A generalized estimating equations approach for testing ordered group effects with repeated measurements

In repeated measures studies, we are often interested in comparing group effects in which groups are associated with a certain order relation. We propose testing procedures for ordered group effects using the generalized estimating equations (GEE) approach of Liang and Zeger (1986, Biometrika 73, 13-22). The order-constrained GEE estimators of group effects are approximated by the isotonic regression of the unconstrained GEE estimators. Based on these constrained estimators, we construct test statistics for detecting ordered group effects. The limiting distributions of the test statistics are mixtures of chi-square distributions. A Monte Carlo experiment shows improved performances of the proposed tests over the usual chi-square tests in detecting ordered group effects. The proposed test procedures are illustrated by familial polyposis supplementation trial data.