Nonparametric models and methods for designs with dependent censored data: Part II

Abstract

We consider a fully nonparametric marginal model for the analysis of mixed models with censored data. Hypotheses in this context are formulated by decomposing the set of (marginal) distributions as introduced in Akritas and Arnold [Akritas, M. G. and Arnold, S. F. (1994). Fully nonparametric hypotheses for factorial designs I: Multivariate repeated measures designs. The Journal of the American Statistical Association, 89, 336–343]. The approach should be useful in cases where the assumptions of the proportional hazards or location shift models fail to be satisfied. The large sample distribution of the test statistics is based on a representation for Kaplan–Meier integrals. The methodology is illustrated with two real life examples using clustered data. These results generalize the results of O’Gorman and Akritas [O’Gorman, J. T. and Akritas, M. G. (2001). Nonparametric models and methods for designs with dependent censored data: Part I. Biometrics, 57, 88–95] for the case of repeated measures data.

Keywords:

• Correlated survival data
• Kaplan–Meier estimator
• Nonparametric hypotheses
• Rank test
• Martingales for counting process
• H-class statistics

Acknowledgement

This research was supported by NSF grant SES-031 8200.