Goodness-of-fit tests for GEE modeling with binary responses

Analysis of data with repeated measures is often accomplished through the use of generalized estimating equations (GEE) methodology. Although methods exist for assessing the adequacy of the fitted models for uncorrelated data with likelihood methods, it is not appropriate to use these methods for models fitted with GEE methodology. We propose model-based and robust (empirically corrected) goodness-of-fit tests for GEE modeling with binary responses based on partitioning the space of covariates into distinct regions and forming score statistics that are asymptotically distributed as chi-square random variables with the appropriate degrees of freedom. The null distribution and the statistical power of the proposed goodness-of-fit tests were assessed using simulated data. The proposed goodness-of-fit tests are illustrated by two examples using data from clinical studies.