Cumulative regression function tests for regression models for longitudinal data

The longitudinal regression model Y-i,Y-j = m(V-tau i,j(i)) + epsilon(i,j) where Y-i,Y-j, is the jth measurement of the ith subject at random time tau (i,j), m is the regression function, V-tau i,j(i) is a predictable covariat e process observed at time tau(i,j) and epsilon(i,j) is noise, often provid es an adequate framework for modeling and comparing groups of data. The pro posed longitudinal regression model is based on marked point process theory , and allows a quite general dependency structure among the observations. In this paper we find the asymptotic distribution of the cumulative regress ion function (CRF), and present a nonparametric test to compare the regress ion functions for two groups of longitudinal data. The proposed test, denot ed the CRF test, is based on the cumulative regression function (CRF) and i s the regression equivalent of the log-rank test in survival analysis. We s how as a special case that the CRF test is valid for groups of independent identically distributed regression data. Apart from the CRF test, we also c onsider a maximal deviation statistic that may be used when the CRF test is inefficient.