A Generalized Estimating Equations Approach for Testing Ordered Group Effects with Repeated Measurements

Abstract

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.

Testing for Order-Restricted Hypotheses in Longitudinal Data

“…Park et al . (1998) proposed a Wald test based on the GEEs for testing the order‐restricted hypothesis (i.e.…”

“…Park et al . (1998) proposed a Wald test in the generalized estimating equations (GEEs) framework (Liang and Zeger, 1986) for non‐normal correlated data.…”

“…We also investigate the performance of the QST statistic through simulation experiments under a Gaussian model with covariates for correlated data. The Wald test in the GEE framework that was proposed by Park et al . (1998) does not accommodate covariates in a model.…”

“… present the Wald test that was proposed by Park et al . (1998), propose the QST for testing an order restriction in the treatment effects and derive the asymptotic distribution of the QST statistic under the null hypothesis for detecting an order restriction. …”

Testing for Ordered Group Effects in Binary and Continuous Outcomes

“…Dykstra et al (1991) derived the LRT for uniform stochastic ordering among several distributions. Repeated measurements were incorporated into order restricted testing problems in Shin et al (1996) and Park et al (1998). While general theories on order restricted inference are well described in Robertson et al (1988), more recent accomplishments in this area were surveyed by Sen and Silvapulle (2002) and Agresti and Coull (2002).…”