A comparison of several approaches for choosing between working correlation structures in generalized estimating equation analysis of longitudinal binary data

Abstract

The method of generalized estimating equations (GEE) models the association between the repeated observations on a subject with a patterned correlation matrix. Correct specification of the underlying structure is a potentially beneficial goal, in terms of improving efficiency and enhancing scientific understanding. We consider two sets of criteria that have previously been suggested, respectively, for selecting an appropriate working correlation structure, and for ruling out a particular structure(s), in the GEE analysis of longitudinal studies with binary outcomes. The first selection criterion chooses the structure for which the model-based and the sandwich-based estimator of the covariance matrix of the regression parameter estimator are closest, while the second selection criterion chooses the structure that minimizes the weighted error sum of squares. The rule out criterion deselects structures for which the estimated correlation parameter violates standard constraints for binary data that depend on the marginal means. In addition, we remove structures from consideration if their estimated parameter values yield an estimated correlation structure that is not positive definite. We investigate the performance of the two sets of criteria using both simulated and real data, in the context of a longitudinal trial that compares two treatments for major depressive episode. Practical recommendations are also given on using these criteria to aid in the efficient selection of a working correlation structure in GEE analysis of longitudinal binary data.

Simulating longer vectors of correlated binary random variables via multinomial sampling

“…To improve readability, the Prentice lower and upper values of the constraints are plotted slightly to the left and right, respectively, of the true value of α. Figure 3.2 shows what we have observed earlier [17,20,21], that violation of the Prentice constraints is unlikely unless the true value of α is very close to the upper or lower boundary value for the Prentice constraint. Furthermore, the severity of violation decreases with increasing group size.…”

“…Severe violation of the constraints is likely for larger values of the correlation, and for increasing sample sizes, when the true AR(1) structure is misspecified as exchangeable. The rule-out criterion [17] could be applied in situations like these, to remove working correlation structure from consideration, when its application results in a severe violation of constraints for QLS or GEE. Group Size = 120 …”

“…In [17,20,21] we used simulations to demonstrate that a severe violation of the Prentice constraints could be used as a rule-out criterion when assessing working correlation structures for GEE or QLS analysis of longitudinal binary data. As is appropriate for a short demonstration, here I replicate some of the simulations.…”

“…Assessing power with a method that simulates from a compatible parent distribution will ensure that the results are sound. [17] suggested that a severe violation of constraints during the analysis could be used as a rule-out criterion in the selection of a working correlation structure to describe the pattern of association in the data.…”

Selection of Working Correlation Structure in Generalized Estimating Equations via Empirical Likelihood

“…Rotnitzky and Jewell (1990) proposed generalized Wald and score statistics, and discussed the use of these statistics for checking the adequacy of a particular choice of working correlation structure. This approach was later implemented for correlation structure selection by Hin, Carey, and Wang (2007) and by Shults et al (2009). As shown by the simulation results of Hin, Carey, and Wang (2007), the correct identification rate of the approach of Rotnitzky and Jewell (1990) may be as low as 28% when the true correlation structure is AR-1.…”