Abstract
In this paper we consider different approaches for estimation and assessment of covariate effects for the cumulative incidence curve in the competing risks model. The classic approach is to model all cause-specific hazards and then estimate the cumulative incidence curve based on these cause-specific hazards. Another recent approach is to directly model the cumulative incidence by a proportional model (Fine and Gray, J Am Stat Assoc 94:496–09, 1999), and then obtain direct estimates of how covariates influences the cumulative incidence curve. We consider a simple and flexible class of regression models that is easy to fit and contains the Fine-Gray model as a special case. One advantage of this approach is that our regression modeling allows for non-proportional hazards. This leads to a new simple goodness-of-fit procedure for the proportional subdistribution hazards assumption that is very easy to use. The test is constructive in the sense that it shows exactly where non-proportionality is present. We illustrate our methods to a bone marrow transplant data from the Center for International Blood and Marrow Transplant Research (CIBMTR). Through this data example we demonstrate the use of the flexible regression models to analyze competing risks data when non-proportionality is present in the data.
Similar content being viewed by others
References
Andersen PK, Borgan Ø, Gill RD, Keiding N (1993) Statistical models based on counting processes. Springer-Verlag, New York
Cheng SC, Fine JP, Wei LJ (1998) Prediction of cumulative incidence function under the proportional hazards model. Biometrics 54: 219–28
Fine PF, Gray RJ (1999) A proportional hazards model for the subdistribution of a competing risk. J Am Stat Assoc 94: 496–09
Gray RJ (1988) A class of K-sample tests for comparing the cumulative incidence of a competing risk. Ann Stat 16: 1141–154
Koul HL, Susarla V, Van Ryzin J (1981) Regression analysis with randomly right-censored data. Ann Stat 9: 1276–288
Lin DY, Ying Z (1994) Semiparametric analysis of the additive risk model. Biometrika 81: 61–1
Mckeague IW, Sasieni PD (1994) A partly parametric additive risk model. Biometrika 81: 501–14
Mckeague IW, Utikal KL (1990) Identifying nonlinear covariate effects in semimartingale regression models. Probab Theory Relat Fields 87: 1172–187
Nadeau C, Lawless J (1998) Inference for means and covariances of point processes through estimating functions. Biometrika 85: 893–06
Pepe MS (1991) Inference for events with dependent risks in multiple endpoint studies. J Am Stat Assoc 86: 770–78
Scheike TH, Zhang MJ (2002) An additive-multiplicative Cox-Aalen regression model. Scand J Stat 29: 75–8
Scheike TH, Zhang MJ (2003) Extensions and applications of the Cox-Aalen survival model. Biometrics 59: 1036–045
Scheike TH, Zhang MJ, Gerds T (2008) Predicting cumulative incidence probability by direct binomial regression. Biometrika 95: 205–20
Shen Y, Cheng SC (1999) Confidence bands for cumulative incidence curves under the additive risk model. Biometrics 55: 1093–100
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Scheike, T.H., Zhang, MJ. Flexible competing risks regression modeling and goodness-of-fit. Lifetime Data Anal 14, 464–483 (2008). https://doi.org/10.1007/s10985-008-9094-0
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10985-008-9094-0