It is well-known that the correlation among binary outcomes is constrained by the marginal means, yet approaches such as generalized estimating equations (GEE) do not check that the constraints for the correlations are satisfied. We explore this issue for Markovian dependence in the context of a GEE analysis of a clinical trial that compares Venlafaxine with Lithium in the prevention of major depressive episode. We obtain simplified expressions for the constraints for the logistic model and the equicorrelated and first-order autoregressive correlation structures. We then obtain the limiting values of the GEE and quasi-least squares (QLS) estimates of the correlation parameter when the working structure has been misspecified and prove that misidentification can lead to a severe violation of bounds. As a result, we suggest that violation of bounds can provide additional evidence in ruling out application of a particular working correlation structure. For a structure that is otherwise plausible and results in only a minor violation, we propose an iterative algorithm that yields an estimate that satifies the constraints. We compare our algorithm with two other approaches for estimation of the correlation that have been proposed to avoid a violation of bounds and demonstrate that it estimates the correlation parameter and bivariate probabilities with smaller mean square error and bias, especially when the correlation is large.
Longitudinal Data Analysis and Time Series
Shults, Justine; Sun, Wenguang; Tu, Xin; and Amsterdam, Jay, "On The Violation Of Bounds For The Correlation In Generalized Estimating Equation Analyses Of Binary Data From Longitudinal Trials" (February 2006). UPenn Biostatistics Working Papers. Working Paper 8.