Comparison of generalized estimating equations and Gaussian copula regression results using data from the randomized control trial

Abstract Background: In repeated measures data the observations tend to be correlated within each subject and such data are often analysed using Generalized Estimating Equations which is robust to assumptions that many methods hold. Correlation within-subject can be accounted for in working correlation structures. The main limitation of GEE is that its method of estimation is quasi-likelihood. The latest framework of the copula is very popular for handling correlated data. The likelihood-based analysis for correlated data can be obtained using Gaussian copula regression. The main advantage of copula regression model is that there are no boundaries on the probability distributions that can be used. The purpose of this study is to compare the findings of GEE and Gaussian copula regression using randomized controlled trial data for a continuous outcome along with different correlation structures. Methods: The prospective, double-blinded, randomized controlled trial data for this study was obtained from the Department of Anaesthesia, Christian Medical College, Vellore. ASA I and II patients were randomized into three groups. Hemodynamic parameters were obtained for 88 patients at thirteen time points. The outcome of interest was mean arterial pressure. Both GEE and Gaussian copula regression were compared assuming four different correlation structures. The optimal correlation structures were selected with the Akaike Information Criterion (AIC) and Correlation Information Criterion (CIC) goodness of fit criteria according to the method of estimation of Gaussian copula regression and GEE respectively. Results: The correlation structures unstructured and autoregressive were found to be optimal using simulation studies for Gaussian copula regression and GEE based on AIC and CIC criteria values respectively. Comparison between the estimated values of the selected models showed no major differences, except that Gaussian copula regression identifies interaction term, intrathecal morphine over time having significant association with MAP, this significance is considered to be important as the study uses a randomized controlled trial data. Conclusions: Both methods have almost similar results, but Gaussian copula regression provides better results by identifying significant variables associated with the outcome variable using maximum likelihood estimation that GEE fails to identify using quasi-likelihood estimation.