A covariance estimator for GEE with improved small-sample properties

In this paper, we propose an alternative covariance estimator to the robust covariance estimator of generalized estimating equations (GEE). Hypothesis tests using the robust covariance estimator can have inflated size when th e number of independent clusters is small. Resampling methods, such as the jackknife and bootstrap, have been suggested for covariance estimation when the number of clusters is small. A drawback of the resampling methods when the response is binary is that the methods can break down when the number of subjects is small due to zero or near-zero cell counts caused by resampl ing. We propose a bias-corrected covariance estimator that avoids this prob lem. In a small simulation study, we compare the bias-corrected covariance estimator to the robust and jackknife covariance estimators for binary resp onses for situations involving 10-40 subjects with equal and unequal cluste r sizes of 16-64 observations. The bias-corrected covariance estimator gave tests with sizes close to the nominal level even when the number of subjec ts was 10 and cluster sizes were unequal, whereas the robust and jackknife covariance estimators gave tests with sizes that could be 2-3 times the nom inal level. The methods are illustrated using data from a randomized clinic al trial on treatment for bone loss in subjects with periodontal disease.