Abstract
Regression analysis for competing risks data can be based on generalized estimating equations. For the case with right censored data, pseudo-values were proposed to solve the estimating equations. In this article we investigate robustness of the pseudo-values against violation of the assumption that the probability of not being lost to follow-up (un-censored) is independent of the covariates. Modified pseudo-values are proposed which rely on a correctly specified regression model for the censoring times. Bias and efficiency of these methods are compared in a simulation study. Further illustration of the differences is obtained in an application to bone marrow transplantation data and a corresponding sensitivity analysis.
Similar content being viewed by others
References
Aalen O (1978) Nonparametric estimation of partial transition probabilities in multiple decrement models. Ann Stat 6(3):534–545
Andersen PK, Borgan Ø, Gill RD, Keiding N (1993) Statistical models based on counting processes. Springer, New York
Andersen PK, Klein JP, Rosthøj S (2003) Generalised linear models for correlated pseudo-observations, with applications to multi-state models. Biometrika 90(1):15–27
Andersen PK, Pohar Perme M (2010) Pseudo-observations in survival analysis. Stat Methods Med Res 19(1):71–99
Begun JM, Hall WJ, Huang W-M, Wellner JA (1983) Information and asymptotic efficiency in parametric–nonparametric models. Ann Stat 11(2):432–452
Fine JP, Gray RJ (1999) A proportional hazards model for the subdistribution of a competing risk. J Am Stat Assoc 94(446):496–509
Gerds TA, Scheike TH, Andersen PK (2012) Absolute risk regression for competing risks: interpretation, link functions, and prediction. Stat Med 31(29):3921–3930
Gill RD (1980) Censoring and stochastic integrals. PhD thesis, Math. Centre Tracts 124. Mathematical Centre, Amsterdam
Graw F, Gerds TA, Schumacher M (2009) On pseudo-values for regression analysis in competing risks models. Lifetime Data Anal 15(2):241–255
Kalbfleisch JD, Prentice RL (2002) The statistical analysis of failure time data, 2nd edn. Wiley, New York
Klein JP, Andersen PK (2005) Regression modeling of competing risks data based on pseudovalues of the cumulative incidence function. Biometrics 61(1):223–229
Scheike TH, Zhang MJ, Gerds TA (2008) Predicting cumulative incidence probability by direct binomial regression. Biometrika 95:205–220
Szydlo R, Goldman JM, Klein JP, Gale RP, Ash RC, Bach FH, Bradley BA, Casper JT, Flomenberg N, Gajewski JL et al (1997) Results of allogeneic bone marrow transplants for leukemia using donors other than HLA-identical siblings. J Clin Oncol 15(5):1767–1777
Acknowledgments
The research was supported by the Danish Natural Science Research Council [grant number 272-06-0442 “Point process modeling and statistical inference”]. We are grateful to CIBMTR for providing us with the example data [Public Health Service Grant/Cooperative Agreement No. U24-CA76518 from the National Cancer Institute (NCI), the National Heart, Lung and Blood Institute (NHLBI), and the National Institute of Allergy and Infectious Diseases (NIAID)].
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Binder, N., Gerds, T.A. & Andersen, P.K. Pseudo-observations for competing risks with covariate dependent censoring. Lifetime Data Anal 20, 303–315 (2014). https://doi.org/10.1007/s10985-013-9247-7
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10985-013-9247-7