We consider a longitudinal study of interstitial cystitis (IC) in women, in which the time between bouts of repeated measurements is large relative to the within-bout separation in time. Our outcome of interest is the number of nocturnal voids that we model via quasi-least squares (QLS) in the framework of generalized estimating equations (GEE). To account for potential intra-subject correlation, we directly apply a banded Toeplitz correlation structure that previously was only implemented in an ad hoc approach using GEE. We describe this structure, its appropriateness for data from the IC study, and the results of our analysis. We then demonstrate that correct specification of the underlying correlation structure versus incorrectly applying a simpler structure can prevent substantial losses in efficiency in estimation of the regression parameter. These comparisons involve the limiting values of the estimates of the correlation parameters, which are not consistent for the misspecification scenarios considered here. We therefore obtain the limiting values of the QLS estimates when the structure is incorrectly specified.