Nonparametric Two-Sample Tests of Longitudinal Data with Termination Events

Abstract

In longitudinal data, observations of response variables occur at fixed or random time points, and can be stopped by a termination event. When comparing longitudinal data for two groups, such irregular observation behavior must be considered to yield suitable results. In this article, we propose the use of nonparametric tests based on the difference between weighted cumulative mean functions for comparing two mean functions with an adjustment for difference in the timing of termination events. We also derive the asymptotic null distributions of the test statistics and examine their small sample properties through simulations. We apply our method to data from a study of liver cirrhosis.

Keywords:

• Liver cirrhosis data
• Marked point processes
• Termination event times
• Weighted cumulative mean function

Mathematics Subject Classification:

• Primary 60G55
• Secondary 60G46

Acknowledgments

This work was partially supported by the Korea Science and Engineering Foundation (KOSEF) grant funded by the Korea government (No. R01-2008-000-20538-0; J. Kim) and the Korea Research Foundation (KRF) grant funded by the Korean government (No. KRF-2008-331-C00062; Y.-J. Kim).