A flexible approach to the crossing hazards problem

Statistics in Medicine

Volumn 29, Issue 18, 2010, Pages 1947-1957

  Muggeo, Vito M R ^a   Tagliavia, Miriam ^a  

^a UNIVERSITY OF PALERMO   (Italy)

Author keywords

Crossing hazards; Crossing point; P splines; Restricted estimation; Time varying effect

Indexed keywords

ARTICLE; DATA ANALYSIS; HAZARD RATIO; PROPORTIONAL HAZARDS MODEL; SIMULATION; STATISTICAL ANALYSIS; SURVIVAL;

ALGORITHMS; BIOMETRY; FEMALE; HUMANS; LIKELIHOOD FUNCTIONS; MALE; PROPORTIONAL HAZARDS MODELS; SURVIVAL ANALYSIS;

EID: 77955395452     PISSN: 02776715     EISSN: 10970258     Source Type: Journal    
DOI: 10.1002/sim.3959     Document Type: Article

References (31)

1. Cox DR. Regression models and life tables (with discussion). Journal of the Royal Statistical Society, Series B 1972; 34:187-220.
2. Gray RJ. Flexible methods for analyzing survival data using splines, with applications to breast cancer prognosis. Journal of the American Statistical Association 1992; 87:942-951.
3. Hess K. Assessing time-by-covariate interactions in proportional hazards regression models using cubic spline functions. Statistics in Medicine 1994; 13:1045-1062.
4. Verweij P, van Houwelingen H. Time-dependent effects of fixed covariates in Cox regression. Biometrics 1995; 51:1550-1556.
5. Nan B, Lin X, Lisabeth LD, Harlow SD. A varying-coefficient Cox model for the effect of age at a marker event on age at menopause. Biometrics 2005; 61:576-583. DOI: 10.1111/j.1541-0420.2005.030905.x.
6. Cai Z, Sun Y. Local linear estimation for time dependent coefficients in Cox's regression models. Scandinavian Journal of Statistics 2003; 30:93-111. DOI: 10.1111/1467-9469.00320.
7. Xu R, Adak S. Survival analysis with time-varying regression effects using a tree-based approach. Biometrics 2002; 58:305-315. DOI: 10.1111/j.0006-341X.2002.00305.x.
8. Berger U, Schäfer J, Ulm K. Dynamic Cox modelling based on fractional polynomials: time-variations in gastric cancer prognosis. Statistics in Medicine 2003; 22:1163-1180. DOI: 10.1002/sim.1411.
9. Anderson JA, Senthilselvan A. A two-step regression model for hazard functions. Applied Statistics 1982; 31:44-51.
10. Breslow N, Edler L, Berger J. A two-sample censored-data rank test for acceleration. Biometrics 1984; 40:1049-1062.
11. Mantel N, Stablein D. The crossing hazard function problem. The Statistician 1988; 37:59-64.
12. O'Quigley J, Pessione F. The problem of a covariate-time qualitative interaction in a survival study. Biometrics 1991; 47:101-115.
13. Liu K, Qiu P, Sheng J. Comparing two crossing hazard rates by Cox proportional hazards modelling. Statistics in Medicine 2007; 26:375-391. DOI: 10.1002/sim.2544.
14. Logan BR, Klein JP, Zhang M. Comparing treatments in the presence of crossing survival curves: an application to bone marrow transplantation. Biometrics 2008; 64:733-740. DOI: 10.1111/j.1541-0420.2007.00975.x.
15. Dinse GE, Piegorsch WW. Confidence statements about the time range over which survival curves differ. Applied Statistics 1993; 42:21-30.
16. Bagdonavicius V, Hafdi MA, Nikulin M. Analysis of survival data with cross-effects of survival functions. Biostatistics 2004; 5:415-425. DOI: 10.1093/biostatistics/kxg045.
17. Qiu P, Sheng J. A two-stage procedure for comparing hazard rate functions. Journal of the Royal Statistical Society 2008; 70:191-208. DOI: 10.1111/j.1467-9868.2007.00622.x.
18. Tutz G, Binder H. Flexible modelling of discrete failure time including time-varying smooth effects. Statistics in Medicine 2004; 23:2445-2461. DOI: 10.1002/sim.1824.
19. Eilers PHC, Marx BD. Flexible smoothing with B-splines and penalties. Statistical Sciences 1996; 11:89-121.
20. Gray RJ. Spline-based tests in survival analysis. Biometrics 1994; 50:640-652.
21. Therneau T, Grambsch P. Modeling Survival Data: Extending the Cox Model. Springer: New York, 2000.
22. Welham SJ, Cullis BR, Kenwards MG, Thompson R. A comparison of mixed model splines for curve fitting. Australian and New Zealand Journal of Statistics 2007; 49:1-23. DOI: 10.1111/j.1467-842X.2006.00454.x.
23. Efron B, Tibshirani RJ. An Introduction to the Bootstrap. Chapman & Hall: London, 1993.
24. Zucker D, Lakatos E. Weighted log rank type statistics for comparing survival curves when there is a time-lag in the effectiveness of treatment. Biometrika 1990; 77:853-864.
25. Moreau T, Maccario J, Lellouch J, Huber C. Weighted log rank statistics for comparing two distributions. Biometrika 1992; 79:195-198.
26. Claeskens G. Restricted likelihood ratio lack-of-fit tests using mixed spline models. Journal of the Royal Statistical Society, B 2004; 66:909-926. DOI: 10.1111/j.1467-9868.2004.05421.x.
27. 2 random variables. Applied Statistics 1980; 29:323-333.
28. Brem H, Piantadosi S, Burger P, Walker M, Selker R, Black NVK, Sisti M, Brem S, Mohr G. Placebo-controlled trial of safety and efficacy of intraoperative controlled delivery by biodegradable polymers of chemotherapy for recurrent gliomas. The polymer-brain tumor treatment group. The Lancet 1995; 345:1008-1012.
29. Piantadosi S. Clinical Trials: A Methodologic Perspective. Wiley: New York, 1997.
30. Ripatti S, Palmgren J. Estimation of multivariate frailty models using penalized partial likelihood. Biometrics 2000; 56:1016-1022. DOI: 10.1111/j.0006-341X.2000.01016.x.
31. R Development Core Team. R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna, Austria, 2006. Available from: http://www.R-project.org. ISBN 3-900051-07-0.