. Geoadditive survival models. Discussion Paper 414, Ludwig Maximilians University Munich, 2005. http://www.stat.uni-muenchen.de/sfb386/papers/dp2005.html
23. Whittaker ET. On a new method of graduation. Proceedings of the Edinburgh Mathematical Society 1923; 41:63-75.
24. Eilers P. A perfect smoother. Analytical Chemistry 2003; 75:3631-3636.