Factorial designs have been widely used in many scientific fields. Traditionally, such designs can be analyzed by the generalized linear mixed models (GLMMs). When making inference for the fixed effects in GLMM, however, even the robust generalized estimating equations (GEE) method may give biased results when the distributional assumption is violated. In this case, rank-based tests can be an option for inferential procedures. This paper applies the GEE technique to rank transformed data and derives a unified Wald-type rank test which can be used in any factorial design. The asymptotic properties of the proposed test are derived under the null and contiguous local alternative hypotheses. As a major contribution of this article, incorporating the rank transform statistic into the GEE framework provides a powerful tool to derive general asymptotic results of the rank-based methods and facilitates the migration of inferential procedures for GEE to rank-based methods. Small sample corrections for the proposed Wald-type rank test using GEE are also investigated. Simulation studies confirmed the validity of the proposed Wald-type rank test using GEE in large sample studies as well as that performances of the proposed small sample corrected tests are similar to the Wald-type rank test proposed in previous studies in a two-way repeated measures design. A mouse DIO study is used to illustrate the investigated methods together with SAS® code to realize select small sample corrected Wald-type rank tests using GEE supplied.
