Estimating correlation parameters in cluster intervention trials with binary responses using estimating equations

The proposed work is concerned with estimating equation approaches to modelling the correlation structure in cluster intervention trials. There are at least three potential benefits. First, modelling the correlation may provide mild gains in efficiency with respect to estimating the intervention effect parameters in the marginal mean model. Second, a plausible model for the correlation provides a situation for use of the model-based variance estimator for the marginal mean model parameter estimates. Third, correlation estimates are of direct interest as they provide information about clustering which is useful in planning future cluster intervention trials with the same outcomes.; Generalized estimating equation (GEE) procedures for correlation parameter estimation may be summarized into the methods based on unconditional residuals (Prentice, 1988) and conditional residuals (Lipsitz and Fitzmaurice, 1996). Published evidence has shown that the methods based on conditional residuals give more efficient estimates of correlation parameters than unconditional residuals methods. However all these previous studies were based on a large number of clusters and small cluster size (<4). No evidence has been provided for large cluster sizes typical in cluster intervention trial settings. Our simulation study was conducted to evaluate the performance of these two estimating procedures with respect to estimation of marginal mean model and correlation model parameters in a broad range of cluster trial settings. The results show that GEE based on conditional residuals tends to give more precise estimation for correlation parameters over the GEE based on unconditional residuals. But the differences are very small in cluster intervention trial scenarios.; Mancl and DeRouen (2001) proposed a bias-corrected covariance estimator for regression parameter estimates of GEE with improved small-sample properties over the empirical estimator. Extending their work, we develop a bias-corrected covariance estimator for correlation parameter estimates of correlated binary data using GEE based on unconditional residuals (Prentice 1988). The simulation study results show that the new bias-corrected covariance estimator for correlation parameter estimates performed better than the empirical sandwich estimator in terms of less bias and coverage probabilities for 95% confidence intervals closer to the nominal level. The methods are illustrated using data from a nested cross-sectional cluster trial on reducing underage drinking.