Power and Type I error rates of goodness-of-fit statistics for binomial generalized estimating equations (GEE) models

Binary outcomes are very common in medical studies. Logistic regression is typically used to analyze independent binary outcomes while generalized estimating equations regression methods (GEE) are often used to analyze correlated binary data. Several goodness-of-fit (GoF) statistics for the GEE methods have been developed recently. The objective of this study is to compare the power and Type I error rates of existing GEE GoF statistics using simulated data under different conditions. The number of clusters was varied in each condition. Different tested models included discrete, continuous, observation-specific and/or cluster-specific covariates. Two or three observations per cluster were generated with various correlations between observations.No single GEE GoF statistic performed best across all conditions. Generally, the larger the number of clusters, the more powerful the GEE GoF statistics. The GEE GoF statistics with correctly specified working correlation matrices tended to be robust in terms of Type I error rates and more powerful. For data with two observations per cluster, both Evans and Pan's statistics [1998. Goodness of fit in two models for clustered binary data. Ph.D. Dissertation, University of Massachusetts; 2002a. Goodness-of-fit tests for GEE with correlated binary data. Scand. J. Stat. 29(1), 101–110.] and Barnhart–Williamson's statistics [1998. Goodness-of-fit tests for GEE modeling with binary data. Biometrics 54, 720–729.] performed well for detecting the effect of the omitted interaction between two binary covariates. Barnhart–Williamson's statistics were generally the most powerful for detecting other types of interactions in models with at least one continuous covariate. For data with three observations per cluster, Evans and Pan's statistics performed best.