Nonparametric models for clustered data: Application to root survival study

Abstract

Root survival data are discrete, have censoring and there is dependence due to clustering. The assumptions of the common semiparametric models seem to be violated for the data set under consideration. A fully nonparametric model for such clustered data is proposed and methods for testing hypotheses about the main effects and interaction are developed. Simulation studies indicate that the procedures have reasonable accuracy for moderate sample sizes. For small sample sizes, bootstrapping from the permutation distribution performs rather well for testing simple effects. The nonparametric analysis of the data set is compared with that based on semiparametric models, and the effect of allowing for the dependence caused by the clustering is examined.

Keywords:

• Nonparametric modeling
• Mixed designs
• Random effects
• Nonparametric hypotheses
• Censoring
• Ordinal data
• Ties

Acknowledgement

This research was partially supported by a STIR award from the Pennsylvania Space Grant Consortium at Pennsylvania State University (NGT-40002) and NSF grants IBN-9596050, SBR-9709891. The authors are grateful to Eric Good and Lars Pralle for their work on the initial stage of programming and Ulrich Hartmond and Dora Flores for data collection.